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Related papers: The exact Schur index in closed form

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We study the Schur index of 4-dimensional $\mathcal{N}=2$ circular quiver theories. We show that the index can be expressed as a weighted sum over partition functions describing systems of free Fermions living on a circle. For circular…

High Energy Physics - Theory · Physics 2016-12-13 Jun Bourdier , Nadav Drukker , Jan Felix

We show that specializations of the 4d $\mathcal{N}=2$ superconformal index labeled by an integer $N$ is given by $\textrm{Tr}\,{\cal M}^N$ where ${\cal M}$ is the Kontsevich-Soibelman monodromy operator for BPS states on the Coulomb…

High Energy Physics - Theory · Physics 2015-11-13 Sergio Cecotti , Jaewon Song , Cumrun Vafa , Wenbin Yan

We generalize, in a manifestly Weyl-invariant way, our previous expressions for irregular singularity wave functions in two-dimensional SU(2) q-deformed Yang-Mills theory to SU(N). As an application, we give closed-form expressions for the…

High Energy Physics - Theory · Physics 2017-10-25 Matthew Buican , Takahiro Nishinaka

We study superconformal indices of four-dimensional $SU(N)$ gauge theories with $\mathcal{N}=1,2,4$ supersymmetry. The usual representation of a gauge theory index involves multiple contour integrals and reflects the BPS spectrum at zero…

High Energy Physics - Theory · Physics 2026-03-24 Sam van Leuven , Kayleigh Mathieson , Pratik Roy

We elaborate on the relation between the generalized Schur index of $N=2$ SCFTs in four dimensions and the non-relativistic limit of the elliptic Ruijsenaars-Schneider model. In particular we discuss explicitly how to express generalized…

High Energy Physics - Theory · Physics 2026-04-28 Rotem Ben Zeev , Anirudh Deb , Hee-Cheol Kim , Shlomo S. Razamat

The Witten index counts the difference in the number of bosonic and fermionic states of a quantum mechanical system. The Schur index, which can be defined for theories with at least $\mathcal{N}=2$ supersymmetry in four dimensions is a…

High Energy Physics - Theory · Physics 2016-01-27 Jun Bourdier , Nadav Drukker , Jan Felix

The Schur index of a $4$ dimensional $\mathcal{N}=2$ superconformal field theory counts (with sign) bosonic and fermionic states that preserve $4$ supercharges. We consider the Schur indices of $4$d $\mathcal{N}=4$ super Yang-Mills and…

High Energy Physics - Theory · Physics 2023-03-22 Giorgos Eleftheriou

The flavored superconformal Schur index of $\mathcal N=4$ $U(N)$ SYM has finite $N$ corrections encoded in its giant graviton expansion in terms of D3 branes wrapped in $AdS_{5}\times S^{5}$. The key element of this decomposition is the…

High Energy Physics - Theory · Physics 2024-03-19 Matteo Beccaria , Alejandro Cabo-Bizet

We study a set of four-dimensional $\mathcal{N}=2$ superconformal field theories (SCFTs) $\widehat{\Gamma}(G)$ labeled by a pair of simply-laced Lie groups $\Gamma$ and $G$. They are constructed out of gauging a number of $\mathcal{D}_p(G)$…

High Energy Physics - Theory · Physics 2021-11-12 Monica Jinwoo Kang , Craig Lawrie , Jaewon Song

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…

High Energy Physics - Theory · Physics 2015-03-19 Abhijit Gadde , Leonardo Rastelli , Shlomo S. Razamat , Wenbin Yan

We study superconformal indices of 4d N=2 class S theories with certain irregular punctures called type $I_{k, N}$. This class of theories include generalized Argyres-Douglas theories of type $(A_{k-1}, A_{N-1})$ and more. We conjecture the…

High Energy Physics - Theory · Physics 2016-06-21 Jaewon Song

We consider families of theories with large N=4 superconformal symmetry. We define an index generalizing the elliptic genus of theories with N=2 symmetry. In contrast to the N=2 case, the new index constrains part of the non-BPS spectrum.…

High Energy Physics - Theory · Physics 2007-05-23 Sergei Gukov , Emil Martinec , Gregory Moore , Andrew Strominger

In this paper we analytically explore the modularity of the flavored Schur index of 4d $\mathcal{N} = 2$ SCFTs. We focus on the $A_1$ theories of class-$\mathcal{S}$ and $\mathcal{N} = 4$ theories with $SU(N)$ gauge group. We work out the…

High Energy Physics - Theory · Physics 2024-04-16 Yiwen Pan , Peihe Yang

We find a four-dimensional N=1 gauge theory which flows to the minimal interacting N=2 superconformal field theory, the Argyres-Douglas theory, in the infrared up to the extra free chiral multiplets. The gauge theory is obtained from a…

High Energy Physics - Theory · Physics 2017-04-19 Kazunobu Maruyoshi , Jaewon Song

We propose two novel methods for computing the superconformal index of 5d superconformal field theories that cannot be described by conventional Lagrangian descriptions under mass deformations. The first approach involves the use of Higgs…

High Energy Physics - Theory · Physics 2023-07-10 Hee-Cheol Kim , Minsung Kim , Sung-Soo Kim , Gabi Zafrir

We consider the Schur index of $\mathcal N=4$ $U(N)$ SYM theory in 4d and its holographic giant graviton-type expansion at finite $N$. We compute the world-volume brane superconformal index by a recently proposed definition of the gauge…

High Energy Physics - Theory · Physics 2023-06-01 Matteo Beccaria , Alejandro Cabo-Bizet

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…

High Energy Physics - Theory · Physics 2015-06-15 Abhijit Gadde , Sergei Gukov

We present a trace formula for an index over the spectrum of four dimensional superconformal field theories on $S^3 \times $ time. Our index receives contributions from states invariant under at least one supercharge and captures all…

High Energy Physics - Theory · Physics 2017-09-07 Justin Kinney , Juan Maldacena , Shiraz Minwalla , Suvrat Raju

The superconformal index is an important invariant of superconformal field theories. In this note we refine the superconformal index by inserting the charge conjugation operator C. We construct a matrix integral for this charged index for…

High Energy Physics - Theory · Physics 2015-06-03 Benjamin I. Zwiebel

We develop techniques to calculate an index for four dimensional superconformal field theories. This superconformal index is counting BPS operators which preserve only one supercharge. To calculate the superconformal index we quantize the…

High Energy Physics - Theory · Physics 2007-07-26 Christian Romelsberger