Abhijit Gadde

California Institute of Technology, Pasadena, California, United States

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Publications (23)49.03 Total impact

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    Abhijit Gadde, Sergei Gukov, Pavel Putrov
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    ABSTRACT: We study dynamics of two-dimensional non-abelian gauge theories with N=(0,2) supersymmetry that include N=(0,2) supersymmetric QCD and its generalizations. In particular, we present the phase diagram of N=(0,2) SQCD and determine its massive and low-energy spectrum. We find that the theory has no mass gap, a nearly constant distribution of massive states, and lots of massless states that in general flow to an interacting CFT. For a range of parameters where supersymmetry is not dynamically broken at low energies, we give a complete description of the low-energy physics in terms of 2d N=(0,2) SCFTs using anomaly matching and modular invariance. Our construction provides a vast landscape of new N=(0,2) SCFTs which, for small values of the central charge, could be used for building novel heterotic models with no moduli and, for large values of the central charge, could be dual to AdS_3 string vacua.
    04/2014;
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    Abhijit Gadde, Sergei Gukov, Pavel Putrov
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    ABSTRACT: We propose a unified approach to a general class of codimension-2 defects in field theories with non-trivial duality symmetries and discuss various constructions of such "duality defects" in diverse dimensions. In particular, in d=4 we propose a new interpretation of the Seiberg-Witten u-plane by "embedding" it in the physical space-time: we argue that it describes a BPS configuration of two duality defects (at the monopole/dyon points) and propose its vast generalization based on Lefschetz fibrations of 4-manifolds.
    04/2014;
  • Christopher Beem, Abhijit Gadde
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    ABSTRACT: We investigate the superconformal index of four-dimensional superconformal field theories that arise on coincident M5 branes wrapping a holomorphic curve in a local Calabi-Yau three-fold. The structure of the index is very similar to that which appears in the special case preserving = 2 supersymmetry. We first compute the index for the fixed points that admit a known four-dimensional ultraviolet description and prove infrared equivalence at the level of the index for all such constructions. These results suggest a formulation of the index as a two-dimensional topological quantum field theory that generalizes the one that computes the = 2 index. The TQFT structure leads to an expression for the index of a much larger family of = 1 class S fixed points in terms of the index of the = 2 theories. Calculations of simple quantities with the index suggests a connection between these families of fixed points and the mathematics of SU(2) Yang-Mills theory on the wrapped curve.
    03/2014;
  • Abhijit Gadde, Sergei Gukov, Pavel Putrov
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    ABSTRACT: Motivated by the connection between 4-manifolds and 2d = (0, 2) theories, we study the dynamics of a fairly large class of 2d = (0, 2) gauge theories. We see that physics of such theories is very rich, much as the physics of 4d = 1 theories. We discover a new type of duality that is very reminiscent of the 4d Seiberg duality. Surprisingly, the new 2d duality is an operation of order three: it is IR equivalence of three different theories and, as such, is actually a triality. We also consider quiver theories and study their triality webs. Given a quiver graph, we find that supersymmetry is dynamically broken unless the ranks of the gauge groups and flavor groups satisfy stringent inequalities. In fact, for most of the graphs these inequalities have no solutions. This supports the folklore theorem that generic 2d = (0, 2) theories break supersymmetry dynamically.
    02/2014;
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    Abhijit Gadde, Sergei Gukov, Pavel Putrov
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    ABSTRACT: Motivated by the connection between 4-manifolds and 2d N=(0,2) theories, we study the dynamics of a fairly large class of 2d N=(0,2) gauge theories. We see that physics of such theories is very rich, much as the physics of 4d N=1 theories. We discover a new type of duality that is very reminiscent of the 4d Seiberg duality. Surprisingly, the new 2d duality is an operation of order three: it is IR equivalence of three different theories and, as such, is actually a triality. We also consider quiver theories and study their triality webs. Given a quiver graph, we find that supersymmetry is dynamically broken unless the ranks of the gauge groups and flavor groups satisfy stringent inequalities. In fact, for most of the graphs these inequalities have no solutions. This supports the folklore theorem that generic 2d N=(0,2) theories break supersymmetry dynamically.
