Holographic Subregion Complexity and Fidelity Susceptibility in Noncommutative Yang--Mills Theory

TL;DR

This paper investigates how noncommutativity affects holographic subregion complexity and fidelity susceptibility, revealing a minimum length scale, phase transitions, and temperature-dependent behaviors in noncommutative Yang--Mills theory.

Contribution

It introduces the effects of noncommutativity on holographic complexity and fidelity susceptibility, highlighting a minimum length scale and phase transition phenomena.

Findings

Minimum length scale induces behavioral transition in HSC.

HFS effectively measures the degree of noncommutativity.

Temperature influences the lower bound and sensitivity of HSC and HFS.

Abstract

We analyze the behavior of holographic subregion complexity (HSC) and holographic fidelity susceptibility (HFS) in noncommutative Yang--Mills theory. The emergence of a minimum length scale, dictated by the degree of noncommutativity, induces a behavioral transition in the HSC and establishes a lower bound. In the large noncommutativity regime, the qualitative features of the complexity deviate significantly from the commutative case. The HFS is shown to provide an effective measure of the degree of noncommutativity. Although the HSC generally satisfies strong subadditivity, this property fails abruptly when the subregion size approaches the minimum length scale. At finite temperature, the long-range behavior of the HSC is modified, and its lower bound scales positively with temperature. Furthermore, temperature enhances the sensitivity of the fidelity susceptibility to the degree of noncommutativity. Within the AdS soliton background, a competition between connected and disconnected configurations arises in the HSC, signaling a phase-transition-like behavior. Finally, the compactification scale is found to diminish the sensitivity of the HFS to the degree of noncommutativity.