# Families of gauge conditions in BV formalism

Journal of High Energy Physics, Jul 2017

In BV formalism we can consider a Lagrangian submanifold as a gauge condition. Starting with the BV action functional we construct a closed form on the space of Lagrangian submanifolds. If the action functional is invariant with respect to some group H and Λ is an H-invariant family of Lagrangian submanifold then under certain conditions we construct a form on Λ that descends to a closed form on Λ/H. Integrating the latter form over a cycle in Λ/H we obtain numbers that can have interesting physical meaning. We show that one can get string amplitudes this way. Applying this construction to topological quantum field theories one obtains topological invariants.

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Andrei Mikhailov, Albert Schwarz. Families of gauge conditions in BV formalism, Journal of High Energy Physics, 2017, 63, DOI: 10.1007/JHEP07(2017)063