Penrose Limits and RG Flows

TL;DR

This paper explores how Penrose limits of supergravity backgrounds relate to RG flows in dual gauge theories, providing solvable models and insights into the behavior of string states and gauge operators during flow transitions.

Contribution

It establishes a map between quantum mechanical problems from Penrose limits and RG flows in gauge theories, including explicit examples and analysis of different brane configurations.

Findings

Exact solvability of quantum particle in simplified backgrounds

Identification of dual gauge operators for string states

Observation of negative mass-squared in IR limits for certain branes

Abstract

The Penrose-Gueven limit simplifies a given supergravity solution into a pp-wave background. Aiming at clarifying its relation to renormalization group flow we study the Penrose-Guven limit of supergravity backgrounds that are dual to non-conformal gauge theories. The resulting backgrounds fall in a class simple enough that the quantum particle is exactly solvable. We propose a map between the effective time-dependent quantum mechanical problem and the RG flow in the gauge theory. As a testing ground we consider explicitly two Penrose limits of the infrared fixed point of the Pilch-Warner solution. We analyze the corresponding gauge theory picture and write down the operators which are the duals of the low lying string states. We also address RG flows of a different nature by considering the Penrose-Gueven limit of a stack of N D_p branes. We note that in the far IR (for p<3)the limit generically has negative mass-squared. This phenomenon signals, in the world sheet picture, the necessity to transform to another description. In this regard, we consider explicitly the cases of M2 from D2 and F1 from D1 .