Quantum-Corrected Holographic Wilson Loop Expectation Values and Super-Yang-Mills Confinement

Abstract

Confinement is a well-known phenomenon in the infrared regime of (supersymmetric) Yang-Mills theory. While both experimental observations and numerical simulations have robustly confirmed its existence, the underlying physical mechanism remains elusive. Unraveling the theoretical origin of confinement continues to be a profound and longstanding challenge in both physics and mathematics. Motivated by recent advances in quantum Jackiw-Teitelboim gravity, we investigate the Wilson loop expectation values in the large-$N$ limit of $\mathscr{N}=4$ super-Yang-Mills theory at finite chemical potential, employing a holographic approach within the background of an extremal AdS$_5$ Reissner-Nordström black brane. Our results reveal that quantum gravitational fluctuations in the near-horizon region significantly modify the holographic Wilson loop expectation values. These values exhibit an area-law behavior, indicative of a confining quark-antiquark potential. Within this framework, our findings suggest that confinement in the super-Yang-Mills theory arises as a consequence of near-horizon quantum gravity fluctuations in the bulk extremal AdS$_5$ black brane geometry.

Figures (5)

• Figure 1: The schematic phase diagram of SYM theory (see e.g. Yamada:2006rxEvans:2010iy)
• Figure 2: The minimal surface anchored to the rectangular temporal Wilson loop (denoted by the red line)
• Figure 3: The numerical result of the quark-antiquark potential from the rectangular temporal Wilson loop with the parameters $R=1$, $Q=\sqrt{2}$, and $C=0.01$
• Figure 4: The minimal surface anchored to the circular spatial Wilson loop (denoted by the red line)
• Figure 5: The numerical result of $S_{\text{NG}}$ from the circular spatial Wilson loop with the parameters $R=1$, $Q=\sqrt{2}$, and $C=0.0001$