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

TL;DR

This work analyzes holographic subregion complexity (HSC) and holographic fidelity susceptibility (HFS) in noncommutative Yang–Mills theory using the CV conjecture. The noncommutative scale $a$ introduces a minimum length $l_{ m min}$ and UV/IR mixing, imprinting distinctive features on both HSC and HFS, including a universal finite part of HSC and a nonzero lower bound for HFS. For rectangular subregions, the universal HSC term exhibits a lower bound and a connected/disconnected transition emerges in AdS soliton backgrounds, signaling phase-transition-like behavior. Finite temperature further modifies the large-distance behavior of HSC and enhances the sensitivity of HFS to noncommutativity, while dimensional reduction can suppress this sensitivity, highlighting rich thermodynamic and geometric structure in NCYM.

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.

Figures (14)

• Figure 1: The variation of the dimensionless quantity ${\cal C}_{A} \equiv \dfrac{6\pi^{2}a^{2}}{N^{2}L^{2}}C_{A}^{({\rm univ})}$ with respect to the dimensionless length $l/a$, in units where $a=1$. The solid and dotted lines correspond to the noncommutative case and the commutative limit ($a \to 0$), respectively.
• Figure 2: The variation of the dimensionless quantity ${\cal C}_{A} \equiv \dfrac{6\pi^{2}a^{2}}{N^{2}L^{2}}C_{A}^{({\rm univ})}$ with respect to the dimensionless length $l/a$, in units where $a=1$. The solid and dashed lines correspond to the noncommutative case and the noncommutative limit, respectively.
• Figure 3: The variation of the dimensionless quantity ${\cal G}_{a} \equiv \dfrac{12\pi^{2}}{au_{\Lambda}^{3}N^{2}L^{2}} G_{a}$ as a function of the parameter $au_{\ast}$, in units where $a=1$. The solid and dotted lines correspond to the noncommutative case and the commutative limit, respectively.
• Figure 4: The variation of the dimensionless quantity $\Delta{\cal G}_{a} \equiv \dfrac{12\pi^{2}u_{\ast}}{u_{\Lambda}^{3}N^{2}L^{2}} \Delta G_{a}$ as a function of the dimensionless parameter $au_{\ast}$, in units where $u_{\ast}=1$.
• Figure 5: (Left) Two overlapping infinite boundary strips $A$ and $B$, with their respective volumes ${\cal V}_{A}$ and ${\cal V}_{B}$ enclosed by the Ryu--Takayanagi surface. (Right) Two overlapping infinite boundary strips $A \cup B$ and $A \cap B$, with their respective volumes ${\cal V}_{A \cup B}$ and ${\cal V}_{A \cap B}$ enclosed by the Ryu--Takayanagi surface.