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 Kähler 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.
Highlights
Geometry, developed by Wess and Bagger [2], we perform computations for the Lagrangian of twistedchiral representations
We define a set of twisted superspace coordinates, which allows to obtain Lagrangian terms for generic Kahler potential and generic twisted superpotential; this is done in analogy to the corresponding chiral superfields calculations [2]
As twisted superfields play a central role for T-dualities and Mirror Symmetry in gauged linear sigma model (GLSM), we expect the pedagogical exposition of this technique to be useful in those studies
Summary
We search for space-time coordinates redefinitions, involving superspace coordinates, which satisfy the constraints on twisted (anti-)chiral superfields. This will allow to write expansions satisfying (2.1) and (2.2). Let us rewrite the Grassman superspace coordinates as: θα = θ+ θ− = θ+ θ− ̇ , θ ̃α = (θα)† = They fulfill the set of relations θ2 = θαθα = −2θ+θ− = −2θ+θ− ̇ , θ ̃2 = θ ̃αθ ̄ ̃α = 2θ ̃+ ̇ θ ̃− ̇ = 2θ+ ̇ θ−, dθ2 = dθαdθα = −2dθ+dθ− = −2dθ+dθ− ̇ , dθ ̃2 = dθ ̃αdθ ̃α = 2dθ ̃1 ̇ dθ ̃2 ̇ = 2dθ+ ̇ dθ−. We leave this for section, where the more general Kahler potential and twisted superpotential are studied
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