Quark-antiquark potential in AdS at one loop

TL;DR

This paper calculates the one-loop quantum corrections to the quark-antiquark potential in AdS_5xS^5, providing an exact analytical expression and confirming previous results through numerical evaluation.

Contribution

It derives an exact analytical expression for the one-loop partition function in AdS_5xS^5 with implications for the quark-antiquark potential in N=4 SYM.

Findings

First strong coupling correction expressed as mathematical constants and an integral.

Numerical value of correction matches previous results.

Quantum fluctuations governed by integrable Lame' operators.

Abstract

We derive an exact analytical expression for the one-loop partition function of a string in AdS_5xS^5 background with world-surface ending on two anti-parallel lines. All quantum fluctuations are shown to be governed by integrable, single-gap Lame' operators. The first strong coupling correction to the quark-antiquark potential, as defined in N=4 SYM, is derived as the sum of known mathematical constants and a one-dimensional integral representation. Its full numerical value can be given with arbitrary precision and confirms a previous result.