Notes on BV formalism

introduction  notations  BV-formalism  BRST-formalism  equivariant-cohomology  worldsheet-complex-structure  bosonic-string  omega  omega-BRST  contact-structure  transfer  tangent-space-of-double-coset  integrated-vertex  unintegrated-vertex  boundary  picture-changing  Heterotic-RNS  Type-II-RNS  N2Superconformal  twisting  pure-spinor  left-sector  open-problems 

Andrei Mikhailov

I recently wrote a paper with Albert Schwarz about the BV formalism. Many things were completely new to me. I am writing these personal notes just to keep my head from exploding 😃.

    1 Brief reviews

    2 Integration over the moduli space of Lagrangian submanifolds

    3 Applications to string theory

    4 Open problems

Introduction

Notations

1 Brief reviews

BV formalism

BRST formalism

Equivariant cohomology

Worldsheet complex structure

N=2 superconformal symmetry

2 Integration over the moduli space of Lagrangian submanifolds

Form in BV formalism

Form in BRST formalism

Quantomorphisms

Homotopy transfer

3 Applications to string theory

Bosonic string

Integrated vertex

Unintegrated vertex

Worldsheet with boundary

Picture changing

Heterotic string in RNS formalism

Type II string in RNS formalism  (unfinished)

Topological string

Pure spinor formalism

4 Open problems

Open problems

Literature

introduction  notations  BV-formalism  BRST-formalism  equivariant-cohomology  worldsheet-complex-structure  bosonic-string  omega  omega-BRST  contact-structure  transfer  tangent-space-of-double-coset  integrated-vertex  unintegrated-vertex  boundary  picture-changing  Heterotic-RNS  Type-II-RNS  N2Superconformal  twisting  pure-spinor  left-sector  open-problems 

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