Exact Results in SUSY Gauge Theories in Various Dimensions
from
Monday, 11 August 2014 (10:00)
to
Friday, 22 August 2014 (15:30)
Monday, 11 August 2014
10:00
Coffee Break
Coffee Break
10:00  10:30
Room: 4/2011  TH common room
10:30
The Physics of Sphere Partition Functions and M2brane Surface Operators

Jaume Gomis
(
Perimeter Institute
)
The Physics of Sphere Partition Functions and M2brane Surface Operators
Jaume Gomis
(
Perimeter Institute
)
10:30  11:30
Room: 4/3006  TH Conference Room
We will characterize the physical content of the partition function of conformal and superconformal field theories on a sphere. These results will be used to give a complete microscopic gauge theory description of arbitrary M2branes ending on M5branes wrapped on a Riemann surface.
14:00
Curved Space Supersymmetry and the Partition Function

Cyril Closset
(
Simons Center
)
Curved Space Supersymmetry and the Partition Function
Cyril Closset
(
Simons Center
)
14:00  15:00
Room: 4/3006  TH Conference Room
The study of supersymmetric quantum field theories on compact manifolds has led to a plethora of new exact results in recent years. One of the simplest observable in this context is the supersymmetric partition function on a manifold M, Z_M, which can often be computed exactly. In the case of theories with four supercharges in flat space, I will explain some general properties of Z_M which can be understood on general ground. This understanding explains many properties of previously obtained localization results and makes sharp predictions for future computations.
15:00
Coffee Break
Coffee Break
15:00  15:30
Room: 4/2011  TH common room
Tuesday, 12 August 2014
10:00
Coffee Break
Coffee Break
10:00  10:30
Room: 4/2011  TH common room
10:30
Witten Index and Wall Crossing

Kentaro Hori
(
Kavli IPMU
)
Witten Index and Wall Crossing
Kentaro Hori
(
Kavli IPMU
)
10:30  11:30
Room: 4/3006  TH Conference Room
We compute the Witten index of onedimensional gauged linear sigma models with at least N=2 supersymmetry. In the phase where the gauge group is broken to a finite group, the index is expressed as a certain residue integral. It is subject to a change as the FayetIliopoulos parameter is varied through the phase boundaries. The wall crossing formula is expressed as an integral at infinity of the Coulomb branch. The result is applied to many examples, including quiver quantum mechanics that is relevant for BPS states in d=4 N=2 theories.
14:00
WallCrossing, Quiver Invariants, and Index for d=1 GLSM

Piljin Yi
(
KIAS
)
WallCrossing, Quiver Invariants, and Index for d=1 GLSM
Piljin Yi
(
KIAS
)
14:00  15:00
Room: 4/3006  TH Conference Room
Witten index of d=1 N=2,4 supersymmetric gauged quantum mechanics is considered. A canonical set of examples is the N=4 quiver dynamics, wellknown to capture wallcrossing behaviors of BPS states of d=4 N=2 theories. Such wallcrossing behaviors, as we change FI constants continuously, is in fact generic for these supersymmetric theories. For N=4 quivers, index were traditionally computed either by Coulomb or Higgs approximations. However, this is neither the most efficient nor the most complete computation. The Coulomb one in particular is known to miss a large number of wallcrossingsafe states, known as quiver invariants, After outlining recent progress on this front, we turn to honest and complete Witten index computation via localization. While the naive localization argument seems to preclude wallcrossing behvaior, this is merely due to neglecting important subtleties with new flat or runaway asymptotic direction that emerges when some of FI constant vanishes. After taking account of this subtlety, one arrives at universal index formula, via JK residue, determined entirely by field contents and Rcharge assignment, which reproduces most uptodate results in literature, also reproducing many wallcrossing formulae. We close with diverse examples, and illustrate how invariant d=2 indices and wallcrossing d=1 indices should be related. Also, we comment on the wallcrossingsafe subsector of d=1 GLSM, analogous to the quiver invariants, and propose how this invariant subsector might be counted again as a path integral.
15:00
Coffee Break
Coffee Break
15:00  15:30
Room: 4/2011  TH common room
Wednesday, 13 August 2014
10:00
Coffee Break
Coffee Break
10:00  10:30
Room: 4/2011  TH common room
10:30
The Coulomb Branch Formula for Quiver Moduli Spaces

