Static heavy quark-antiquark potential within string theory in arbitrary stationary backgrounds

Abstract:

We analyze the dynamics of a static open string in arbitrary stationary spacetime, which can represent a heavy quark-antiquark pair within the holographic framework or effective theory. We establish that for a simple U-shaped string with only radial dependence on the space string coordinate, x_s, the string profile is generally not symmetric about its turning point, and the symmetry restores only for backgrounds with G_{00} G_{pr} – G_{0p} G_{0r} = 0 (here, p refers to the space coordinate on the string worldsheet). Consequently, such asymmetric strings may probe a possibility of the parity violation in the quark-antiquark interaction. Nevertheless, we identify a wide family of metrics for which the symmetry is preserved, enabling a direct isolation of the linear-in-distance term in the static interquark potential for simple symmetric string configurations, even in non-diagonal backgrounds. Applying the holographic framework, we further study several setups: N coincident D3-branes in large-N limit, Ker-AdS and Rindler-AdS backgrounds, dual to the N=4 super Yang-Mills plasma at finite temperature, with rotation and acceleration, correspondingly.