Publications (27)95.15 Total impact
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ABSTRACT: We discuss reductions of general \( \mathcal{N}=1 \) four dimensional gauge theories on \( {\mathbb{S}}^2 \). The effective two dimensional theory one obtains depends on the details of the coupling of the theory to background fields, which can be translated to a choice of Rsymmetry. We argue that, for special choices of Rsymmetry, the resulting two dimensional theory has a natural interpretation as an \( \mathcal{N}=\left(0,2\right) \) gauge theory. As an application of our general observations, we discuss reductions of \( \mathcal{N}=1 \) and \( \mathcal{N}=2 \) dualities and argue that they imply certain two dimensional dualities.  [Show abstract] [Hide abstract]
ABSTRACT: We discuss reductions of general N=1 four dimensional gauge theories on S^2. The effective two dimensional theory one obtains depends on the details of the coupling of the theory to background fields, which can be translated to a choice of Rsymmetry. We argue that, for special choices of Rsymmetry, the resulting two dimensional theory has a natural interpretation as an N=(0,2) gauge theory. As an application of our general observations, we discuss reductions of N=1 and N=2 dualities and argue that they imply certain two dimensional dualities.  [Show abstract] [Hide abstract]
ABSTRACT: We suggest an N=1 Lagrangian flowing in the infrared to the N=2 rank one superconformal field theory with E_6 flavor symmetry. We utilize this description to compute several supersymmetric partition functions.  [Show abstract] [Hide abstract]
ABSTRACT: We study dynamics of twodimensional nonabelian 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 lowenergy 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 lowenergy 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. 
Article: Duality Defects
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ABSTRACT: We propose a unified approach to a general class of codimension2 defects in field theories with nontrivial 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 SeibergWitten uplane by "embedding" it in the physical spacetime: 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 4manifolds.  [Show abstract] [Hide abstract]
ABSTRACT: We investigate the superconformal index of fourdimensional superconformal field theories that arise on coincident M5 branes wrapping a holomorphic curve in a local CalabiYau threefold. 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 fourdimensional 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 twodimensional 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) YangMills theory on the wrapped curve. 
Article: (0, 2) Trialities
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ABSTRACT: Motivated by the connection between 4manifolds 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. 
Article: (0,2) Trialities
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ABSTRACT: Motivated by the connection between 4manifolds 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.  [Show abstract] [Hide abstract]
ABSTRACT: We study the integrability properties of planar \( \mathcal{N}=2 \) superconformal field theories in four dimensions. We show that the spin chain associated to the planar dilation operator of \( \mathcal{N}=2 \) superconformal QCD fails to be integrable at two loops. In our analysis we focus on a closed SU(21) sector, whose twoloop spin chain we fix by symmetry arguments (up to a few undetermined coefficients). It turns out that the YangBaxter equation for magnon scattering is not satisfied in this sector. On the other hand, we suggest that the closed SU(2, 12) sector, which exists in any \( \mathcal{N}=2 \) superconformal gauge theory, may be integrable to all loops. We summarize the known results in the literature that are consistent with this conjecture. 
Article: Fivebranes and 4manifolds
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ABSTRACT: We describe rules for building 2d theories labeled by 4manifolds. Using the proposed dictionary between building blocks of 4manifolds 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 VafaWitten partition functions on 4manifolds. 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 
Article: New \mathcal{N} =1 dualities
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ABSTRACT: We show that the $ \mathcal{N} $ =1 supersymmetric SU(N) gauge theory with 2N flavors without superpotential has not only the standard Seiberg dual description but also another dual description involving two copies of the socalled T N theory. This is a natural generalization to N > 2 of a dual description of SU(2) gauge theory with 4 flavors found by Csaki, Schmaltz, Skiba and Terning. We also study dualities of other $ \mathcal{N} $ =1 SCFTs involving copies of T N theories. Our duality is the basic operation from which a recentlyfound web of $ \mathcal{N} $ =1 dualities obtained by compactifying M5branes on Riemann surfaces can be derived fieldtheoretically. 
Article: New N=1 dualities
