Publications (33)83.61 Total impact

Article: Finite N from Resurgent Large N
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ABSTRACT: Due to instanton effects, gaugetheoretic large N expansions yield asymptotic series, in powers of 1/N^2. The present work shows how to generically make such expansions meaningful via their completion into resurgent transseries, encoding both perturbative and nonperturbative data. Large N resurgent transseries compute gaugetheoretic finite N results nonperturbatively (no matter how small N is). Explicit calculations are carried out within the gauge theory prototypical example of the quartic matrix model. Due to integrability in the matrix model, it is possible to analytically compute (fixed integer) finite N results. At the same time, the large N resurgent transseries for the free energy of this model was recently constructed. Together, it is shown how the resummation of the large N resurgent transseries matches the analytical finite N results up to remarkable numerical accuracy. Due to lack of Borel summability, Stokes phenomena has to be carefully taken into account, implying that instantons play a dominant role in describing the finite N physics. The final resurgence results can be analytically continued, defining gauge theory for any complex value of N. 
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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 ChernSimons and ABJM gauge theories in three dimensions, and of N=2 supersymmetric YangMills theories in four dimensions. For each case, the complete structure of Borel singularities is exactly determined, and the relation of these singularities with the largeorder behavior of (multiinstanton) perturbative expansions is made fully precise. 
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ABSTRACT: The holomorphic anomaly equations describe Bmodel closed topological strings in CalabiYau 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 CalabiYau background, and by addressing the associated (resurgent) largeorder analysis of both perturbative and multiinstanton 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 largeorder growth of the oneinstanton 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 multibranched Borel structure, and that resonance must be properly taken into account in order to describe the full transseries solution.Communications in Mathematical Physics 07/2014; 338(1). DOI:10.1007/s0022001523580 · 1.90 Impact Factor 
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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 Bmodel closed topological strings in local CalabiYau 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) multiinstanton sectors, where the instanton actions are holomorphic. The asymptotic expansions around the multiinstanton sectors have both holomorphic and antiholomorphic 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 antiholomorphic 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 largeorder analysis and resurgent nonperturbative completions within closed topological string theory. 
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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 illdefined 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 nonBorel 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 couplingconstant real axis. While the median resummation is easily implemented for oneparameter transseries, once one considers more general multiparameter 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 multiparameter median resummations. In the cases where quantumtheoretical 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.Communications in Mathematical Physics 08/2013; 335(1). DOI:10.1007/s002200142165z · 1.90 Impact Factor 
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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) multiinstanton sector to each other via largeorder 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 multicuts solutions of generic matrix models, constructing nonperturbative solutions for their free energies and exploring the asymptotic largeorder behavior around distinct multiinstanton sectors. Explicit formulae are presented for the Z_2 symmetric twocuts setup, addressing the cases of the quartic matrix model in its twocuts Stokes phase; the "triple" Penner potential which yields fourpoint correlation functions in the AGT framework; and the Painleve II equation describing minimal superstrings.Communications in Mathematical Physics 02/2013; 330(2). DOI:10.1007/s0022001420287 · 1.90 Impact Factor 
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ABSTRACT: Nonperturbative effects in string theory are usually associated to Dbranes. In many cases it can be explicitly shown that Dbrane instantons control the largeorder behavior of string perturbation theory, leading to the wellknown (2g)! growth of the genus expansion. This paper presents a detailed treatment of nonperturbative solutions in string theory, and their relation to the largeorder behavior of perturbation theory, making use of transseries and resurgent analysis. These are powerful techniques addressing general nonperturbative contributions within nonlinear 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 Dbrane sector.Communications in Number Theory and Physics 06/2011; DOI:10.4310/CNTP.2012.v6.n2.a3 · 1.43 Impact Factor 
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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):08230408230435. DOI:10.1063/1.3449328 · 1.18 Impact Factor 
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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. 
Article: Borel and Stokes Nonperturbative Phenomena in Topological String Theory and c=1 Matrix Models
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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 largeorder behavior of the 1/N expansion. We consider the Gaussian, Penner and ChernSimons matrix models, together with their holographic duals, the c=1 minimal string at selfdual radius and topological string theory on the resolved conifold. We employ Borel analysis to obtain the exact allloop multiinstanton corrections to the free energies of the aforementioned models, and show that the leading poles in the Borel plane control the largeorder 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 multisheeted 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 multiinstanton expansions are confirmed within the transseries setup, which in the doublescaling limit describes nonperturbative corrections to the Toda equation. Finally, we provide a spacetime realization of our nonperturbative corrections in terms of toric Dbrane instantons which, in the doublescaling limit, precisely match Dinstanton contributions to c=1 minimal strings. Comment: 71 pages, 14 figures, JHEP3.cls; v2: added refs, minor changesAnnales Henri Poincare 07/2009; DOI:10.1007/s0002301000445 · 1.37 Impact Factor 
Article: Multiinstantons and multicuts
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ABSTRACT: We discuss various aspects of multiinstanton configurations in generic multicut matrix models. Explicit formulas are presented in the twocut case and, in particular, we obtain general formulas for multiinstanton amplitudes in the onecut matrix model case as a degeneration of the twocut 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 multiinstanton amplitudes can be also computed with orthogonal polynomials. As an application, we derive general expressions for multiinstanton contributions in twodimensional 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 ZZbranes, which take into full account their backreaction on the target geometry. Finally, we also derive structural properties of the transseries solution to the Painlevé I equation.Journal of Mathematical Physics 05/2009; 50(5). DOI:10.1063/1.3097755 · 1.18 Impact Factor 