Jan Manschot
(
U Lyon
)
The Coulomb Branch Formula for Quiver Moduli Spaces
Jan Manschot
(
U Lyon
)
10:30  11:30
Room: 4/3006  TH Conference Room
The semiclassical description of BPS bound states of 4d N=2 supersymmetric theories naturally gives rise to a N=4 quiver quantum mechanics (QQM). The regime where the constituents of the bound states have a finite spatial separation corresponds to the Coulomb branch of the QQM. I will explain in this talk how the bound state perspective leads to the Coulomb Branch Formula. This is an explicit formula for the computation of the BPS index of BPS bound states in terms of a set of invariants associated to 'singlecentered' or 'pure Higgs' states. Suitable specialization of the Coulomb Branch Formula gives topological invariants of the quiver moduli space, which parametrizes semistable quiver representations
14:00
New Methods in Supersymmetric Theories and Emergent Gauge Symmetry

Zohar Komargodski
(
Weizmann Inst.
)
New Methods in Supersymmetric Theories and Emergent Gauge Symmetry
Zohar Komargodski
(
Weizmann Inst.
)
14:00  15:00
Room: 4/3006  TH Conference Room
It is remarkable that light or even massless spin 1 particles can be composite. Consequently, gauge invariance is not fundamental but emergent. This idea can be realized in detail in supersymmetric gauge theories. We will describe the recent development of nonperturbative methods that allow to test this idea. One finds that the emergence of gauge symmetry is linked to some results in contemporary mathematics. We speculate on the possible applications of the idea of emergent gauge symmetry to realistic models.
15:00
Coffee Break
Coffee Break
15:00  15:30
Room: 4/2011  TH common room
Thursday, 14 August 2014
10:00
Coffee Break
Coffee Break
10:00  10:30
Room: 4/2011  TH common room
10:30
Quantum geometry and small distances in Mtheory

Marcos Marino Beiras
(
Univ Geneva
)
Quantum geometry and small distances in Mtheory
Marcos Marino Beiras
(
Univ Geneva
)
10:30  11:30
Room: 4/3006  TH Conference Room
By using localization, we derive exact and closed expressions for partition functions of N=8 ChernSimonsmatter theories. This allows us to address the nature of quantum geometry and of small distances in Mtheory. We show that, although classical geometry is modified due to membranes, there is a smooth interpolation from the semiclassical gravity regime all the way down to the Planck scale. In these examples, geometry is not discretized and there is no natural notion of a minimum distance.
14:00
Quantum Geometry of CalabiYau manifolds from GLSM

Hans Jockers
(
Univ Bonn
)
Quantum Geometry of CalabiYau manifolds from GLSM
Hans Jockers
(
Univ Bonn
)
14:00  15:00
Room: 4/3006  TH Conference Room
I discuss the power of gauge theory techniques in the context of gauged linear sigma models (GLSMs) with CalabiYau manifolds as their target spaces, so as to analyze the string quantum geometry of CalabiYau manifolds, arising from perturbative and nonperturabtive string worldsheet corrections. The former corrections are associated to a certain characteristic class of the CalabiYau target space, which arises naturally in the GLSM picture. The latter corrections correspond to GromovWitten invariants of the target space. I briefly comment on higher genus GromovWitten invariants for CalabiYau threefolds.
15:00
Coffee Break
Coffee Break
15:00  15:30
Room: 4/2011  TH common room
Friday, 15 August 2014
10:00
Coffee Break
Coffee Break
10:00  10:30
Room: 4/2011  TH common room
10:30
Dualities in twodimensional nonabelian gauge theories

Eric Sharpe
(
Virginia Tech
)
Dualities in twodimensional nonabelian gauge theories
Eric Sharpe
(
Virginia Tech
)
10:30  11:30
Room: 4/3006  TH Conference Room
In this talk we will discuss various advances in Seiberglike dualities in twodimensional gauge theories with (2,2) and (0,2) supersymmetry. We begin with a quick review of the (2,2) supersymmetric CP^n model and nonabelian analogues, and review other (2,2) and (0,2) dualities, such as in gauge theories with both fundamentals and antifundamentals. In two dimensions, the gauge field has no dynamics, so it is possible to get a very concrete handle on IR behaviors, and also to see some phenomena one would not expect in four dimensions, such as dualities between abelian and nonabelian gauge theories. In addition, techniques such as supersymmetric localization enable for example exact partition function computations, which form a powerful tool for checking dualities, as we shall discuss. If time permits, we will also discuss `decomposition,' relating twodimensional nonabelian gauge theories with centerinvariant matter to disjoint unions of nonabelian gauge theories with variable discrete theta angles.
14:00
Selfdual Strings and 2D SYM

