Holographic study of $T\bar{T}$ like deformed HV QFTs: holographic entanglement entropy

Abstract

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 $\theta$ 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, $S_T-S_{T=0}\sim {\ell }^{\lambda }$, in the small subsystem size $\ell$ limit. We find that $\lambda$ interpolates between $\lambda =1+z$ in the small cutoff and $\lambda =3$ in the large cutoff, independent of the parameter range. We also provide the analytic holographic result at $z=d-\theta$ and discuss its possibility of comparison with the field theoretic result.

19 pages, 4 figures

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• One-loop partition functions in $T\overline{T}$-deformed AdS${}_3$
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• Mixed state entanglement in deformed field theory at finite temperature
• Holographic n-partite Information in Hyperscaling Violating Geometry
• Root-$T\overline{T}$ deformed CFT partition functions at large central charge
• Toward a Unified de Sitter Holography: A Composite $T\bar{T}$ and $T\bar{T}+{\Lambda }_2$ Flow
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