Related papers: Exact ABJM Partition Function from TBA

It is known that the large N expansion of the partition function in ABJM theory on a three-sphere is completely determined by the topological string on local Hirzebruch surface F_0. In this note, we investigate the ABJM partition function…

Let $p(n)$ denote the partition function and define $p(n,k)=\sum_{j=0}^{k}\binom{n-j}{k-j}p(j)$ where $p(0)=1$. We prove that $p(n,k)$ is unimodal and satisfies $p(n,k) < \frac{2.825}{\sqrt{n}}\, 2^n $ for fixed $n\ge 1$ and all $1\le k\le…

We survey recent results on quantum corrections to the hypermultiplet moduli space M in type IIA/B string theory on a compact Calabi-Yau threefold X, or, equivalently, the vector multiplet moduli space in type IIB/A on X x S^1. Our main…

The coefficients of the membrane instantons in the ABJM theory are known to be quadratic polynomials of the chemical potential. We show that, after deforming the ABJM theory into more general superconformal Chern-Simons theories labelled by…

We derive a formula for the BPS partition functions of arbitrary S-fold theories. We first generalize the known result for the ${\cal N}=4$ $U(N)$ supersymmetric Yang-Mills theory to $SO$ and $Sp$ theories, and then we extend the formula to…

We consider the partition function of the superconformal Chern-Simons theories with the quiver diagram being the affine D-type Dynkin diagram. Rewriting the partition function into that of a Fermi gas system, we show that the perturbative…

We consider $\mathcal{N}=2$ supersymmetric pure gauge theories on toric K\"ahler manifolds, with particular emphasis on $\mathbb{CP}^2$. By choosing a vector generating a $U(1)$ action inside the torus of the manifold, we construct…

We present a structural resolution to the exact evaluation of the partition function $p_k(n)$, systematically overcoming the limitations of traditional recursive and asymptotic methods. By framing the partition polytope $\mathcal{P}_{n,k}$…

We extend the Fermi gas approach to a class of ABJM-like necklace quiver theories without parity invariance. The resulting partition function on $S^3$ retains the form of an Airy function, but now includes a phase that scales as $Nk$ in the…

This note reports on the number of s-partitions of a natural number n. In an s-partition each cell has the form $2^k-1$ for some integer k. Such partitions have potential applications in cryptography, specifically in distributed…

It was known that the ABJM matrix model is dual to the topological string theory on a Calabi-Yau manifold. Using this relation it was possible to write down the exact instanton expansion of the partition function of the ABJM matrix model.…

The D-instanton partition function is a fascinating quantity because in the presence of N D3-branes, and in a certain decoupling limit, it reduces to the functional integral of N=4 U(N) supersymmetric gauge theory for multi-instanton…

We establish the average-case hardness of the algorithmic problem of exact computation of the partition function associated with the Sherrington-Kirkpatrick model of spin glasses with Gaussian couplings and random external field. In…

Partition functions of certain classes of "spin glass" models in statistical physics show strong connections to combinatorial graph invariants. Also known as homomorphism functions they allow for the representation of many such invariants,…

We generalize Nakajima-Yoshioka blowup equations to arbitrary gauge group with hypermultiplets in arbitrary representations. Using our blowup equations, we compute the instanton partition functions for 4d N=2 and 5d N=1 gauge theories for…

We present a quantum M2 brane computation of the instanton prefactor in the leading non-perturbative contribution to the ABJM 3-sphere free energy at large $N$ and fixed level $k$. Using supersymmetric localization, such instanton…

We propose a recipe for determination of the partition function of ${\cal N}=4$ $ADE$ gauge theory on $K3$ by generalizing our previous results of the SU(N) case. The resulting partition function satisfies Montonen-Olive duality for $ADE $…

The partition function on the three-sphere of many supersymmetric Chern-Simons-matter theories reduces, by localization, to a matrix model. We develop a new method to study these models in the M-theory limit, but at all orders in the 1/N…

We present a new expression for the partition function of refined Chern-Simons theory on $S^3$ with arbitrary gauge group, which is explicitly equal to $1$, when the coupling constant is zero. Using this form of partition function we show…

We prove a simple identity relating the $k$th moment of the partition function $Z_N(\cdot)$ in the SK model to the $N$th moment of the partition function $Z_k(\cdot)$. As a corollary we find a characterisation of the limit $\lim_{N \to…