Holographic study of $T\bar{T}$ like deformed HV QFTs: holographic entanglement entropy
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866909232623779840 |
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| author | Jeong, Hyun-Sik Pan, Wen-Bin Sun, Ya-Wen Wang, Yuan-Tai |
| author_facet | Jeong, Hyun-Sik Pan, Wen-Bin Sun, Ya-Wen Wang, Yuan-Tai |
| contents | We study the $(d+2)$-dimensional Hyperscaling Violating (HV) geometries in the presence of both a finite temperature $T$ and a UV cutoff $r_c$. This gravitational system is conjectured to be dual to $T\bar{T}$ like deformed HV QFTs. We consider the representative quantum entanglement quantity in holography, i.e. the entanglement entropy $S(A)$, and perform a complete analysis in all possible parameter ranges of the hyperscaling violation exponent $θ$ and the critical dynamical exponent $z$ to study the effect of the temperature and the cutoff. We find that the temperature has a universal effect independent of the parameters: it enhances $S(A)$ in the small cutoff limit, while it is irrelevant in the large cutoff limit. For the cutoff effect, we find that the cutoff monotonically suppresses $S(A)$ where its behavior depends on the parameter range. As an application of the finite temperature analysis, we study the first law of entanglement entropy, $S_{T}-S_{T=0}\sim\ell^λ$, in the small subsystem size $\ell$ limit. We find that $λ$ interpolates between $λ=1+z$ in the small cutoff and $λ=3$ in the large cutoff, independent of the parameter range. We also provide the analytic holographic result at $z=d-θ$ and discuss its possibility of comparison with the field theoretic result. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_00518 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Holographic study of $T\bar{T}$ like deformed HV QFTs: holographic entanglement entropy Jeong, Hyun-Sik Pan, Wen-Bin Sun, Ya-Wen Wang, Yuan-Tai High Energy Physics - Theory We study the $(d+2)$-dimensional Hyperscaling Violating (HV) geometries in the presence of both a finite temperature $T$ and a UV cutoff $r_c$. This gravitational system is conjectured to be dual to $T\bar{T}$ like deformed HV QFTs. We consider the representative quantum entanglement quantity in holography, i.e. the entanglement entropy $S(A)$, and perform a complete analysis in all possible parameter ranges of the hyperscaling violation exponent $θ$ and the critical dynamical exponent $z$ to study the effect of the temperature and the cutoff. We find that the temperature has a universal effect independent of the parameters: it enhances $S(A)$ in the small cutoff limit, while it is irrelevant in the large cutoff limit. For the cutoff effect, we find that the cutoff monotonically suppresses $S(A)$ where its behavior depends on the parameter range. As an application of the finite temperature analysis, we study the first law of entanglement entropy, $S_{T}-S_{T=0}\sim\ell^λ$, in the small subsystem size $\ell$ limit. We find that $λ$ interpolates between $λ=1+z$ in the small cutoff and $λ=3$ in the large cutoff, independent of the parameter range. We also provide the analytic holographic result at $z=d-θ$ and discuss its possibility of comparison with the field theoretic result. |
| title | Holographic study of $T\bar{T}$ like deformed HV QFTs: holographic entanglement entropy |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2211.00518 |