Article: Nonperturbative Effects and the LargeOrder Behavior of Matrix Models and Topological Strings
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ABSTRACT: This work addresses nonperturbative effects in both matrix models and topological strings, and their relation with the largeorder behavior of the 1/N expansion. We study instanton configurations in generic onecut matrix models, obtaining explicit results for the oneinstanton 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 CalabiYau manifolds. This yields very precise predictions for the largeorder 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 twodimensional gravity, we also obtain in this way the largeorder 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 largegenus asymptotics of simple Hurwitz numbers and of local GromovWitten invariants.Communications in Number Theory and Physics 12/2007; DOI:10.4310/CNTP.2008.v2.n2.a3 · 1.43 Impact Factor 
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ABSTRACT: Gravitational greybody factors are analytically computed for static, spherically symmetric black holes in ddimensions, 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 lowenergy 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 IshibashiKodama 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 nontrivial 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; DOI:10.4310/ATMP.2010.v14.n3.a1 · 1.78 Impact Factor 
Article: Eikonal Approximation in AdS/CFT: Conformal Partial Waves and Finite N FourPoint Functions
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ABSTRACT: We introduce the impactparameter 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 partialwave decomposition in the limit of large spin and dimension of the exchanged primary. Using recent results on the twopoint function < O_1 O_1 >_{shock} in the presence of a shock wave in Antide Sitter, and its relation to the discontinuity of the fourpoint amplitude A across a kinematical branchcut, we find the high spin and dimension conformal partial wave decomposition of all treelevel Antide Sitter Witten diagrams. We show that, as in flat space, the eikonal kinematical regime is dominated by the Tchannel exchange of the massless particle with highest spin (graviton dominance). We also compute the anomalous dimensions of the highspin O_1 O_2 composites. Finally, we conjecture a formula resumming crossedladder Witten diagrams to all orders in the gravitational coupling.Nuclear Physics B 12/2006; 767(3). DOI:10.1016/j.nuclphysb.2007.01.007 · 3.95 Impact Factor 
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ABSTRACT: We initiate a program to generalize the standard eikonal approximation to compute amplitudes in Antide Sitter spacetimes. Inspired by the shock wave derivation of the eikonal amplitude in flat space, we study the twopoint function E ~ < O_1 O_1 >_{shock} in the presence of a shock wave in Antide 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 twopoint function E to the discontinuity across a kinematical branch cut of the conformal field theory fourpoint function A ~ < O_1 O_2 O_1 O_2 >, where O_2 creates the shock geometry in Antide 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 Antide Sitter spacetimes. Comment: JHEP3.cls, 34 pages, 10 figures; v2: added paragraph, footnote + reference, minor changesJournal of High Energy Physics 11/2006; DOI:10.1088/11266708/2007/08/019 · 6.22 Impact Factor 
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ABSTRACT: This work addresses spherically symmetric, static black holes in higherderivative stringy gravity. We focus on the curvaturesquared correction to the EinsteinHilbert action, present in both heterotic and bosonic string theory. The string theory lowenergy effective action necessarily describes both a graviton and a dilaton, and we concentrate on the CallanMyersPerry solution in ddimensions, describing stringy corrections to the Schwarzschild geometry. We develop the perturbation theory for the higherderivative corrected action, along the guidelines of the IshibashiKodama 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 CallanMyersPerry geometry also allows for a study of greybody factors and quasinormal frequencies. We address gravitational scattering at low frequencies, computing corrections arising from the curvaturesquared term in the stringy action. We find that the absorption crosssection receives \alpha' corrections, even though it is still proportional to the area of the black hole eventhorizon. We also suggest an expression for the absorption crosssection which could be valid to all orders in \alpha'.Classical and Quantum Gravity 05/2006; DOI:10.1088/02649381/24/2/006 · 3.10 Impact Factor 
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ABSTRACT: We study the construction of Dbrane 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 Dbrane 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 Dbrane boundary state in a flat spacetime background. While the nonzero 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 Dbrane. Finally, we also briefly discuss the coupling to the worldvolume gauge field and show that the Dbrane lowenergy effective action is correctly reproduced. Comment: 42 pagesJournal of High Energy Physics 03/2005; DOI:10.1088/11266708/2005/07/070 · 6.22 Impact Factor 
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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 IshibashiKodama 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 nonextremal 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 nonblack hole spacetimes, such as pure dS spacetimewhere there are quasinormal modes only in odd dimensionsand pure AdS spacetimewhere 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 selfcontained 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 SAdS and RNAdS black holes in d=5 lead to a continuous spectrumAdvances in Theoretical and Mathematical Physics 11/2004; DOI:10.4310/ATMP.2004.v8.n6.a4 · 1.78 Impact Factor 
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ABSTRACT: The exact computation of asymptotic quasinormal frequencies is a technical problem which involves the analytic continuation of a Schrödingertype 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 ddimensional space–times.Journal of Mathematical Physics 11/2004; 45(12):46984713. DOI:10.1063/1.1812828 · 1.18 Impact Factor 
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ABSTRACT: We initiate a programme to compute curvature corrections to the nonAbelian 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 nonAbelian 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 nonAbelian Born–Infeld actions, by showing how Abelian derivative corrections yield nonAbelian 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 nonAbelian 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; DOI:10.1016/j.nuclphysb.2004.12.019 · 3.95 Impact Factor
Publication Stats
1k  Citations  
83.61  Total Impact Points  
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Institutions

2006–2014

CERN
 Physics Department (PH)
Genève, Geneva, Switzerland


2004–2010

Instituto Técnico y Cultural
Santa Clara de Portugal, Michoacán, Mexico 
Universidade Católica Portuguesa
 Faculdade de Engenharia
Lisboa, Lisbon, Portugal


2001

Harvard University
Cambridge, Massachusetts, United States


1997–1998

Massachusetts Institute of Technology
 Center for Theoretical Physics
Cambridge, Massachusetts, United States
