New recursion relations for M2-brane matrix models

Fuente: arXiv
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Main Authors: He, Bin, Nosaka, Tomoki
Format: Preprint
Published: 2025
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author He, Bin
Nosaka, Tomoki
author_facet He, Bin
Nosaka, Tomoki
contents In this paper we investigate the finite $N$ exact values of the $S^3$ partition function of the ${\cal N}=4$ super Yang-Mills theory with one adjoint hypermultiplet and $N_\text{f}$ fundamental hypermultiplets, which describes $N$ M2-branes on $\mathbb{C}^2\times \mathbb{C}^2/\mathbb{Z}_{N_\text{f}}$, with mass and FI deformations. We claim that the grand canonical sum of the partition function obeys a bilinear difference relation with respect to the shifts of the mass parameters of the fundamental hypermultiplets, which results in a new recursion relation for the partition function with respect to $N$. As an application, we also determine the analytic expression for the leading $1/N$ non-perturbative correction to the free energy of these models, which would correspond holographically to the contribution from an M2-brane wrapped on a 3d volume in the internal space of $\text{AdS}_4\times S^7/\mathbb{Z}_{N_\text{f}}$.
format Preprint
id arxiv_https___arxiv_org_abs_2509_15801
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle New recursion relations for M2-brane matrix models
He, Bin
Nosaka, Tomoki
High Energy Physics - Theory
In this paper we investigate the finite $N$ exact values of the $S^3$ partition function of the ${\cal N}=4$ super Yang-Mills theory with one adjoint hypermultiplet and $N_\text{f}$ fundamental hypermultiplets, which describes $N$ M2-branes on $\mathbb{C}^2\times \mathbb{C}^2/\mathbb{Z}_{N_\text{f}}$, with mass and FI deformations. We claim that the grand canonical sum of the partition function obeys a bilinear difference relation with respect to the shifts of the mass parameters of the fundamental hypermultiplets, which results in a new recursion relation for the partition function with respect to $N$. As an application, we also determine the analytic expression for the leading $1/N$ non-perturbative correction to the free energy of these models, which would correspond holographically to the contribution from an M2-brane wrapped on a 3d volume in the internal space of $\text{AdS}_4\times S^7/\mathbb{Z}_{N_\text{f}}$.
title New recursion relations for M2-brane matrix models
topic High Energy Physics - Theory
url https://arxiv.org/abs/2509.15801