# A toolkit for twisted chiral superfields

## TL;DR

This paper develops a comprehensive toolkit for constructing Lagrangians of twisted chiral superfields in 2D supersymmetric theories, facilitating advanced studies in T-duality and Mirror Symmetry.

## Contribution

It introduces a set of twisted superspace coordinates and explicit formulas for generic Lagrangians involving twisted chiral superfields, including examples of Abelian and non-Abelian dual models.

## Key findings

- Derived the most general Lagrangian terms for twisted chiral superfields.
- Provided explicit kinetic and interaction terms for various models.
- Enabled systematic construction of dual models in supersymmetric theories.

## Abstract

We calculate the most general terms for arbitrary Lagrangians of twisted chiral superfields in 2D (2,2) supersymmetric theories [1]. The scalar and fermion kinetic terms and interactions are given explicitly. We define a set of twisted superspace coordinates, which allows to obtain Lagrangian terms for generic K\"ahler potential and generic twisted superpotential; this is done in analogy to the corresponding chiral superfields calculations [2]. As examples we obtain the Lagrangian of a single twisted superfield, i.e. the Abelian-dual of the gauged linear sigma model (GLSM) of a single chiral superfield, and the Lagrangian for the non-Abelian SU(2) dual of the $\mathbb{CP}^1$ GLSM model. Generic Lagrangians contain both twisted-chiral and chiral superfields, with distinct representations. We write down the kinetic terms for all bosons and fermions as well as their interactions for these generic cases. As twisted superfields play a central role for T-dualities and Mirror Symmetry in GLSMs, we expect the pedagogical exposition of this techniques to be useful in those studies.