Year: 2025
Type: preprint
Abstract: 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 $\text{AdS}_4\times S^7/\mathbb{Z}_{N_\text{f}}$.
Source: arXiv (Cornell University)
Authors: He, Bin, Nosaka, Tomoki
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7083076151
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