    10/2013;
  • Abhijit Gadde, Sergei Gukov, Pavel Putrov
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    ABSTRACT: We describe rules for building 2d theories labeled by 4-manifolds. Using the proposed dictionary between building blocks of 4-manifolds and 2d N=(0,2) theories, we obtain a number of results, which include new 3d N=2 theories T[M_3] associated with rational homology spheres and new results for Vafa-Witten partition functions on 4-manifolds. In particular, we point out that the gluing measure for the latter is precisely the superconformal index of 2d (0,2) vector multiplet and relate the basic building blocks with coset branching functions. We also offer a new look at the fusion of defect lines / walls, and a physical interpretation of the 4d and 3d Kirby calculus as dualities of 2d N=(0,2) theories and 3d N=2 theories, respectively
    06/2013;
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    Abhijit Gadde, Sergei Gukov
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    ABSTRACT: In this paper we compute the superconformal index of 2d (2,2) supersymmetric gauge theories. The 2d superconformal index, a.k.a. flavored elliptic genus, is computed by a unitary matrix integral much like the matrix integral that computes 4d superconformal index. We compute the 2d index explicitly for a number of examples. In the case of abelian gauge theories we see that the index is invariant under flop transition and CY-LG correspondence. The index also provides a powerful check of the Seiberg-type duality for non-abelian gauge theories discovered by Hori and Tong. In the later half of the paper, we study half-BPS surface operators in N=2 superconformal gauge theories. They are engineered by coupling the 2d (2,2) supersymmetric gauge theory living on the support of the surface operator to the 4d N=2 theory, so that different realizations of the same surface operator with a given Levi type are related by a 2d analogue of the Seiberg duality. The index of this coupled system is computed by using the tools developed in the first half of the paper. The superconformal index in the presence of surface defect is expected to be invariant under generalized S-duality. We demonstrate that it is indeed the case. In doing so the Seiberg-type duality of the 2d theory plays an important role.
    05/2013;
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    Abhijit Gadde, Sergei Gukov, Pavel Putrov
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    ABSTRACT: In this paper we analyze various half-BPS defects in a general three dimensional N=2 supersymmetric gauge theory T. They correspond to closed paths in SUSY parameter space and their tension is computed by evaluating period integrals along these paths. In addition to such defects, we also study wall defects that interpolate between T and its SL(2,Z) transform by coupling the 3d theory to a 4d theory with S-duality wall. We propose a novel spectral duality between 3d gauge theories and integrable systems. This duality complements a similar duality discovered by Nekrasov and Shatashvili. As another application, for 3d N=2 theories associated with knots and 3-manifolds we compute periods of (super) A-polynomial curves and relate the results with the spectrum of domain walls and line operators.
    01/2013;
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    Christopher Beem, Abhijit Gadde
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    ABSTRACT: We investigate the superconformal index of four-dimensional N=1 superconformal field theories that arise on coincident M5 branes wrapping a holomorphic curve in a local Calabi-Yau three-fold. The structure of the index is very similar to that which appears in the special case preserving N=2 supersymmetry. We first compute the index for the fixed points that admit a known four-dimensional ultraviolet description and prove infrared equivalence at the level of the index for all such constructions. These results suggest a formulation of the index as a two-dimensional topological quantum field theory that generalizes the one that computes the N=2 index. The TQFT structure leads to an expression for the index of all class S fixed points in terms of the index of the N=2 theories. Calculations of spectral data using the index suggests a connection between these families of fixed points and the mathematics of SU(2) Yang-Mills theory on the wrapped curve.
    12/2012;
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    ABSTRACT: We study the integrability properties of planar N=2 superconformal field theories in four dimensions. We show that the spin chain associated to the planar dilation operator of N=2 superconformal QCD fails to be integrable at two loops. In our analysis we focus on a closed SU(2|1) sector, whose two-loop spin chain we fix by symmetry arguments (up to a few undetermined coefficients). It turns out that the Yang-Baxter equation for magnon scattering is not satisfied in this sector. On the other hand, we suggest that the closed SU(2,1|2) sector, which exists in any N=2 superconformal gauge theory, may be integrable to all loops.
    11/2012;
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    ABSTRACT: We study the N=2 four-dimensional superconformal index in various interesting limits, such that only states annihilated by more than one supercharge contribute. Extrapolating from the SU(2) generalized quivers, which have a Lagrangian description, we conjecture explicit formulae for all A-type quivers of class S, which in general do not have one. We test our proposals against several expected dualities. The index can always be interpreted as a correlator in a two-dimensional topological theory, which we identify in each limit as a certain deformation of two-dimensional Yang-Mills theory. The structure constants of the topological algebra are diagonal in the basis of Macdonald polynomials of the holonomies.
    Communications in Mathematical Physics 10/2011; 319(1). · 1.97 Impact Factor
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    ABSTRACT: We show that the superconformal index (the partition function on the three-sphere times a circle) of a certain class of 4D supersymmetric field theories is exactly equal to a partition function of q-deformed nonsupersymmetric 2D Yang-Mills theory.
    Physical Review Letters 06/2011; 106(24):241602. · 7.73 Impact Factor
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    ABSTRACT: We identify the 2d topological theory underlying the N=2 4d superconformal index with an explicit model: q-deformed 2d Yang-Mills. By this route we are able to evaluate the index of some strongly-coupled 4d SCFTs, such as Gaiotto's T_N theories.
    04/2011;
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    Abhijit Gadde, Wenbin Yan
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    ABSTRACT: The superconformal index of a 4d gauge theory is computed by a matrix integral arising from localization of the supersymmetric path integral on S^3 x S^1 to the saddle point. As the radius of the circle goes to zero, it is natural to expect that the 4d path integral becomes the partition function of dimensionally reduced gauge theory on S^3. We show that this is indeed the case and recover the matrix integral of Kapustin, Willet and Yaakov from the matrix integral that computes the superconformal index. Remarkably, the superconformal index of the "parent" 4d theory can be thought of as the q-deformation of the 3d partition function.
