The free energy of the large-$N$ fermionic Chern$\unicode{x2013}$Simons theory in the 'temporal' gauge
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866918219507302400 |
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| author | Minwalla, Shiraz Nath, Souparna Tanwar, Nikhil Vatsal |
| author_facet | Minwalla, Shiraz Nath, Souparna Tanwar, Nikhil Vatsal |
| contents | Most of the computational evidence for the Bose$\unicode{x2013}$Fermi duality of fundamental fields coupled to $U(N)$ Chern$\unicode{x2013}$Simons theories originates in large-$N$ calculations performed in the light-cone gauge. This gauge is ill-suited to computations in curved spacetimes, like the evaluation of the partition function on $Σ_g\times S^1$ for arbitrary genus $g$. In this paper, we use another gauge, the 'temporal' gauge, to set up the computation of this partition function. In the large-$N$ limit, and the special case $Σ_g=\mathbb{R}^2$, we take the computation through to the end by setting up and solving the gap equations, generalizing tricks explored in arXiv:1410.0558 to finite temperature. Our final results are in perfect agreement with earlier light-cone gauge results, providing a consistency check of both the formalism developed in this paper as well as previously performed light-cone gauge computations. In a follow-up paper, we will report on using our formalism to explicitly compute the partition function on $S^2 \times S^1$ for a finite-sized sphere. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_11020 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The free energy of the large-$N$ fermionic Chern$\unicode{x2013}$Simons theory in the 'temporal' gauge Minwalla, Shiraz Nath, Souparna Tanwar, Nikhil Vatsal High Energy Physics - Theory Mathematical Physics Most of the computational evidence for the Bose$\unicode{x2013}$Fermi duality of fundamental fields coupled to $U(N)$ Chern$\unicode{x2013}$Simons theories originates in large-$N$ calculations performed in the light-cone gauge. This gauge is ill-suited to computations in curved spacetimes, like the evaluation of the partition function on $Σ_g\times S^1$ for arbitrary genus $g$. In this paper, we use another gauge, the 'temporal' gauge, to set up the computation of this partition function. In the large-$N$ limit, and the special case $Σ_g=\mathbb{R}^2$, we take the computation through to the end by setting up and solving the gap equations, generalizing tricks explored in arXiv:1410.0558 to finite temperature. Our final results are in perfect agreement with earlier light-cone gauge results, providing a consistency check of both the formalism developed in this paper as well as previously performed light-cone gauge computations. In a follow-up paper, we will report on using our formalism to explicitly compute the partition function on $S^2 \times S^1$ for a finite-sized sphere. |
| title | The free energy of the large-$N$ fermionic Chern$\unicode{x2013}$Simons theory in the 'temporal' gauge |
| topic | High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2307.11020 |