A toolkit for twisted chiral superfields
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Springer
Received: October 2, 2019 Accepted: December 13, 2019 Published: January 7, 2020
A toolkit for twisted chiral superfields
Departamento de F´ısica, Divisi´ on de Ciencias e Ingenier´ıas, Universidad de Guanajuato, Loma del Bosque 103, C.P. 37150, Le´ on, Guanajuato, M´exico Departamento Ciencias Naturales y Exactas, CUValles, Universidad de Guadalajara, Carretera Guadalajara-Ameca Km. 45.5, C.P. 46600, Ameca, Jalisco M´exico
E-mail: [email protected], [email protected] 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 CP1 GLSM model, for these examples of dual models we discuss the U(1)A and U(1)V R-symmetries. 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 technique to be useful in those studies. Keywords: Duality in Gauge Field Theories, Sigma Models, Superspaces, Supersymmetry and Duality ArXiv ePrint: 1908.05816
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP01(2020)019
JHEP01(2020)019
Nana Cabo Bizet and Roberto Santos-Silva
Contents 1 Introduction
1
2 A new set of coordinates and twisted chiral expansions
2
3 K¨ ahler geometry
5 8 9 11
5 Actions for chiral and twisted chiral
14
6 Final remarks
19
A Notation and conventions
20
B Fermionic contribution chiral and twisted chiral action
22
1
Introduction
Twisted chiral representations of 2D Supersymmetry were discovered in the foundational work of Gates, Hull and Rocek [1]. They constitute representations which only appear in two dimensions, because in this case the supersymmetric covariant derivatives D+ and ¯ − anticommute. In particular twisted chiral superfields describe field strengths of vector D superfields [3] and are obtained as T-duals to chiral superfields [4]. In theories where chiral and twisted-chiral representations are present, they are distinguished, otherwise they can be mapped to each other. The infrared limit of a 2D supersymmetric GLSM describe string theory compactified on target spaces, given by the supersymmetric vacua of the GLSM [5]. Moreover Mirror Symmetry can be obtained as T-duality [6]. For complete intersection Calabi-Yaus described
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