More about One-Loop Effective Action of Open Superstring in $AdS_5\times S^5$

TL;DR

This paper recalculates the one-loop effective action for an open superstring in AdS_5×S^5, demonstrating that the determinant ratio is independent of the AdS regularization parameter and analyzing boundary condition effects.

Contribution

It provides an explicit determinant ratio computation showing independence from the AdS regularization parameter and examines boundary condition impacts on the effective action.

Findings

Determinant ratio does not depend on the AdS regularization parameter ε.

Boundary conditions affect individual mode contributions but not the overall product.

The classical boundary action's reparametrization path integral contains the ε dependence.

Abstract

We reconsider the calculation of the one-loop effective action for an open Green-Schwarz superstring in the $AdS_5\times S^5$ background for a circular boundary loop. By an explicit computation of the ratio of relevant determinants, describing semi-classical fluctuations about the minimal surface in AdS and flat spaces, we show that it does not depend upon the AdS regularizing parameter $\epsilon$. The only dependence upon $\epsilon$ resides in the reparametrization path integral of the exponential of the classical boundary action. We analyze how the result depends on the choice of the boundary condition imposed on fluctuating fields and show that, despite the fact that the contribution of individual angular modes changes, the product over the modes remains unchanged.