Penrose Limits, PP-Waves and Deformed M2-branes

TL;DR

This paper explores supersymmetric pp-wave solutions in type IIB string theory, their relation to deformed M2-branes, and the implications for dual three-dimensional field theories with phase transitions.

Contribution

It introduces new supersymmetric pp-wave backgrounds with enhanced supersymmetries and connects them to deformed M2-branes and solvable string models.

Findings

Identification of pp-wave solutions with supernumerary supersymmetries.

Connection between T-duality, pp-waves, and deformed M2-branes.

Observation of a phase transition at an intermediate energy scale.

Abstract

Motivated by the recent discussions of the Penrose limit of AdS_5\times S^5, we examine a more general class of supersymmetric pp-wave solutions of the type IIB theory, with a larger number of non-vanishing structures in the self-dual 5-form. One of the pp-wave solutions can be obtained as a Penrose limit of a D3/D3 intersection. In addition to 16 standard supersymmetries these backgrounds always allow for supernumerary supersymmetries. The latter are in one-to-one correspondence with the linearly-realised world-sheet supersymmetries of the corresponding exactly-solvable type IIB string action. The pp-waves provide new examples where supersymmetries will survive in a T-duality transformation on the x^+ coordinate. The T-dual solutions can be lifted to give supersymmetric deformed M2-branes in D=11. The deformed M2-brane is dual to a three-dimensional field theory whose renormalisation group flow runs from the conformal fixed point in the infra-red regime to a non-conformal theory as the energy increases. At a certain intermediate energy scale there is a phase transition associated with a naked singularity of the M2-brane. In the ultra-violet limit the theory is related by T-duality to an exactly-solvable massive IIB string theory.