T-Duality Transformation and Universal Structure of Non-Critical String Field Theory

TL;DR

This paper explores T-duality in the c=1/2 matrix model, revealing symmetry in the sphere approximation and its violation at higher genus, along with universal properties and new amplitude results.

Contribution

It introduces a detailed analysis of T-duality in a nonperturbative string theory toy model, including symmetry properties and amplitude computations.

Findings

T-duality symmetry holds in the sphere approximation.

Higher-genus effects break the T-duality symmetry.

Universal properties of stochastic Hamiltonians are refined and new amplitude results are provided.

Abstract

We discuss a T-duality transformation for the c=1/2 matrix model for the purpose of studying duality transformations in a possible toy example of nonperturbative frameworks of string theory. Our approach is to first investigate the scaling limit of the Schwinger-Dyson equations and the stochastic Hamiltonian in terms of the dual variables and then compare the results with those using the original spin variables. It is shown that the c=1/2 model in the scaling limit is T-duality symmetric in the sphere approximation. The duality symmetry is however violated when the higher-genus effects are taken into account, owing to the existence of global Z_2 vector fields corresponding to nontrivial homology cycles. Some universal properties of the stochastic Hamiltonians which play an important role in discussing the scaling limit and have been discussed in a previous work by the last two authors are refined in both the original and dual formulations. We also report a number of new explicit results for various amplitudes containing macroscopic loop operators.