${\hat{I}}^2$-deformation on a slanted torus and deformed pp-wave

Abstract

We discuss the ${\hat{I}}^2$-deformation of $Ad{S}_5\times S^5$ which incorporates the $SL(2,\mathbb{R})$ symmetry of the type IIB theory. The axion-dilaton is identified with a two-torus from an eleven dimensional viewpoint. We consider the null geodesic with equal component angular momenta to take the Penrose limit of the deformed $Ad{S}_5\times S^5$. We study the bosonic part of the string sigma model and the spectrum of the string in the pp-wave background.

9 pages, Final version, incorporating the referee comments