arXiv:2304.11430 · Journal of High Energy Physics

Holographic n-partite information in hyperscaling violating geometry

Xin-Xiang Ju, Tengzhou Lai, Ya-Wen Sun, Yuan-Tai Wang

Published Aug 14, 2023• 5 citations

Abstract

A bstract The n -partite information (nI) is formulated as a measure of multi-partite entanglement. Field theory computation revealed that the sign of nI is indefinite for n ≥ 3, while holographic studies conjectured a sign property that holographic nI is non-negative/non-positive for even/odd n , with tripartite information (TI, n = 3) proved. We investigate the aspects of nI with holographic duality in hyperscaling violating geometry. We confirm the conjectured sign property for strips of equal length with equal separation distance, and disprove this conjecture for n > 3 with general configurations. Therefore, nI in field theories and holography exhibits compatibility except for n = 3. We also discuss other properties of holographic nI with analytic computation: the monotonicity, linearity, relation to hyperscaling violating parameters, temperature and UV cutoff effects, and the physical implications. It is doubtful that nI is an effective measure of entanglement considering the indefinite sign, non-monotonicity, and quasi-linearity of its holographic dual. In this respect, we propose constraints on the multi-partite entanglement measures.

DOI: 10.1007/jhep08(2023)064

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arXiv:2304.11430 · Journal of High Energy Physics

Holographic n-partite information in hyperscaling violating geometry

Xin-Xiang Ju, Tengzhou Lai, Ya-Wen Sun, Yuan-Tai Wang

Published Aug 14, 2023• 5 citations

arXiv HTML PDF

Abstract

DOI: 10.1007/jhep08(2023)064

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A bstract In this paper, we systematically study the measures of multi-partite entanglement with the aim of constructing those measures that can be computed in probe approximation in the holographic dual. We classify and count general measures as invariants of local unitary transformations. After formulating these measures in terms of permutation group elements, we derive conditions that a probe measure should satisfy and find a large class of solutions. These solutions are generalizations of the multi-entropy introduced in [1]. We derive their holographic dual with the assumption that the replica symmetry is unbroken in the bulk and check our prescription with explicit computations in 2 d CFTs. Analogous to the multi-entropy, the holographic dual of these measures is given by the weighted area of the minimal brane-web but with branes having differing tensions. We discuss the replica symmetry assumption and also how the already known entanglement measures, such as entanglement negativity and reflected entropy fit in our framework.A bstract In this paper, we systematically study the measures of multi-partite entanglement with the aim of constructing those measures that can be computed in probe approximation in the holographic dual. We classify and count general measures as invariants of local unitary transformations. After formulating these measures in terms of permutation group elements, we derive conditions that a probe measure should satisfy and find a large class of solutions. These solutions are generalizations of the multi-entropy introduced in [1]. We derive their holographic dual with the assumption that the replica symmetry is unbroken in the bulk and check our prescription with explicit computations in 2 d CFTs. Analogous to the multi-entropy, the holographic dual of these measures is given by the weighted area of the minimal brane-web but with branes having differing tensions. We discuss the replica symmetry assumption and also how the already known entanglement measures, such as entanglement negativity and reflected entropy fit in our framework.

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We investigate the monogamy of holographic

n

-partite information for a system consisting of

n

disjoint parallel strips with the same width and separation in AdS and AdS black brane geometries. More precisely, we study the sign of this quantity, e.g., for

n=4

, 5, in various dimensions and for different parameters. Our results show that for quantum field theories with holographic duals, the holographic 4-partite information is always positive, and the sign of holographic 5-partite information is found to be negative in the dual strongly coupled

1+1

dimensional conformal field theory. This latter result indicates that the holographic 4-partite information is monogamous. We also find the critical points corresponding to the possible phase transitions of these quantities.

Holographic study of

T\overline{T}

like deformed HV QFTs: holographic entanglement entropy

T\overline{T}

T 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, ST – ST =0 ~ ℓλ, 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.

We study various entanglement measures associated with certain nonconformal field theories. We consider nonconformal

\mathrm{D}p

-brane backgrounds, which are dual to these field theories, for our holographic analysis. Restricting our interests in

p=1

, 2, 4, we explicitly compute properties of holographic entanglement entropy and the entanglement wedge cross section,

{\mathrm{E}}_{W}

, corresponding to two parallel strip shaped boundary subregions in these setups. We study low and high temperature behaviors of these quantities analytically as well as by using numerical methods. In all cases, the

{\mathrm{E}}_{W}

decreases monotonically with temperature. We observe discontinuous jumps in

{\mathrm{E}}_{W}

, while the width of (as well as the separation between) the subregions reaches critical values in all the cases considered. However, the corresponding holographic mutual information

{\mathtt{I}}_{M}

continuously decreases to zero for the aforementioned configurations. We also notice that the conjectured inequality ${\mathrm{E}}_{W}\ensuremath{\ge}{\mathtt{I}}_{M}/2$ still holds for nonconformal field theories as well. We analytically determine the critical separation between these subregions that triggers a phase transition in the holographic mutual information.