Ricardo Schiappa

Instituto Técnico y Cultural, Santa Clara de Portugal, Michoacán, Mexico

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Publications (32)81.06 Total impact

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    Inês Aniceto, Jorge G. Russo, Ricardo Schiappa
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    ABSTRACT: Localization methods have recently led to a plethora of new exact results in supersymmetric gauge theories, as certain observables may be computed in terms of matrix integrals. These can then be evaluated by making use of standard large N techniques, or else via perturbative expansions in the gauge coupling. Either approximation often leads to observables given in terms of asymptotic series, which need to be properly defined in order to obtain nonperturbative results. At the same time, resurgent analysis has recently been successfully applied to several problems, e.g., in quantum, field and string theories, precisely to overcome this issue and construct nonperturbative answers out of asymptotic perturbative expansions. The present work uses exact results from supersymmetric localization to address the resurgent structure of the free energy and partition function of Chern-Simons and ABJM gauge theories in three dimensions, and of N=2 supersymmetric Yang-Mills theories in four dimensions. For each case, the complete structure of Borel singularities is exactly determined, and the relation of these singularities with the large-order behavior of (multi-instanton) perturbative expansions is made fully precise.
    10/2014;
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    ABSTRACT: The holomorphic anomaly equations describe B-model closed topological strings in Calabi-Yau geometries. Having been used to construct perturbative expansions, it was recently shown that they can also be extended past perturbation theory by making use of resurgent transseries. These yield formal nonperturbative solutions, showing integrability of the holomorphic anomaly equations at the nonperturbative level. This paper takes such constructions one step further by working out in great detail the specific example of topological strings in the mirror of the local $\mathbb{C}\mathbb{P}^2$ toric Calabi-Yau background, and by addressing the associated (resurgent) large-order analysis of both perturbative and multi-instanton sectors. In particular, analyzing the asymptotic growth of the perturbative free energies, one finds contributions from three different instanton actions related by $Z_3$ symmetry, alongside another action related to the K\"ahler parameter. Resurgent transseries methods then compute, from the extended holomorphic anomaly equations, higher instanton sectors and it is shown that these precisely control the asymptotic behavior of the perturbative free energies, as dictated by resurgence. The asymptotic large-order growth of the one-instanton sector unveils the presence of resonance, i.e., each instanton action is necessarily joined by its symmetric contribution. The structure of different resurgence relations is extensively checked at the numerical level, both in the holomorphic limit and in the general nonholomorphic case, always showing excellent agreement with transseries data computed out of the nonperturbative holomorphic anomaly equations. The resurgence relations further imply that the string free energy displays an intricate multi-branched Borel structure, and that resonance must be properly taken into account in order to describe the full transseries solution.
    07/2014;
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    ABSTRACT: The gauge theoretic large N expansion yields an asymptotic series which requires a nonperturbative completion in order to be well defined. Recently, within the context of random matrix models, it was shown how to build resurgent transseries solutions encoding the full nonperturbative information beyond the 't Hooft genus expansion. On the other hand, via large N duality, random matrix models may be holographically described by B-model closed topological strings in local Calabi-Yau geometries. This raises the question of constructing the corresponding holographically dual resurgent transseries, tantamount to nonperturbative topological string theory. This paper addresses this point by showing how to construct resurgent transseries solutions to the holomorphic anomaly equations. These solutions are built upon (generalized) multi-instanton sectors, where the instanton actions are holomorphic. The asymptotic expansions around the multi-instanton sectors have both holomorphic and anti-holomorphic dependence, may allow for resonance, and their structure is completely fixed by the holomorphic anomaly equations in terms of specific polynomials multiplied by exponential factors and up to the holomorphic ambiguities -- which generalizes the known perturbative structure to the full transseries. In particular, the anti-holomorphic dependence has a somewhat universal character. Furthermore, in the nonperturbative sectors, holomorphic ambiguities may be fixed at conifold points. This construction shows the nonperturbative integrability of the holomorphic anomaly equations, and sets the ground to start addressing large-order analysis and resurgent nonperturbative completions within closed topological string theory.
