Related papers: The ${\cal N}=4$ Schur index with Polyakov loops

We study the Schur line defect correlation functions in $\mathcal{N}=4$ and $\mathcal{N}=2^*$ $U(N)$ super Yang-Mills (SYM) theory. We find exact closed-form formulae of the correlation functions of the Wilson line operators in the…

We consider Schur line defect correlators in four dimensional $\mathcal N=4$ $U(N)$ SYM and their giant graviton expansion encoding finite $N$ corrections to the large $N$ limit. We compute in closed form the single giant graviton…

For all 4d $\mathcal{N} = 4$ SYM theories with simple gauge groups $G$, we show that the residues of the integrands in the $\mathcal{N} = 4$ Schur indices, which are related to Gukov-Witten type surface defects in the theories, equal the…

We consider the gauged free fermionic matrix model, for a single fermionic matrix. In the large $N$ limit this system describes a $c=1/2$ chiral fermion in $1+1$ dimensions. The Gauss' law constraint implies that to obtain a physical state,…

We present the Sudakov form factor in full color $\mathcal{N}=4$ supersymmetric Yang-Mills theory to four loop order and provide uniformly transcendental results for the relevant master integrals through to weight eight.

Using techniques from hopping expansion we identically map the lattice Schwinger model with Wilson fermions to a model of oriented loops on the lattice. This is done by first computing the explicit form of the fermion determinant in the…

We study 1/2 BPS Wilson loops in 3d $\mathcal{N}=4$ $U(N)$ Yang-Mills theory with one adjoint and $N_f$ fundamental hypermultiplets from the Fermi gas approach. By numerical fitting, we find the first few worldsheet instanton corrections to…

A class of matrix models which arises as partition function in U(N) Chern-Simons matter theories on three sphere is investigated. Employing the standard technique of the 1/N expansion we solve the system beyond the planar limit. In…

We study matrix integration over the classical Lie groups $U(N),Sp(2N),O(2N)$ and $O(2N+1)$, using symmetric function theory and the equivalent formulation in terms of determinants and minors of Toeplitz$\pm$Hankel matrices. We establish a…

A new representation of the 2N fold integrals appearing in various two-matrix models that admit reductions to integrals over their eigenvalues is given in terms of vacuum state expectation values of operator products formed from…

We investigate the unflavoured Schur indices of class $\mathcal S$ theories of modest rank, and in the case of $\mathcal{N}=4$ super Yang-Mills theory with special unitary gauge group of somewhat more general rank, with an eye towards their…

We disentangle the contribution of scalars to the OPE series of null polygonal Wilson loops/MHV gluon scattering amplitudes in multicolour ${\cal N}=4$ SYM. In specific, we develop a systematic computation of the $SO(6)$ matrix part of the…

We discuss orbifold version of the Schur index defined as the supersymmetric partition function in S^3/Z_n x S^1. We first give a general formula for Lagrangian theories obtained by localization technique, and then suggest a generalization…

We present a DSSYK-like interpretation of the Schur half-indices of $\mathcal{N}=2$ $SU(2)$ gauge theories with matter, in the presence of fundamental Wilson lines. The Schur half-indices of these theories can be understood as transition…

We propose a novel modular anomaly equation for the unflavored Schur index in the $\mathcal{N}=4$ $SU(N)$ super-Yang-Mills theory. The vanishing conditions overdetermine the modular ambiguity ansatz from the equation, thus together they are…

A method for determining the generalised scaling function(s) arising in the high spin behaviour of long operator anomalous dimensions in the planar $sl(2)$ sector of ${\cal N}=4$ SYM is proposed. The all-order perturbative expansion around…

The Schur decomposition of a square matrix $A$ is an important intermediate step of state-of-the-art numerical algorithms for addressing eigenvalue problems, matrix functions, and matrix equations. This work is concerned with the following…

In this work, we revisit the exact computation of the round sphere partition function of 3d $\mathcal{N}=4$ circular quiver Chern-Simons theories with mass and Fayet-Iliopoulos (FI) deformations. Utilizing the Fermi gas formalism, we derive…

We compute to all loop orders correlation function of four heavy BPS operators in $\mathcal{N}$= 4 SYM with special polarisations considered recently by Frank Coronado. Our main result is an expression for the octagon form factor as…

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…