Geometry of gauged LG-model with compatible boundary conditions
Abstract
This paper introduces the geometry of the open string Floer theory of gauged Landau-Ginzburg model via gauged Witten equations. Given a G-invariant Morse-Bott holomorphic function W on a Hamiltonian space (M,ω,G), Lefschetz thimbles are constructed from proper Lagrangian submanifolds of critical set of W. We study an energy functional on path space whose gradient flow equation corresponds to the gauged Witten equations with temporal gauge on a strip end, and whose critical points are Lagrangian intersections in the reduced critical space of W.
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