Kazuo Hosomichi
(
Yukawa Institute
)
Selfdual Strings and 2D SYM
Kazuo Hosomichi
(
Yukawa Institute
)
14:00  15:00
Room: 4/3006  TH Conference Room
We study the system of M2branes suspended between parallel M5branes using ABJM model with a natural halfBPS boundary condition. For small separation between M5branes, the worldvolume theory is shown to reduce to a 2D N=(4,4) super YangMills theory with some similarity to qdeformed YangMills theory. The gauge coupling is related to the position of the branes in an interesting manner. The theory is considerably different from the 2D theory proposed for multiple "Mstrings". We make a detailed comparison of elliptic genus of the two descriptions and find only a partial agreement.
15:00
Coffee Break
Coffee Break
15:00  15:30
Room: 4/2011  TH common room
Saturday, 16 August 2014
Sunday, 17 August 2014
Monday, 18 August 2014
10:00
Coffee Break
Coffee Break
10:00  10:30
Room: 4/2011  TH common room
10:30
Gauge theories, quantum algebras and integrable systems

Vasily Pestun
(
IHES
)
Gauge theories, quantum algebras and integrable systems
Vasily Pestun
(
IHES
)
10:30  11:30
Room: 4/3006  TH Conference Room
Equivariantly deformed N=2 fourdimensional gauge theories in the limit when one epsilondeformation parameter is set to zero relate to quantum integrable systems. I will describe in details the correspondence for a large class of N=2 theories (quiver gauge theories)
14:00
Supersymmetric Partition Sums of 2d (4,4) GLSMs

Sungjay Lee
(
Univ Chicago
)
Supersymmetric Partition Sums of 2d (4,4) GLSMs
Sungjay Lee
(
Univ Chicago
)
14:00  15:00
Room: 4/3006  TH Conference Room
In the first part of this talk, we discuss the equivariant elliptic genera of ALE and ALF manifolds. The elliptic genera exhibit interesting pole structure as a function of the chemical potentials. We use this to decompose the answers into polar terms that exhibit wallcrossing and universal terms. We also discuss applications of our results to counting of BPS worldsheet spectrum of selfdual strings in the 6d N=(2,0) theories. In the second part of the talk, we consider twodimensional N = (4, 4) supersymmetric gauge theories which do not have classical Higgs branches. These theories however are believed to have isolated quantum Higgs vacua with a mass gap. We provide a field theoretic argument for the existence of such vacua.
15:00
Coffee Break
Coffee Break
15:00  15:30
Room: 4/2011  TH common room
Tuesday, 19 August 2014
10:00
Coffee Break
Coffee Break
10:00  10:30
Room: 4/2011  TH common room
10:30
Cluster algebras from 2d gauge theories

Francesco Benini
(
Simons Center
)
Cluster algebras from 2d gauge theories
Francesco Benini
(
Simons Center
)
10:30  11:30
Room: 4/3006  TH Conference Room
In the first part of the talk we study some dualities of twodimensional supersymmetric N=(2,2) gauge theories, reminiscent of 4d Seiberg duality, focusing on chiral and twisted chiral rings and the socalled sphere partition function. In the second part we observe that, when applied to quiver gauge theories, those dualities realize the cluster algebras of Fomin and Zelevinsky in their full completeness, with consequences in physics and mathematics.
14:00
General instanton counting and 5d SCFT

Jaemo Park
(
Postech
)
General instanton counting and 5d SCFT
Jaemo Park
(
Postech
)
14:00  15:00
Room: 4/3006  TH Conference Room
Instanton partition functions of 5d N=1 gauge theories are Witten indices for the ADHM gauged quantum mechanics with (0,4) SUSY. We derive the integral contour prescriptions for these indices using the JeffreyKirwan method, for gauge theories with hypermultiplets in various representations. The results can be used to study various 4d/5d/6d QFTs. In this paper, we study 5d SCFTs which are at the UV fixed points of 5d SYM theories. In particular, we focus on the Sp(N) theories with N_f <8 fundamental and 1 antisymmetric hypermultiplets, living on the D4D8O8 systems. Their superconformal indices calculated from instantons all show E type symmetry enhancements.It is crucial to understand the UV incompleteness of the 5d SYM, coming from small instantons in our problem. We explain in our examples how to fix them.
15:00
Coffee Break
Coffee Break
15:00  15:30
Room: 4/2011  TH common room
15:30
Exact results for 5D supersymmetric YangMills on toric SasakiEinstein manifolds

Maxim Zabzine
(
Univ Uppsala
)
Exact results for 5D supersymmetric YangMills on toric SasakiEinstein manifolds
Maxim Zabzine
(
Univ Uppsala
)
15:30  16:30
Room: 4/3006  TH Conference Room
I will review the localization on 5D YangMills theory with matter on toric SasakiEinstein manifolds. I wil review some contact toric geometry, briefly explain the calculation and its relation to CalabiYau cone. I will discuss the conjecture for the full answer and some other open problems.
Wednesday, 20 August 2014
10:00
Coffee Break
Coffee Break
10:00  10:30
Room: 4/2011  TH common room
10:30
On M5branes

