Penrose Limits, PP-Waves and Deformed M2-branes

TL;DR

This work extends the landscape of type IIB pp-waves by turning on a general self-dual 5-form, elucidating how 16 standard Killing spinors plus possible supernumerary ones arise and how they relate to linearly realised world-sheet supersymmetry in exactly solvable string theories. It shows that certain pp-waves admit spacelike (and in some regions timelike) T-duality along $x^+$, after which the solutions lift to supersymmetric deformed M2-branes whose dual 3D theories flow from IR conformality to UV non-conformality, with a phase transition linked to a naked singularity. The analysis reveals a one-to-one correspondence between supernumerary world-sheet supersymmetries and additional Killing spinors that survive T-duality, even when the standard 11D supersymmetry criterion appears violated, via cancellations involving the extra flux. These results unify Penrose-limit examples like $AdS_5\times S^5$ and $AdS_3\times S^3$ and show how new supersymmetric M2-branes arise, enriching the connections between pp-waves, T-duality, and holographic RG flows.

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.