Exact large $N$ expansion of mass deformed ABJM theory on squashed sphere
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866912238842937344 |
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| author | Kubo, Naotaka Nosaka, Tomoki Pang, Yi |
| author_facet | Kubo, Naotaka Nosaka, Tomoki Pang, Yi |
| contents | In this paper we study the partition function of the mass deformed ABJM theory on a squashed three sphere. In particular, we focus on the case with the Chern-Simons levels being $\pm 1$ and apply a duality between this theory and the $\mathcal{N}=4$ $\mathrm{U}\left(N\right)$ super Yang-Mills theory with an adjoint hypermultiplet and a fundamental hypermultiplet. For a special mass parameter depending on the squashing parameter, we find that the partition function can be written as that of an ideal Fermi gas with a non-trivial density matrix. By studying this density matrix, we analytically derive the all order perturbative expansion of the partition function in $1/N$, which turns out to take the form of the Airy function. Our results not only align with previous findings and conjectures but also lead to a new formula for the overall constant factor of the partition function. We also study the exact values of the partition function for small but finite values of $N$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_07334 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Exact large $N$ expansion of mass deformed ABJM theory on squashed sphere Kubo, Naotaka Nosaka, Tomoki Pang, Yi High Energy Physics - Theory In this paper we study the partition function of the mass deformed ABJM theory on a squashed three sphere. In particular, we focus on the case with the Chern-Simons levels being $\pm 1$ and apply a duality between this theory and the $\mathcal{N}=4$ $\mathrm{U}\left(N\right)$ super Yang-Mills theory with an adjoint hypermultiplet and a fundamental hypermultiplet. For a special mass parameter depending on the squashing parameter, we find that the partition function can be written as that of an ideal Fermi gas with a non-trivial density matrix. By studying this density matrix, we analytically derive the all order perturbative expansion of the partition function in $1/N$, which turns out to take the form of the Airy function. Our results not only align with previous findings and conjectures but also lead to a new formula for the overall constant factor of the partition function. We also study the exact values of the partition function for small but finite values of $N$. |
| title | Exact large $N$ expansion of mass deformed ABJM theory on squashed sphere |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2411.07334 |