Quantum entanglement measures from Hyperscaling violating geometries with finite radial cut off at general d, $\theta$ from the emergent global symmetry

TL;DR

This paper investigates quantum entanglement measures in hyperscaling violating geometries with finite radial cutoff, revealing an emergent global symmetry that constrains these measures across parameter regimes, despite the complexity of exact solutions.

Contribution

It demonstrates the emergence of a global symmetry in hyperscaling violating geometries that allows approximate determination of entanglement measures over broad parameter ranges.

Findings

Global symmetry constrains entanglement measures.

Exact solutions for turning points are only locally solvable.

Derived behaviors match predictions in deformed theories.

Abstract

The quantum entanglement measures for $T{\overline{T}}$ deformed field theory on boundary, deformation coefficient $\mu$, with dual bulk geometry with finite radial cutoff $\rho_c$, for entangling region is single or disjoint intervals on the boundary, of length l is expected to give global description of these measures over the complete parameter-regime of $(l, \mu)$ or on 2D $(l,\rho_c)$ plane, because it is solvable irrelevant deformation. Here, to find quantum-measures through RT prescription, from Hyperscaling violating bulk geometry with finite radial cut off, we found mathematically it is impossible, to obtain such global form, since the turning point $\rho_0 (l,\rho_c)$, neither in its exact or in any perturbative form, is solvable globally, can describe these quantum measures at most locally over some specific regime in 2D $(l,\rho_c)$ plane! However, to find such global form, we found, on application of RT formalism, a global symmetry structure, from the considered geometry emerges, over 2D parameter-space, irrespective of d, $\theta$, which alongwith global b.c and other consistency conditions, fix $\rho_0(l,\rho_c)$ globally, exactly in $l >> \rho_c $ and $\rho_c >> l$ regime and as some interpolating expressions, very close to the exact one in other regime. Some of the quantum entanglement measures with this $\rho_0 (l,\rho_c)$, with our intuitively predicted behaviour for them in the deformed theory, derived and shown, behaving accordingly. The impact of this emergent symmetry on these quantum-measures is discussed, the possible space time origin of this symmetry is explored, although the later aspect is subjected to a proper and detailed study.