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A minimal BV action for Vasiliev's four-dimensional higher spin gravity

Nicolas Boulanger, Nicolo Colombo, Per Sundell

TL;DR

The paper develops a minimal BV master action for four-dimensional higher-spin gravity built from Vasiliev's equations by applying the AKSZ construction to unfolded systems. It promotes classical fields to vectorial superfields, enforces BRST nilpotency through carefully chosen boundary conditions and chart-transitions, and demonstrates a globally-defined fiber-bundle formulation. It then extends the AKSZ framework to graded- associative non-commutative base manifolds, articulating both odd and even bulk actions and their boundary deformations, and showing that the master equations hold within this generalized setting. The results provide a bridge between unfolded dynamics, deformation quantization, and holographic perspectives, and outline clear paths for future work on quantum BV structure, holographic correlators, and non-perturbative completions.

Abstract

The action principle for Vasiliev's four-dimensional higher-spin gravity proposed recently by two of the authors, is converted into a minimal BV master action using the AKSZ procedure, which amounts to replacing the classical differential forms by vectorial superfields of fixed total degree given by the sum of form degree and ghost number. The nilpotency of the BRST operator is achieved by imposing boundary conditions and choosing appropriate gauge transitions between charts leading to a globally-defined formulation based on a principal bundle.

A minimal BV action for Vasiliev's four-dimensional higher spin gravity

TL;DR

The paper develops a minimal BV master action for four-dimensional higher-spin gravity built from Vasiliev's equations by applying the AKSZ construction to unfolded systems. It promotes classical fields to vectorial superfields, enforces BRST nilpotency through carefully chosen boundary conditions and chart-transitions, and demonstrates a globally-defined fiber-bundle formulation. It then extends the AKSZ framework to graded- associative non-commutative base manifolds, articulating both odd and even bulk actions and their boundary deformations, and showing that the master equations hold within this generalized setting. The results provide a bridge between unfolded dynamics, deformation quantization, and holographic perspectives, and outline clear paths for future work on quantum BV structure, holographic correlators, and non-perturbative completions.

Abstract

The action principle for Vasiliev's four-dimensional higher-spin gravity proposed recently by two of the authors, is converted into a minimal BV master action using the AKSZ procedure, which amounts to replacing the classical differential forms by vectorial superfields of fixed total degree given by the sum of form degree and ghost number. The nilpotency of the BRST operator is achieved by imposing boundary conditions and choosing appropriate gauge transitions between charts leading to a globally-defined formulation based on a principal bundle.

Paper Structure

This paper contains 37 sections, 192 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Plan of paper
  3. Action principles for unfolded systems on commutative manifolds
  4. General ideas
  5. Unfolded dynamics.
  6. BV-AKSZ implementation.
  7. Classical sigma model
  8. Classical unfolded dynamics on commutative manifolds.
  9. Classical generalized Hamiltonian action.
  10. Total variation and gauge variation.
  11. Global base-manifold formulation of fiber-bundle type.
  12. Equations of motion
  13. Canonical coordinates.
  14. Transition amplitudes.
  15. Generalized action-angles.
  16. ...and 22 more sections

Figures (1)

  • Figure 1: Compatibility condition for the fiber bundle