| Summary: | 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 T ¯ $$ T\overline{T} $$ 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 ~ 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.
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