    08/2013;
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    Inês Aniceto, Ricardo Schiappa
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    ABSTRACT: In a wide range of quantum theoretical settings -- from quantum mechanics to quantum field theory, from gauge theory to string theory -- singularities in the complex Borel plane, usually associated to instantons or renormalons, render perturbation theory ill-defined as they give rise to nonperturbative ambiguities. These ambiguities are associated to choices of an integration contour in the resummation of perturbation theory, along (singular) Stokes directions in the complex Borel plane (rendering perturbative expansions non-Borel summable along any Stokes line). More recently, it has been shown that the proper framework to address these issues is that of resurgent analysis and transseries. In this context, the cancelation of all nonperturbative ambiguities is shown to be a consequence of choosing the transseries median resummation as the appropriate family of unambiguous real solutions along the coupling-constant real axis. While the median resummation is easily implemented for one-parameter transseries, once one considers more general multi-parameter transseries the procedure becomes highly dependent upon properly understanding Stokes transitions in the complex Borel plane. In particular, all Stokes coefficients must now be known in order to explicitly implement multi-parameter median resummations. In the cases where quantum-theoretical physical observables are described by resurgent functions and transseries, the methods described herein show how one may cancel nonperturbative ambiguities, and define these observables nonperturbatively starting out from perturbation theory. Along the way, structural results concerning resurgent transseries are also obtained.
    08/2013;
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    Ricardo Schiappa, Ricardo Vaz
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    ABSTRACT: Resurgent transseries have recently been shown to be a very powerful construction in order to completely describe nonperturbative phenomena in both matrix models and topological or minimal strings. These solutions encode the full nonperturbative content of a given gauge or string theory, where resurgence relates every (generalized) multi-instanton sector to each other via large-order analysis. The Stokes phase is the adequate gauge theory phase where an 't Hooft large N expansion exists and where resurgent transseries are most simply constructed. This paper addresses the nonperturbative study of Stokes phases associated to multi-cuts solutions of generic matrix models, constructing nonperturbative solutions for their free energies and exploring the asymptotic large-order behavior around distinct multi-instanton sectors. Explicit formulae are presented for the Z_2 symmetric two-cuts set-up, addressing the cases of the quartic matrix model in its two-cuts Stokes phase; the "triple" Penner potential which yields four-point correlation functions in the AGT framework; and the Painleve II equation describing minimal superstrings.
    Communications in Mathematical Physics 02/2013; 330(2). · 1.97 Impact Factor
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    Inês Aniceto, Ricardo Schiappa, Marcel Vonk
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    ABSTRACT: Nonperturbative effects in string theory are usually associated to D-branes. In many cases it can be explicitly shown that D-brane instantons control the large-order behavior of string perturbation theory, leading to the well-known (2g)! growth of the genus expansion. This paper presents a detailed treatment of nonperturbative solutions in string theory, and their relation to the large-order behavior of perturbation theory, making use of transseries and resurgent analysis. These are powerful techniques addressing general nonperturbative contributions within non-linear systems, which are developed at length herein as they apply to string theory. The cases of topological strings, the Painleve I equation describing 2d quantum gravity, and the quartic matrix model, are explicitly addressed. These results generalize to minimal strings and general matrix models. It is shown that, in order to completely understand string theory at a fully nonperturbative level, new sectors are required beyond the standard D-brane sector.
    Communications in Number Theory and Physics 06/2011; · 1.41 Impact Factor
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    Ricardo Schiappa, Niclas Wyllard
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    ABSTRACT: We explore the connections between three classes of theories: Ar quiver matrix models, d = 2 conformal Ar Toda field theories, and d = 4 N = 2 supersymmetric conformal Ar quiver gauge theories. In particular, we analyze the quiver matrix models recently introduced by Dijkgraaf and Vafa (unpublished) and make detailed comparisons with the corresponding quantities in the Toda field theories and the N = 2 quiver gauge theories. We also make a speculative proposal for how the matrix models should be modified in order for them to reproduce the instanton partition functions in quiver gauge theories in five dimensions.
