Holographic study of TT like deformed HV QFTs: holographic entanglement entropy

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 TT 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 ℓ λ , in the small subsystem size ℓ 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.