Green-Schwarz String in AdS_5 x S^5: Semiclassical Partition Function

TL;DR

This paper develops a systematic semiclassical approach to analyze string fluctuations in AdS_5 x S^5 using the Green-Schwarz formalism, ensuring the partition function's finiteness and exploring various classical solutions relevant to gauge theory observables.

Contribution

It introduces a comprehensive method for calculating semiclassical string partition functions in AdS_5 x S^5, clarifying gauge issues and applying it to key classical solutions.

Findings

Partition function is well-defined and finite.

Explicit calculations for classical solutions ending on boundary lines or circles.

First corrections to Wilson loop expectation values in strong coupling.

Abstract

A systematic approach to the study of semiclassical fluctuations of strings in AdS_5 x S^5 based on the Green-Schwarz formalism is developed. We show that the string partition function is well defined and finite. Issues related to different gauge choices are clarified. We consider explicitly several cases of classical string solutions with the world surface ending on a line, on a circle or on two lines on the boundary of AdS. The first example is a BPS object and the partition function is one. In the third example the determinants we derive should give the first corrections to the Wilson loop expectation value in the strong coupling expansion of the n=4 SYM theory at large N.