    Journal of Mathematical Physics 08/2010; 51(8):082304-082304-35. · 1.30 Impact Factor
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    Ricardo Schiappa, Niclas Wyllard
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    ABSTRACT: We explore the connections between three classes of theories: A_r quiver matrix models, d=2 conformal A_r Toda field theories and d=4 N=2 supersymmetric conformal A_r quiver gauge theories. In particular, we analyse the quiver matrix models recently introduced by Dijkgraaf and Vafa and make detailed comparisons with the corresponding quantities in the Toda field theories and the N=2 quiver gauge theories. We also make a speculative proposal for how the matrix models should be modified in order for them to reproduce the instanton partition functions in quiver gauge theories in five dimensions.
    11/2009;
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    Sara Pasquetti, Ricardo Schiappa
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    ABSTRACT: We address the nonperturbative structure of topological strings and c=1 matrix models, focusing on understanding the nature of instanton effects alongside with exploring their relation to the large-order behavior of the 1/N expansion. We consider the Gaussian, Penner and Chern-Simons matrix models, together with their holographic duals, the c=1 minimal string at self-dual radius and topological string theory on the resolved conifold. We employ Borel analysis to obtain the exact all-loop multi-instanton corrections to the free energies of the aforementioned models, and show that the leading poles in the Borel plane control the large-order behavior of perturbation theory. We understand the nonperturbative effects in terms of the Schwinger effect and provide a semiclassical picture in terms of eigenvalue tunneling between critical points of the multi-sheeted matrix model effective potentials. In particular, we relate instantons to Stokes phenomena via a hyperasymptotic analysis, providing a smoothing of the nonperturbative ambiguity. Our predictions for the multi-instanton expansions are confirmed within the trans-series set-up, which in the double-scaling limit describes nonperturbative corrections to the Toda equation. Finally, we provide a spacetime realization of our nonperturbative corrections in terms of toric D-brane instantons which, in the double-scaling limit, precisely match D-instanton contributions to c=1 minimal strings. Comment: 71 pages, 14 figures, JHEP3.cls; v2: added refs, minor changes
    Annales Henri Poincare 07/2009; · 1.53 Impact Factor
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    Marcos Mariño, Ricardo Schiappa, Marlene Weiss
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    ABSTRACT: We discuss various aspects of multi-instanton configurations in generic multicut matrix models. Explicit formulas are presented in the two-cut case and, in particular, we obtain general formulas for multi-instanton amplitudes in the one-cut matrix model case as a degeneration of the two-cut case. These formulas show that the instanton gas is ultradilute due to the repulsion among the matrix model eigenvalues. We exemplify and test our general results in the cubic matrix model, where multi-instanton amplitudes can be also computed with orthogonal polynomials. As an application, we derive general expressions for multi-instanton contributions in two-dimensional quantum gravity, verifying them by computing the instanton corrections to the string equation. The resulting amplitudes can be interpreted as regularized partition functions for multiple ZZ-branes, which take into full account their backreaction on the target geometry. Finally, we also derive structural properties of the trans-series solution to the Painlevé I equation.
    Journal of Mathematical Physics 05/2009; 50(5). · 1.30 Impact Factor
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    Marcos Marino, Ricardo Schiappa, Marlene Weiss
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    ABSTRACT: This work addresses nonperturbative effects in both matrix models and topological strings, and their relation with the large-order behavior of the 1/N expansion. We study instanton configurations in generic one-cut matrix models, obtaining explicit results for the one-instanton amplitude at both one and two loops. The holographic description of topological strings in terms of matrix models implies that our nonperturbative results also apply to topological strings on toric Calabi-Yau manifolds. This yields very precise predictions for the large-order behavior of the perturbative genus expansion, both in conventional matrix models and in topological string theory. We test these predictions in detail in various examples, including the quartic matrix model, topological strings on the local curve, and Hurwitz theory. In all these cases we provide extensive numerical checks which heavily support our nonperturbative analytical results. Moreover, since all these models have a critical point describing two-dimensional gravity, we also obtain in this way the large-order asymptotics of the relevant solution to the Painleve I equation, including corrections in inverse genus. From a mathematical point of view, our results predict the large-genus asymptotics of simple Hurwitz numbers and of local Gromov-Witten invariants.
