Is entanglement a probe of confinement?

TL;DR

This work addresses whether holographic entanglement measures can diagnose confinement in a one-parameter family of 3D YM–CS theories by analyzing their gravity duals. Using the Ryu–Takayanagi prescription, the authors compute EE for strips and disks and study associated quantities such as the mutual information and F-functions across the parameter $b_0\in[0,1]$, which interpolates between an IR OP fixed point ($b_0\approx0$) and a confining-like IR ($b_0=1$). They find that EE, mutual information, and $F$-functions are sensitive to the presence of a mass gap but do not distinguish confining from non-confining gapped phases; near the fixed point, these information measures recover conformal values over a range of energies, illustrating walking behavior. The results challenge the view that entanglement phase transitions at large $N$ are universal indicators of confinement and highlight that confinement diagnostics in holography should rely on multiple probes, including Wilson loops and other observables. The study thus clarifies the nuanced relationship between confinement, mass gaps, and entanglement in holographic gauge theories, and suggests directions for richer diagnostics via multiparty entanglement and finite-temperature analyses.

Abstract

We study various entanglement measures in a one-parameter family of three-dimensional, strongly coupled Yang-Mills-Chern-Simons field theories by means of their dual supergravity descriptions. A generic field theory in this family possesses a mass gap but does not have a linear quark-antiquark potential. For the two limiting values of the parameter, the theories flow either to a fixed point or to a confining vacuum in the infrared. We show that entanglement measures are unable to discriminate confining theories from non-confining ones with a mass gap. This lends support on the idea that the phase transition of entanglement entropy at large-N can be caused just by the presence of a sizable scale in a theory and just by itself should not be taken as a signal of confinement. We also examine flows passing close to a fixed point at intermediate energy scales and find that the holographic entanglement entropy, the mutual information, and the F-functions for strips and disks quantitatively match the conformal values for a range of energies.

Figures (13)

• Figure 1: Pictorial representation of the $\mathbb{B}_8$ family of solutions. The asymptotic UV regime is given by the 3D super Yang-Mills theory with Chern-Simons interactions for the gauge fields (SYM-CSM). As we come down in energy (descending in the plot) the RG flow generically drives the theory to an IR regime with a mass gap. Only for extreme value of $b_0=1$ do we flow to a confining theory, as depicted on the bottom-right corner of the plot. For $b_0=0$ the IR is governed by an Ooguri-Park (OP) conformal fixed point. The hue or the warmth of the curves will be roughly in one-to-one correspondence with the values of $b_0$ on the horizontal axis; in the figures to follow we will try to maintain this mapping.
• Figure 2: Quark-antiquark potential for a non-confining theory with a mass gap $\mathbb{B}_8^0$ (Left) and for the confining theory $\mathbb{B}_8^{\rm{conf}}$ (Right). Solid curves stand for the value of the potential for the dominant configuration whereas dashed curves depict those of unstable configurations. The string breaks in the $\mathbb{B}_8^0$ theory when the curve crosses zero, signaling the splitting of a meson into two quarks in the gauge theory. As explained in the main text, splitting cannot happen in the confining case $\mathbb{B}_8^{\rm{conf}}$, where consequently the connected configuration is always the dominant one, leading to the linear growth of the potential for large values of the separation between the quark and the antiquark. Plot adapted from Faedo:2017fbv and in the units used therein.
• Figure 3: The two possible and competing configurations of the RT surface we have to consider when computing entanglement entropies of strips: for small widths of the strip, a "connected" configuration $\cup$, which does not reach the bottom of the geometry (left), competes with the "disconnected" configuration $\sqcup$, which reaches the end-of-space (right).
• Figure 4: Entanglement entropy of a single strip as a function of the width of the strip in the gapped non-confining theory $\mathbb{B}_8^0$ (Left) and in the confining one $\mathbb{B}_8^{\rm{conf}}$ (Right). We plot the rescaled quantity \ref{['eq:dimensionlessEEstrip']} defined in Appendix \ref{['ap:strip']} as a function of the strip width normalized to the value above which the "disconnected" configuration $\sqcup$ becomes the dominant one.
• Figure 5: Function $\mathsf{F}(l)$ for a single strip as a function of strip width in the gapped non-confining theory $\mathbb{B}_8^0$ (Left) and the confining one $\mathbb{B}_8^{\rm{conf}}$ (Right). Both quantities are normalized to their value at the point where the "disconnected" configuration $\sqcup$ becomes dominant, above which it is strictly zero.