Wilson Loops, D-Branes, and Reparametrization Path-Integrals

TL;DR

This paper investigates path-integrals over boundary reparametrizations in string theory, demonstrating their finiteness in AdS/CFT for Wilson loops, analyzing divergences in critical strings, and computing corrections to brane actions.

Contribution

It provides a detailed analysis of boundary reparametrization path-integrals, including their finiteness in AdS/CFT, divergence structure in critical strings, and their role in computing brane effective actions.

Findings

The integral is finite and yields a 1-loop correction in AdS/CFT.

In critical string theory, the integral exhibits UV divergences.

Divergences can be renormalized by contour adjustments, and the 2-loop beta-function relates to D0-brane actions.

Abstract

We study path-integrals over reparametrizations of the world-sheet boundary. Such integrals arise when string propagates between fixed space-time contours. In gauge/string duality they are needed to describe gauge theory Wilson loops. We show that (1) in AdS/CFT, the integral is well defined and gives a finite 1-loop correction to the Wilson loop; (2) in critical string theory, the integral is UV divergent, and fixed contour amplitudes are off shell. In the second case, we show that the divergences can be removed by renormalizing the contour. We calculate the 2-loop contour beta-function and explain how it is related to the D0-brane effective action. We also apply this method to compute the first alpha' correction to the effective action of higher dimensional branes.