    Communications in Number Theory and Physics 12/2007; · 1.41 Impact Factor
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    Troels Harmark, Jose Natario, Ricardo Schiappa
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    ABSTRACT: Gravitational greybody factors are analytically computed for static, spherically symmetric black holes in d-dimensions, including black holes with charge and in the presence of a cosmological constant (where a proper definition of greybody factors for both asymptotically dS and AdS spacetimes is provided). This calculation includes both the low-energy case --where the frequency of the scattered wave is small and real-- and the asymptotic case --where the frequency of the scattered wave is very large along the imaginary axis-- addressing gravitational perturbations as described by the Ishibashi-Kodama master equations, and yielding full transmission and reflection scattering coefficients for all considered spacetime geometries. At low frequencies a general method is developed, which can be employed for all three types of spacetime asymptotics, and which is independent of the details of the black hole. For asymptotically dS black holes the greybody factor is different for even or odd spacetime dimension, and proportional to the ratio of the areas of the event and cosmological horizons. For asymptotically AdS black holes the greybody factor has a rich structure in which there are several critical frequencies where it equals either one (pure transmission) or zero (pure reflection, with these frequencies corresponding to the normal modes of pure AdS spacetime). At asymptotic frequencies the computation of the greybody factor uses a technique inspired by monodromy matching, and some universality is hidden in the transmission and reflection coefficients. For either charged or asymptotically dS black holes the greybody factors are given by non-trivial functions, while for asymptotically AdS black holes the greybody factor precisely equals one (corresponding to pure blackbody emission).
    Advances in Theoretical and Mathematical Physics 07/2007; · 1.07 Impact Factor
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    ABSTRACT: We introduce the impact-parameter representation for conformal field theory correlators of the form A ~ < O_1 O_2 O_1 O_2 >. This representation is appropriate in the eikonal kinematical regime, and approximates the conformal partial-wave decomposition in the limit of large spin and dimension of the exchanged primary. Using recent results on the two-point function < O_1 O_1 >_{shock} in the presence of a shock wave in Anti-de Sitter, and its relation to the discontinuity of the four-point amplitude A across a kinematical branch-cut, we find the high spin and dimension conformal partial- wave decomposition of all tree-level Anti-de Sitter Witten diagrams. We show that, as in flat space, the eikonal kinematical regime is dominated by the T-channel exchange of the massless particle with highest spin (graviton dominance). We also compute the anomalous dimensions of the high-spin O_1 O_2 composites. Finally, we conjecture a formula re-summing crossed-ladder Witten diagrams to all orders in the gravitational coupling.
    Nuclear Physics B 12/2006; · 4.33 Impact Factor
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    ABSTRACT: We initiate a program to generalize the standard eikonal approximation to compute amplitudes in Anti-de Sitter spacetimes. Inspired by the shock wave derivation of the eikonal amplitude in flat space, we study the two-point function E ~ < O_1 O_1 >_{shock} in the presence of a shock wave in Anti-de Sitter, where O_1 is a scalar primary operator in the dual conformal field theory. At tree level in the gravitational coupling, we relate the shock two-point function E to the discontinuity across a kinematical branch cut of the conformal field theory four-point function A ~ < O_1 O_2 O_1 O_2 >, where O_2 creates the shock geometry in Anti-de Sitter. Finally, we extend the above results by computing E in the presence of shock waves along the horizon of Schwarzschild BTZ black holes. This work gives new tools for the study of Planckian physics in Anti-de Sitter spacetimes. Comment: JHEP3.cls, 34 pages, 10 figures; v2: added paragraph, footnote + reference, minor changes
    Journal of High Energy Physics 11/2006; · 5.62 Impact Factor
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    Filipe Moura, Ricardo Schiappa
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    ABSTRACT: This work addresses spherically symmetric, static black holes in higher-derivative stringy gravity. We focus on the curvature-squared correction to the Einstein-Hilbert action, present in both heterotic and bosonic string theory. The string theory low-energy effective action necessarily describes both a graviton and a dilaton, and we concentrate on the Callan-Myers-Perry solution in d-dimensions, describing stringy corrections to the Schwarzschild geometry. We develop the perturbation theory for the higher-derivative corrected action, along the guidelines of the Ishibashi-Kodama framework, focusing on tensor type gravitational perturbations. The potential obtained allows us to address the perturbative stability of the black hole solution, where we prove stability in any dimension. The equation describing gravitational perturbations to the Callan-Myers-Perry geometry also allows for a study of greybody factors and quasinormal frequencies. We address gravitational scattering at low frequencies, computing corrections arising from the curvature-squared term in the stringy action. We find that the absorption cross-section receives \alpha' corrections, even though it is still proportional to the area of the black hole event-horizon. We also suggest an expression for the absorption cross-section which could be valid to all orders in \alpha'.
