Gauge-fixing Condition on Prepotential of Chiral Multiplet for Nongeometric Backgrounds

TL;DR

This paper explores gauge-fixing conditions on the prepotential of a chiral superfield in 2D supersymmetric theories to better understand nongeometric backgrounds like exotic five-branes.

Contribution

It introduces a relaxed gauge-fixing condition for the prepotential, enabling configurations suitable for nongeometric backgrounds in GLSMs.

Findings

The gauge-fixed prepotential differs from semichiral superfields.

The relaxed gauge-fixing condition facilitates the construction of nongeometric backgrounds.

The approach clarifies the superfield structure in exotic five-brane models.

Abstract

We study a supergauge transformation of a complex superfield which generates a chiral superfield in two-dimensional ${\cal N}=(2,2)$ theory. This complex superfield is referred to as the prepotential of the chiral superfield. Since there exist redundant component fields in the prepotential, we remove some of them by a gauge-fixing condition. This situation is parallel to that of a vector superfield. In order to obtain a suitable configuration of the GLSM for the exotic five-brane which gives rise to a nongeometric background, we impose a relatively relaxed gauge-fixing condition. It turns out that the gauge-fixed prepotential is different from a semichiral superfield whose scalar field represents a coordinate of generalized K\"{a}hler geometry.