More on Penrose limits and non-local theories

TL;DR

This paper explores Penrose limits of six-dimensional non-commutative string theories, revealing exactly solvable models, phase structures, and connections to dual theories through string spectra and null geodesic analysis.

Contribution

It provides the first detailed analysis of Penrose limits in NCOS$_6$ and related theories, including solvable string models and phase-dependent behaviors.

Findings

Exact solvability of string theory near specific null geodesics in NCOS$_6$

Description of phase structure and Penrose limits in different phases

Relation of string spectra to states in various dual theories

Abstract

We obtain the Penrose limit of six dimensional Non-Commutative Open String (NCOS$_6$) theory and show that in the neighborhood of a particular null geodesic it leads to an exactly solvable string theory (unlike their counterparts in four or in other dimensions). We describe the phase structure of this theory and discuss the Penrose limit in different phases including Open D-string (OD1) theory. We compute the string spectrum and discuss their relations with the states of various theories at different phases. We also consider the case of general null geodesic for which the Penrose limit leads to string theory in the time dependent pp-wave background and comment on the renormalization group flow in the dual theory.