    Classical and Quantum Gravity 05/2006; · 3.56 Impact Factor
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    Ricardo Schiappa, Niclas Wyllard
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    ABSTRACT: We study the construction of D-brane boundary states in the pure spinor formalism for the quantisation of the superstring. This is achieved both via a direct analysis of the definition of D-brane boundary states in the pure spinor conformal field theory, as well as via comparison between standard RNS and pure spinor descriptions of the superstring. Regarding the map between RNS and pure spinor formulations of the superstring, we shed new light on the tree level zero mode saturation rule. Within the pure spinor formalism we propose an explicit expression for the D-brane boundary state in a flat spacetime background. While the non-zero mode sector mostly follows from a simple understanding of the pure spinor conformal field theory, the zero mode sector requires a deeper analysis which is one of the main points in this work. With the construction of the boundary states at hand, we give a prescription for calculating scattering amplitudes in the presence of a D-brane. Finally, we also briefly discuss the coupling to the world-volume gauge field and show that the D-brane low-energy effective action is correctly reproduced. Comment: 42 pages
    Journal of High Energy Physics 03/2005; · 5.62 Impact Factor
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    Jose Natario, Ricardo Schiappa
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    ABSTRACT: We provide a complete classification of asymptotic quasinormal frequencies for static, spherically symmetric black hole spacetimes in d dimensions. This includes all possible types of gravitational perturbations (tensor, vector and scalar type) as described by the Ishibashi-Kodama master equations. The frequencies for Schwarzschild are dimension independent, while for RN are dimension dependent (the extremal RN case must be considered separately from the non-extremal case). For Schwarzschild dS, there is a dimension independent formula for the frequencies, except in dimension d=5 where the formula is different. For RN dS there is a dimension dependent formula for the frequencies, except in dimension d=5 where the formula is different. Schwarzschild and RN AdS black hole spacetimes are simpler: the formulae for the frequencies will depend upon a parameter related to the tortoise coordinate at spatial infinity, and scalar type perturbations in dimension d=5 lead to a continuous spectrum for the quasinormal frequencies. We also address non-black hole spacetimes, such as pure dS spacetime--where there are quasinormal modes only in odd dimensions--and pure AdS spacetime--where again scalar type perturbations in dimension d=5 lead to a continuous spectrum for the normal frequencies. Our results match previous numerical calculations with great accuracy. Asymptotic quasinormal frequencies have also been applied in the framework of quantum gravity for black holes. Our results show that it is only in the simple Schwarzschild case which is possible to obtain sensible results concerning area quantization or loop quantum gravity. In an effort to keep this paper self-contained we also review earlier results in the literature. Comment: JHEP3.cls, 100 pages, 54 figures; v2: added references; v3: final version for ATMP, more references, minor changes + new results: scalar type perturbations of S-AdS and RN-AdS black holes in d=5 lead to a continuous spectrum
    Advances in Theoretical and Mathematical Physics 11/2004; · 1.07 Impact Factor
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    Vitor Cardoso, José Natário, Ricardo Schiappa
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    ABSTRACT: The exact computation of asymptotic quasinormal frequencies is a technical problem which involves the analytic continuation of a Schrödinger-type equation to the complex plane and then performing a method of monodromy matching at several poles in the plane. While this method was successfully used in asymptotically flat space–time, as applied to both the Schwarzschild and Reissner–Nordstrøm solutions, its extension to nonasymptotically flat space–times has not been achieved yet. In this work it is shown how to extend the method to this case, with the explicit analysis of Schwarzschild–de Sitter and large Schwarzschild–anti–de Sitter black holes, both in four dimensions. We obtain, for the first time, analytic expressions for the asymptotic quasinormal frequencies of these black hole space–times, and our results match previous numerical calculations with great accuracy. We also list some results concerning the general classification of asymptotic quasinormal frequencies in d-dimensional space–times.
