Related papers: 5D partition functions, q-Virasoro systems and int…
We present a numerical method to evaluate partition functions and associated correlation functions of inhomogeneous 2--D classical spin systems and 1--D quantum spin systems. The method is scalable and has a controlled error. We illustrate…
The 6d (2,0) theory of $N$ M5 branes compactified on the product geometry $T^2\times S$, where $S$ is a K\"ahler 4-manifold, can be studied in two different limits. In one limit, the size of $T^2$ is taken to zero and together with a…
The superconformal index of a 4d gauge theory is computed by a matrix integral arising from localization of the supersymmetric path integral on S^3 x S^1 to the saddle point. As the radius of the circle goes to zero, it is natural to expect…
We revisit the factorisation of supersymmetric partition functions of 3d $\mathcal{N}=4$ gauge theories. The building blocks are hemisphere partition functions of a class of UV $\mathcal{N}=(2,2)$ boundary conditions that mimic the presence…
Inspired by 5d supersymmetric Yang-Mills theories placed on the compact space $\mathbb{S}^5$, we propose an intriguing algebraic construction for the $q$-Virasoro algebra. We show that, when multiple $q$-Virasoro "chiral" sectors have to be…
We study the large $N$ expansion of twisted partition functions of 3d $\mathcal{N}=2$ superconformal field theories arising from $N$ M5-branes wrapped on a hyperbolic 3-manifold, $M_3$. Via the 3d-3d correspondence, the partition functions…
We study the large $N$ limit of twisted partition functions on $\mathcal{M}_{g,p}$, the $S^1$ bundle of degree $p$ over a Riemann surface of genus $g$, for 3D $\mathcal{N}=2$ superconformal field theories arising as low-energy limit of…
The character integral representation of one loop partition functions is useful to establish the relation between partition functions of conformal fields on Weyl equivalent spaces. The Euclidean space $S^a\times AdS_b$ can be mapped to…
We compute partition functions describing multiplicities and charges of massless and first massive string states of pure-spinor superstrings in 3,4,6,10 dimensions. At the massless level we find a spin-one gauge multiplet of minimal…
We compute the partition function of five-dimensional abelian gauge theory on a five-torus T5 with a general flat metric using the Dirac method of quantizing with constraints. We compare this with the partition function of a single…
Scaling black holes are solutions of supergravity with multiple black hole singularities, which can be adiabatically connected to a single center black hole solution. We develop techniques to determine partition functions for such scaling…
We consider 5d $\mathcal{N}=1$ SU(2) super Yang-Mills theory on $X\times S^1$, with $X$ a closed smooth four-manifold. A partial topological twisting along $X$ renders the theory formally independent of the metric on $X$. The theory depends…
We define an elliptic deformation of the Virasoro algebra. We argue that the $\mathbb{R}^4\times \mathbb{T}^2$ Nekrasov partition function reproduces the chiral blocks of this algebra. We support this proposal by showing that at special…
We compute the Coulomb branch partition function of the 4d $\mathcal{N}=2$ vector multiplet on closed simply-connected quasi-toric manifolds $B$. This includes a large class of theories, localising to either instantons or anti-instantons at…
We establish the relation of partition functions of conformal higher spin fields on Weyl equivalent spaces in $d=4$ dimension. We express the partition function of Weyl graviton and conformal higher spin fields as an integral over…
We study out-of-time ordered four-point functions in two dimensional conformal field theories by suitably analytically continuing the Euclidean correlator. For large central charge theories with a sparse spectrum, chaotic dynamics is…
Based on the construction by Hosomichi, Seong and Terashima we consider N=1 supersymmetric 5D Yang-Mills theory with matter on a five-sphere with radius r. This theory can be thought of as a deformation of the theory in flat space with…
We compute the partition function on S^3 of 3d N=4 theories which arise as the low-energy limit of 4d N=4 super Yang-Mills theory on a segment or on a junction, and propose its 1d interpretation. We show that the partition function can be…
We study the perturbative large-$N$ expansion of the round three-sphere partition function in a class of M2-brane theories, including flavored SYM and ABJM theories as well as more general 3d theories admitting dual $(p,q)$ 5-brane web…
We study the partition functions of topologically twisted 3d $\mathcal{N}=2$ gauge theories on a hemisphere spacetime with boundary $HS^2 \times S^1$. We show that the partition function may be localised to either the Higgs branch or the…