On precision holography for the circular Wilson loop in $AdS_{5}\times S^{5}$

TL;DR

This paper refines the string theory calculation of the 1/2-BPS circular Wilson loop in N=4 SYM at strong coupling, confirming the match with field theory results through advanced spectral analysis techniques.

Contribution

It introduces a conformal transformation and a modified Gel'fand-Yaglom approach to accurately compute the ratio of string partition functions, improving precision in holographic calculations.

Findings

Matching with known field theory results achieved

Zero mode contributions are crucial for the correct result

Methodology clarifies the role of zero modes in holographic computations

Abstract

The string theory calculation of the 1/2-BPS circular Wilson loop of N=4 SYM in the planar limit at next to leading order at strong coupling is revisited in the ratio of its semiclassical string partition function and the one dual to a latitude Wilson loop with trivial expectation value. After applying a conformal transformation from the disk to the cylinder, this problem can be approached by means of the Gel'fand-Yaglom formalism. Using results from the literature and the exclusion of zero modes from a modified Gel'fand-Yaglom formula, we obtain matching with the known field theory result. As seen in the phaseshift method computation, non-zero mode contributions cancel and the end result comes from the zero mode degeneracies of the latitude Wilson loop.