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ABSTRACT: We show that the N=1 supersymmetric SU(N) gauge theory with 2N flavors without superpotential has not only the standard Seiberg dual description but also another dual description involving two copies of the socalled T_N theory. This is a natural generalization to N > 2 of a dual description of SU(2) gauge theory with 4 flavors found by Csaki, Schmaltz, Skiba and Terning. We also study dualities of other N=1 SCFTs involving copies of T_N theories. Our duality is the basic operation from which a recentlyfound web of N=1 dualities obtained by compactifying M5branes on Riemann surfaces can be derived fieldtheoretically. 
Article: 2d Index and Surface operators
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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 the 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 under CYLG correspondence. The index also provides a powerful check of the Seibergtype duality for nonabelian gauge theories discovered by Hori and Tong. In the later half of the paper, we study halfBPS surface operators in \( \mathcal{N} \) = 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 \( \mathcal{N} \) = 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 Sduality. We demonstrate that it is indeed the case. In doing so the Seibergtype duality of the 2d theory plays an important role.  [Show abstract] [Hide abstract]
ABSTRACT: In this paper we analyze various halfBPS 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 Sduality 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 3manifolds we compute periods of (super) Apolynomial curves and relate the results with the spectrum of domain walls and line operators.  [Show abstract] [Hide abstract]
ABSTRACT: We investigate the superconformal index of fourdimensional N=1 superconformal field theories that arise on coincident M5 branes wrapping a holomorphic curve in a local CalabiYau threefold. 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 fourdimensional 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 twodimensional 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) YangMills theory on the wrapped curve.  [Show abstract] [Hide abstract]
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(21) sector, whose twoloop spin chain we fix by symmetry arguments (up to a few undetermined coefficients). It turns out that the YangBaxter equation for magnon scattering is not satisfied in this sector. On the other hand, we suggest that the closed SU(2,12) sector, which exists in any N=2 superconformal gauge theory, may be integrable to all loops.  [Show abstract] [Hide abstract]
ABSTRACT: In this paper we find preliminary evidence that $ \mathcal{N} = {2} $ superconformal QCD, the SU(N c ) SYM theory with N f = 2N c fundamental hypermultiplets, might be integrable in the large N Veneziano limit. We evaluate the oneloop dilation operator in the scalar sector of the $ \mathcal{N} = {2} $ superconformal quiver with SU(N c ) × SU(N č ) gauge group, for N c ≡ N č . Both gauge couplings g and ǧ are exactly marginal. This theory interpolates between the $ {\mathbb{Z}_2} $ orbifold of $ \mathcal{N} = {4} $ SYM, which corresponds to ǧ = g, and $ \mathcal{N} = {2} $ superconformal QCD, which is obtained for ǧ → 0. The planar oneloop dilation operator takes the form of a nearestneighbor spinchain Hamiltonian. For superconformal QCD the spin chain is of novel form: besides the coloradjoint fields $ \phi_b^a, $ which occupy individual sites of the chain, there are “dimers” $ Q_i^a\overline Q_b^i $ of flavorcontracted fundamental fields, which occupy two neighboring sites. We solve the twobody scattering problem of magnon excitations and study the spectrum of bound states, for general ǧ/g. The dimeric excitations of superconformal QCD are seen to arise smoothly for ǧ → 0 as the limit of bound wavefunctions of the interpolating theory. Finally we check the YangBaxter equation for the twomagnon Smatrix. It holds as expected at the orbifold point ǧ = g. While violated for general ǧ ≠ g, it holds again in the limit ǧ → 0, hinting at oneloop integrability of planar $ \mathcal{N} = {2} $ superconformal QCD.  [Show abstract] [Hide abstract]
ABSTRACT: We study the N=2 fourdimensional 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 Atype 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 twodimensional topological theory, which we identify in each limit as a certain deformation of twodimensional YangMills theory. The structure constants of the topological algebra are diagonal in the basis of Macdonald polynomials of the holonomies.  [Show abstract] [Hide abstract]
ABSTRACT: We show that the superconformal index (the partition function on the threesphere times a circle) of a certain class of 4D supersymmetric field theories is exactly equal to a partition function of qdeformed nonsupersymmetric 2D YangMills theory.  [Show abstract] [Hide abstract]
ABSTRACT: We identify the 2d topological theory underlying the N=2 4d superconformal index with an explicit model: qdeformed 2d YangMills. By this route we are able to evaluate the index of some stronglycoupled 4d SCFTs, such as Gaiotto's T_N theories.
Publication Stats
791  Citations  
95.15  Total Impact Points  
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Institutions

20132014

California Institute of Technology
Pasadena, California, United States


20092013

Stony Brook University
 Institute for Theoretical Physics (C.N. Yang)
Stony Brook, New York, United States
