The AdS(n) x S(n) x T(10-2n) BMN string at two loops

TL;DR

This paper computes two-loop corrections to the dispersion relation of worldsheet modes in AdS(n) x S(n) x T(10-2n) backgrounds, confirming some predictions and revealing discrepancies in the massless sector, and derives related S-matrix elements.

Contribution

It provides the first two-loop correction calculations for the BMN string in these backgrounds, clarifies the behavior of massive modes, and explores the massless S-matrix structure.

Findings

Massive modes' dispersion relation matches symmetry predictions with no correction to h.

Massless modes in AdS3 x S3 x T4 show discrepancies from symmetry-based expectations.

The two-loop massless S-matrix phase appears to be zero, indicating no correction at this order.

Abstract

We calculate the two-loop correction to the dispersion relation for worldsheet modes of the BMN string in AdS(n) x S(n) x T(10-2n) for n=2,3,5. For the massive modes the result agrees with the exact dispersion relation derived from symmetry considerations with no correction to the interpolating function h. For the massless modes in AdS(3) x S(3) x T(4) however our result does not match what one expects from the corresponding symmetry based analysis. We also derive the S-matrix for massless modes up to the one-loop order. The scattering phase is given by the massless limit of the Hernandez-Lopez phase. In addition we compute a certain massless S-matrix element at two loops and show that it vanishes suggesting that the two-loop phase in the massless sector is zero.