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Register a new userIntegration over families of Lagrangian submanifolds in BV formalism
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Authors
Andrei Mikhailov
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Gauge fixing is interpreted in BV formalism as a choice of Lagrangian submanifold in an odd symplectic manifold. A natural construction defines an integration procedure on families of Lagrangian submanifolds. In string perturbation theory, the moduli space integrals of higher genus amplitudes can be interpreted in this way. We discuss the role of gauge symmetries in this construction. We derive the conditions which should be imposed on gauge symmetries for the consistency of our integration procedure. We explain how these conditions behave under the deformations of the worldsheet theory. In particular, we show that integrated vertex operator is actually an inhomogeneous differential form on the space of Lagrangian submanifolds.
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In present paper a quantization scheme proposed recently by Morris (arXiv:1806.02206[hep-th]) is analyzed. This method is based on idea to combine the renormalization group with the BV-formalism in an unique quantization procedure. It is shown that the BV-formalism and the new method should be considered as independent approaches to quantization of gauge systems both provided by global supersymmetry.
Differrential Graded Lie Algebra Dg was previously introduced in the context of current algebras. We show that under some conditions, the problem of constructing equivariantly closed form from closed invariant form is reduces to construction of a representation of Dg. This includes equivariant BV formalism. In particular, an analogue of intertwiner between Weil and Cartan models allows to clarify the general relation between integrated and unintegrated vertex operators in string worldsheet theory.
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