    Journal of Mathematical Physics 11/2004; 45(12):4698-4713. · 1.30 Impact Factor
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    Pedro Bordalo, Lorenzo Cornalba, Ricardo Schiappa
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    ABSTRACT: We initiate a programme to compute curvature corrections to the non-Abelian Born–Infeld action. This is based on the calculation of derivative corrections to the Abelian Born–Infeld action, describing a maximal brane, to all orders in F=B+2πα′F. An exact calculation in F allows us to apply the Seiberg–Witten map, reducing the maximal Abelian brane point of view to a minimal non-Abelian brane point of view (replacing 1/F with [X,X] at large F), resulting in matrix model equations of motion in the considered background. We first study derivative corrections to the Abelian Born–Infeld action and compute the two loop beta function for an open bosonic string in a WZW (parallelizable) background. This beta function is the first step in the process of computing open string equations of motion, which can be later obtained by either computing the Weyl anomaly coefficients or the partition function in the given background. The beta function for the gauge field is exact in F and computed to orders O(H,H2,H3) (where H=dB and the curvature is R∼H2) and O(∇F,∇2F,∇3F). In order to carry out this calculation we develop a new regularization method for two loop graphs. We then relate perturbative results for Abelian and non-Abelian Born–Infeld actions, by showing how Abelian derivative corrections yield non-Abelian higher order commutators and vice versa, at large F. We begin the construction of a matrix model describing α′ corrections to Myers' dielectric effect. This construction is carried out by first setting up a perturbative classification of the relevant non-Abelian tensor structures, which can be considerably narrowed down by the physical constraint of translation invariance in the action and the possibility for generic field redefinitions. The final matrix action is not uniquely determined and depends upon two free parameters. These parameters could be computed via further calculations in the Abelian theory.
    Nuclear Physics B 09/2004; · 4.33 Impact Factor
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    Lorenzo Cornalba, Miguel S. Costa, Ricardo Schiappa
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    ABSTRACT: We study the physics of D-branes in the presence of constant Ramond-Ramond potentials. In the string field theory context, we first develop a general formalism to analyze open strings in gauge trivial closed string backgrounds, and then apply it both to the RNS string and within Berkovits' covariant formalism, where the results have the most natural interpretation. The most remarkable finding is that, in the presence of a Dp-brane, both a constant parallel NS-NS B-field and R-R C^(p-1)-field do not solve the open/closed equations of motion, and induce the same non-vanishing open string tadpole. After solving the open string equations in the presence of this tadpole, and after gauging away the closed string fields, one is left with a U(1) field strength on the brane given by F=(1/2)(B-*C^(p-1)), where * is Hodge duality along the brane world-volume. One observes that this result differs from the usually assumed result F=B. Technically, this is due to the fact that supersymmetric and bosonic string world-sheet theories are different. Note, however, that the usual F+B combination is still the combination which remains gauge invariant at the sigma-model level. Also, the standard result F=B is, in the D3-brane case, not compatible with S-duality. On the other hand our result, which is derived automatically given the general formalism, offers a non-trivial check of S-duality, to all orders in F, and this leads to a S-dual invariant Moyal deformation. In an appendix, we solve the source equation describing the open superstring in a generic NS-NS and R-R closed string background, within the super Poincare covariant formalism.
    Advances in Theoretical and Mathematical Physics 10/2002; · 1.07 Impact Factor

Publication Stats

860 Citations
81.06 Total Impact Points

Institutions

  • 2004–2010
    • Instituto Técnico y Cultural
      Santa Clara de Portugal, Michoacán, Mexico
  • 2006
    • CERN
      • Physics Department (PH)
      Genève, Geneva, Switzerland
  • 2001
    • Harvard University
      • Department of Physics
      Cambridge, MA, United States
  • 1997–1998
    • Massachusetts Institute of Technology
      • Center for Theoretical Physics
      Cambridge, MA, United States