    Journal of High Energy Physics 04/2011; · 5.62 Impact Factor
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    ABSTRACT: We evaluate the superconformal index of the Y p,q quiver gauge theories using Römeslberger’s prescription. For the conifold quiver Y 1,0 we find exact agreement at large N with a previous calculation in the dual AdS 5 × T 1,1 supergravity.
    Journal of High Energy Physics 01/2011; 2011(3):1-26. · 5.62 Impact Factor
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    Abhijit Gadde, Leonardo Rastelli
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    ABSTRACT: We study spin chains for superconformal quiver gauge theories in the moduli space of N=2 orbifolds. Independent of integrability, which is generally broken, we use the centrally extended SU(2|2) symmetry of the magnons to fix their dispersion relations and two-body S-matrices, as functions of the exactly marginal couplings. Comment: 26 pages, 6 figures. v2: minor changes
    Journal of High Energy Physics 12/2010; · 5.62 Impact Factor
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    ABSTRACT: We evaluate the superconformal index of the Y^{p,q} quiver gauge theories using Romeslberger's prescription. For the conifold quiver Y^{1,0} we find exact agreement at large N with a previous calculation in the dual AdS_5 X T^{1,1} supergravity.
    11/2010;
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    Abhijit Gadde, Elli Pomoni, Leonardo Rastelli
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    ABSTRACT: In this paper we find preliminary evidence that N=2 superconformal QCD, the SU(N_c) SYM theory with N_f= 2 N_c fundamental hypermultiplets, might be integrable in the large N Veneziano limit. We evaluate the one-loop dilation operator in the scalar sector of the N=2 superconformal quiver with SU(N_c) X SU(N_{\check c}) gauge group, for N_c = N_{\check c}. Both gauge couplings g and \check g are exactly marginal. This theory interpolates between the Z_2 orbifold of N=4 SYM, which corresponds to \check g=g, and N=2 superconformal QCD, which is obtained for \check g -> 0. The planar one-loop dilation operator takes the form of a nearest-neighbor spin-chain Hamiltonian. For superconformal QCD the spin chain is of novel form: besides the color-adjoint fields \phi^a_{b}, which occupy individual sites of the chain, there are "dimers" Q^a_{i} \bar Q^i_{b} of flavor-contracted fundamental fields, which occupy two neighboring sites. We solve the two-body scattering problem of magnon excitations and study the spectrum of bound states, for general \check g/g. The dimeric excitations of superconformal QCD are seen to arise smoothly for \check g -> 0 as the limit of bound wavefunctions of the interpolating theory. Finally we check the Yang-Baxter equation for the two-magnon S-matrix. It holds as expected at the orbifold point \check g = g. While violated for general \check g \neq g, it holds again in the limit \check g -> 0, hinting at one-loop integrability of planar N=2 superconformal QCD.
    05/2010;
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    ABSTRACT: We derive an integral representation for the superconformal index of the strongly-coupled superconformal field theory with E 6 flavor symmetry. The explicit expression of the index allows highly non-trivial checks of Argyres-Seiberg duality and of a class of S-dualities conjectured by Gaiotto.
    Journal of High Energy Physics 01/2010; 2010(8):1-27. · 5.62 Impact Factor
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    Abhijit Gadde, Elli Pomoni, Leonardo Rastelli
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    ABSTRACT: We attack the long-standing problem of finding the AdS dual of N = 2 superconformal QCD, the N=2 super Yang Mills theory with gauge group SU(N_c) and N_f = 2 N_c fundamental hyper multiplets. The theory admits a Veneziano expansion of large N_c and large N_f, with N_f/N_c and lambda = g^2 N_c kept fixed. The topological structure of large N diagrams motivates a general conjecture: the flavor-singlet sector of a gauge theory in the Veneziano limit is dual to a closed string theory; single closed string states correspond to "generalized single-trace" operators, where adjoint letters and flavor-contracted fundamental/antifundamental pairs are stringed together in a closed chain. We look for the string dual of N = 2 superconformal QCD from two fronts. From the bottom-up, we perform a systematic analysis of the protected spectrum using superconformal representation theory. We also evaluate the one-loop dilation operator in the scalar sector, finding a novel spin chain. From the top-down, we consider the decoupling limit of known brane constructions. In both approaches, more insight is gained by viewing the theory as the degenerate limit of the N = 2 Z_2 orbifold of N = 4 SYM, as one of the two gauge couplings is tuned to zero. A consistent picture emerges. We conclude that the string dual is a sub-critical background with seven "geometric" dimensions, containing both an AdS_5 and an S^1 factor. The supergravity approximation is never entirely valid, even for large lambda, indeed the field theory has an exponential degeneracy of exactly protected states with higher spin, which must be dual to a sector of light string states. Comment: 72 pages
    12/2009;