Marginal deformations of SU(2)$_k$ WZW model boundary states in open string field theory

TL;DR

This paper constructs marginally deformed boundary states in the SU(2)$_k$ WZW model using open string field theory, revealing a partial moduli space coverage and a potential universal relation between parameters.

Contribution

It introduces a novel method combining marginal and relevant deformations in open string field theory to analyze boundary states in the SU(2)$_k$ WZW model.

Findings

Solutions exhibit a lower g-function than the background.

Solutions are parameterized by the marginal field coefficient and correspond to boundary states with varying angles.

The marginal parameter and angle relation may be universal across solution classes.

Abstract

We attempt to describe the moduli space of boundary states in the SU(2)$_k$ WZW model by constructing marginally deformed solutions in open string field theory in the level truncation approximation. In contrast with other approaches to marginal deformations, our solutions exhibit a $g$-function different from that of the background (typically lower). Thus, our method effectively combines features of both marginal and relevant deformations. After partially fixing an SU(2) symmetry of the equations of motion, we find families of solutions parameterized by the coefficient of the marginal field associated with the $J^3$ current, and we identify them as Cardy boundary states with varying angle $\theta$. However, it turns out that these solutions become inconsistent once the marginal parameter exceeds a certain value, implying that they cover only a part of the moduli space. Finally, we also compare the relation between the marginal parameter and the angle $\theta$ for different solutions and we find evidence suggesting that this relation is universal for certain classes of solutions.