Kimyeong Lee
(
KIAS
)
On M5branes
Kimyeong Lee
(
KIAS
)
10:30  11:30
Room: 4/3006  TH Conference Room
14:00
Confinement and 4manifolds

Sergei Gukov
(
Caltech
)
Confinement and 4manifolds
Sergei Gukov
(
Caltech
)
14:00  15:00
Room: 4/3006  TH Conference Room
In this talk I will survey a connection between two very challenging problems, one in physics and one in math. The physics problem involves quantitative understanding of confinement in a system with least amount of supersymmetry that has been studied so far and that has a wide range of applications, from semirealistic string models to qualitatively new examples of gaugegravity duality. Surprisingly, the rich physics of this system translates into incredibly rich mathematics of the only remaining unsolved case of the Poincare conjecture.
15:00
Coffee break
Coffee break
15:00  15:30
Room: 4/2011  TH common room
Thursday, 21 August 2014
10:00
Coffee Break
Coffee Break
10:00  10:30
Room: 4/2011  TH common room
10:30
Exact Solutions of 2d Supersymmetric Gauge Theories

Abhijit Gadde
(
Caltech
)
Exact Solutions of 2d Supersymmetric Gauge Theories
Abhijit Gadde
(
Caltech
)
10:30  11:30
Room: 4/3006  TH Conference Room
We study dynamics of twodimensional nonabelian gauge theories with N=(0,2) supersymmetry that include N=(0,2) supersymmetric QCD and its generalizations. 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.
14:00
Coulomb branch and the moduli space of instantons

Stefano Cremonesi
(
Imperial College
)
Coulomb branch and the moduli space of instantons
Stefano Cremonesi
(
Imperial College
)
14:00  15:00
Room: 4/3006  TH Conference Room
I will explain how the Coulomb branch of certain 3d N=4 generalised quiver gauge theories can be used to compute the Hilbert series of the moduli space of k Ginstantons, for any simple Lie group G (including nonsimply laced ones). The generalized quivers are overextended untwisted affine Dynkin diagrams.
15:00
Coffee Break
Coffee Break
15:00  15:30
Room: 4/2011  TH common room
15:30
Localization and quantum AdS_4/CFT_3 holography

Nadav Drukker
(
Humboldt University
)
Localization and quantum AdS_4/CFT_3 holography
Nadav Drukker
(
Humboldt University
)
15:30  16:30
Room: 4/3006  TH Conference Room
I will review the calculation of the partition function of 3d supersymmetric field theories on S^3 using the fermigas approach to solve the matrix integral. The resulting expression is an Airy function and is valid perturbatively to all orders in 1/N for a wide class of theories (including ABJM). This suggests that a similar formula can be derived by studying quantum gravity on AdS_4. I will explain several of the steps needed to implement this idea and some intriguing results.
Friday, 22 August 2014
10:00
Coffee Break
Coffee Break
10:00  10:30
Room: 4/2011  TH common room
10:30
Exact results for probes of Conformal Field Theories

Tomeu Fiol
(
Univ Barcelona
)
Exact results for probes of Conformal Field Theories
Tomeu Fiol
(
Univ Barcelona
)
10:30  11:30
Room: 4/3006  TH Conference Room
We consider a heavy probe coupled to a general fourdimensional conformal ﬁeld theory, and argue that a variety of interesting quantities are determined in terms of a single function, the Bremsstrahlung function, that depends on the probe and on the theory. For the particular case of a heavy probe coupled to N=4 super Yang Mills, we use localization techniques to determine the corresponding Bremsstrahlung function exactly for various gauge groups and representations. We present a number of applications, from computations of exact transport coefficents to a novel prediction for string perturbation theory.
14:00
The N=8 superconformal bootstrap in three dimensions

Silviu Pufu
(
Univ Princeton
)
The N=8 superconformal bootstrap in three dimensions
Silviu Pufu
(
Univ Princeton
)
14:00  15:00
Room: 4/3006  TH Conference Room
There has been a lot of recent progress in applying the conformal bootstrap technique to obtain exact nonperturbative information about various conformal field theories. In this talk, I will use the conformal bootstrap to study superconformal field theories with N=8 supersymmetry in three dimensions. In particular, I will provide bounds on various operator dimensions and OPE coefficients in these theories.
15:00
Coffee Break
Coffee Break
15:00  15:30
Room: 4/2011  TH common room