Insertion of vertex operators using BV formalism

We develop a general framework for the insertion of vertex operator on the string worldsheet, in BV formalism. Such insertions correspond to deformations of the Master Action which breaks the gauge symmetry to a subgroup, and then restoring the full gauge symmetry by integrating over a cycle in the space of Lagrangian submanifolds. We provide the general construction, global on the moduli space, which was previously conjectured in a form local on the worldsheet. We explain how the enhancement of the gauge symmetry in equivariant BV formalism can be seen as an application of the general idea of BV effective action. We derive an integral formula for the deformation of the contraction operator due to the vertex insertion.