$\beta$-deformation on a slanted torus and deformed pp-wave

TL;DR

This paper explores a specific deformation of the $AdS_5 imes S^5$ space incorporating $SL(2, ext{R})$ symmetry, analyzing its Penrose limit and string spectrum in the resulting pp-wave background.

Contribution

It introduces a $eta$-deformation that includes $SL(2, ext{R})$ symmetry and studies the resulting string spectrum in the deformed background.

Findings

Identification of the axion-dilaton with a two-torus from an 11D perspective

Derivation of the Penrose limit for the deformed background

Analysis of the bosonic string spectrum in the deformed pp-wave

Abstract

We discuss the $\beta$-deformation of $AdS_5\times S^5$ 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 $AdS_5\times S^5$. We study the bosonic part of the string sigma model and the spectrum of the string in the pp-wave background.