Related papers: On the 4d superconformal index near roots of unity…

We consider the $S^3\times S^1$ superconformal index $\mathcal{I}(\tau)$ of 4d $\mathcal{N}=1$ gauge theories. The Hamiltonian index is defined in a standard manner as the Witten index with a chemical potential $\tau$ coupled to a…

We study the compactification of 4D $\mathcal{N}=4$ SYM on $S^1$ from the viewpoint of the superconformal index. In the cases that the gauge group of the 4D SYM is $U(N)$ and $Usp(2N)$, the resulting 3D theory is believed to be the ABJM…

We show that ${\cal N} = 4$ supersymmetric-Yang-Mills (SYM) theory on $\mathbb{R} \times S^3$ with gauge group $\text{SU}(N)$ is described in a near-BPS limit by a simple lower-dimensional nonrelativistic field theory with $\text{SU}(1,1)…

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…

We systematically study various sub-leading structures in the superconformal index of ${\cal N}=4$ supersymmetric Yang-Mills theory with SU($N$) gauge group. We concentrate in the superconformal index description as a matrix model of…

We show that both perturbative and non-perturbative parts of universal partition functions of Chern-Simons theory on 3d sphere are ratios of four over four Barnes' quadruple gamma functions with arguments given by linear combinations of…

Superconformal indices (SCIs) of 4d ${\mathcal N}=4$ SYM theories with simple gauge groups are described in terms of elliptic hypergeometric integrals. For $F_4, E_6, E_7, E_8$ gauge groups this yields first examples of integrals of such…

We study the Hamiltonian index of $\frac{1}{16}$-BPS operators in 4d $\mathcal{N}=4$ U(N) super Yang-Mills (SYM) theory numerically for $N=2\,,\dots,10$. We show that the large-charge asymptotics agree with analytic results in the…

A relation between the 4d superconformal index and the S^3 partition function is studied with focus on the 4d and 3d actions used in localization. In the case of vanishing Chern-Simons levels and round S^3 we explicitly show that the 3d…

We study the superconformal index of 4d $\mathcal{N}=4$ $USp(2N_c)$ and $SO(N_c)$ SYM from a matrix model perspective. We focus on the Cardy-like limit of the index. Both in the symplectic and orthogonal case the index is dominated by a…

We analyze a set of contributions to the superconformal index of 4d $\mathcal{N} = 4$ $SU(N)$ super Yang-Mills using the Bethe Ansatz approach. These contributions dominate at the large $N$ limit, where their leading order in $N$ reproduces…

We introduce a class of 3d theories consisting of strongly-coupled ${\mathcal N}=4$ systems coupled to ${\mathcal N}=3$ Chern-Simons gauge multiplets, which exhibit ${\mathcal N}=4$ enhancements when a peculiar condition on the Chern-Simons…

We show that the superconformal index of N=1 superconformal field theories in four dimensions has an asymptotic growth of states which is exponential in the charges. Our analysis holds in a Cardy-like limit of large charges, for which the…

We consider the refined Schur superconformal index of 4d $\mathcal N=4$ $U(N)$ SYM and the first term of its giant-graviton expansion, first predicted in arXiv:2001.11667 using indirect superconformal algebra considerations and analytic…

Supersymmetric partition function of $\mathcal N=1$ superconformal theories on $S^1_{\beta} \times S^3$ is related to the superconformal index receiving contributions from short representations. The leading coefficients in the small $\beta$…

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…

We establish a connection between the superconformal index of $\mathcal{N}=4$ $U(N)$ SYM and the elliptic Ruijsenaars-Schneider integrable system. The index admits an expression in terms of elliptic Macdonald polynomials, which leads to a…

We study 3d theories containing $\mathcal{N}=3$ Chern-Simons vector multiplets coupled to the $\mathrm{SU}(N)^3$ flavour symmetry of 3d $T_N$ theories with Chern-Simons level $k_1$, $k_2$ and $k_3$. It was formerly pointed out that these…

We investigate the large-$N$ asymptotics of the topologically twisted index of $\mathcal N=4$ SU($N$) Super-Yang-Mills (SYM) theory on $T^2\times S^2$ and provide its holographic interpretation based on the black hole Farey tail. In the…

We study the factorization of four dimensional N=1 superconformal index for U(N) (SU(N)) SQCD with N_F fundamental and anti-fundamental chiral multiplets. When both the anomaly free R-charge assignment and the traceless condition for total…