Conformal Defects from String Field Theory

TL;DR

This paper uses open string field theory techniques to explore and classify conformal defects in Virasoro minimal models, providing numerical estimates and identifying families of solutions related to infrared fixed points.

Contribution

It introduces a novel approach employing OSFT to analyze conformal defects, offering new insights and classifications beyond traditional methods.

Findings

Identified a continuum of solutions in the Ising model.

Found six solutions for other minimal models.

Provided numerical estimates of g-function and boundary state coefficients.

Abstract

Unlike conformal boundary conditions, conformal defects of Virasoro minimal models lack classification. Alternatively to the defect perturbation theory and the truncated conformal space approach, we employ open string field theory (OSFT) techniques to explore the space of conformal defects. We illustrate the method by an analysis of OSFT around the background associated to the $(1,2)$ topological defect in diagonal unitary minimal models. Numerical analysis of OSFT equations of motion leads to an identification of a nice family of solutions, recovering the picture of infrared fixed points due to Kormos, Runkel and Watts. In particular, we find a continuum of solutions in the Ising model case and 6 solutions for other minimal models. OSFT provides us with numerical estimates of the g-function and other coefficients of the boundary state.