Abstract
In this paper, we study a class of heterotic Landau-Ginzburg models. We show that the action can be written as a sum of BRST-exact and non-exact terms. The non-exact terms involve the pullback of the complexified Kähler form to the worldsheet and terms arising from the superpotential, which is a Grassmann-odd holomorphic function of the superfields. We then demonstrate that the action is invariant on-shell under supersymmetry transformations up to a total derivative. Finally, we extend the analysis to the case in which the superpotential is not holomorphic. In this case, we find that supersymmetry imposes a constraint which relates the nonholomorphic parameters of the superpotential to the Hermitian curvature. Various special cases of this constraint have previously been used to establish properties of Mathai-Quillen form analogues which arise in the corresponding heterotic Landau-Ginzburg models. There, it was claimed that supersymmetry imposes those constraints. Our goal in this paper is to support that claim. The analysis for the nonholomorphic case also reveals a constraint imposed by supersymmetry that we did not anticipate from studies of Mathai-Quillen form analogues.
Highlights
JHEP11(2020)019 case of a holomorphic superpotential, we will show that the action can be written as a sum of BRST-exact and non-exact terms
We demonstrate that the action is invariant on-shell under supersymmetry transformations up to a total derivative
We find that supersymmetry imposes a constraint which relates the nonholomorphic parameters of the superpotential to the Hermitian curvature
Summary
Let X be a Kähler manifold with metric g, antisymmetric tensor B, local real coordinates φμ, and local complex coordinates φi with complex conjugates φı. Let E be a vector bundle over X with Hermitian fiber metric h. Dz ψ+i = ∂z ψ+i + ∂z φj Γijkψ+k , DiFa = ∂iFa − AbiaFb , Abia = hbb hba,i , Γijk = giı gık,j , Dzλa− = ∂zλa− + ∂zφıAaıb λb− , DıF a = ∂ı F a − Abı a F b , Abı a = hbb hba,ı , Fiıaa = hab Abı a,i. There, we will find that supersymmetry imposes a constraint which relates the nonholomorphic parameters of the superpotential to the Hermitian curvature.
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