Duality Cascade and Oblique Phases in Non-Commutative Open String Theory

TL;DR

This paper explores the complex phase structure of non-commutative open string theory and (P,Q) strings, revealing a fractal cascade of phases driven by S-duality and temperature changes.

Contribution

It uncovers a detailed phase diagram showing a cascade of supergravity, gauge, and matrix string phases in non-commutative string theories, influenced by P and Q parameters.

Findings

Revealed a fractal phase structure with multiple phases

Identified a cascade driven by SL(2,Z) S-duality transformations

Discovered multiple Hagedorn-type transitions with temperature variation

Abstract

We investigate the complete phase diagram of the decoupled world-sheet theory of (P,Q) strings. These theories include 1+1 dimensional super Yang-Mills theory and non-commutative open string theory. We find that the system exhibits a rich fractal phase structure, including a cascade of alternating supergravity, gauge theory, and matrix string theory phases. The cascade proceeds via a series of SL(2,Z) S-duality transformations, and depends sensitively on P and Q. In particular, we find that the system may undergo multiple Hagedorn-type transitions as the temperature is varied.