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Anomaly-free twistorial higher-spin theories

Tung Tran

TL;DR

The work constructs BV-formulated holomorphic twistorial higher-spin theories on twistor space with zero cosmological constant and analyzes their quantum consistency. A higher-spin index theorem generalizes Hirzebruch-Riemann-Roch to determine anomaly-free spectra, while detailed one-loop wheel computations identify which descendant theories are gauge-anomaly-free. When anomalies appear, the authors develop cancellation mechanisms akin to Green-Schwarz ideas, including axion couplings and extra fields, to restore quantum consistency. The results illuminate how twistor-space formulations encode integrable sectors and hint at string-like underpinnings for higher-spin gravities. Overall, the paper maps out a landscape of anomaly-free holomorphic higher-spin twistors and the corresponding spacetime theories they may holographically relate to.

Abstract

We present twistor BV actions that encompasses many classically consistent bosonic holomorphic twistorial higher-spin theories with vanishing cosmological constant. Upon quantization, these actions are shown to be quantum consistent, i.e. no gauge anomaly, for some subclasses of twistorial higher-spin theories. Anomaly-free twistorial theories can be identified through an index theorem, which is a higher-spin extension of the Hirzebruch-Riemann-Roch index theorem. We also discuss the anomaly cancellation mechanisms on twistor space to render anomalous theories quantum consistent at one loop.

Anomaly-free twistorial higher-spin theories

TL;DR

The work constructs BV-formulated holomorphic twistorial higher-spin theories on twistor space with zero cosmological constant and analyzes their quantum consistency. A higher-spin index theorem generalizes Hirzebruch-Riemann-Roch to determine anomaly-free spectra, while detailed one-loop wheel computations identify which descendant theories are gauge-anomaly-free. When anomalies appear, the authors develop cancellation mechanisms akin to Green-Schwarz ideas, including axion couplings and extra fields, to restore quantum consistency. The results illuminate how twistor-space formulations encode integrable sectors and hint at string-like underpinnings for higher-spin gravities. Overall, the paper maps out a landscape of anomaly-free holomorphic higher-spin twistors and the corresponding spacetime theories they may holographically relate to.

Abstract

We present twistor BV actions that encompasses many classically consistent bosonic holomorphic twistorial higher-spin theories with vanishing cosmological constant. Upon quantization, these actions are shown to be quantum consistent, i.e. no gauge anomaly, for some subclasses of twistorial higher-spin theories. Anomaly-free twistorial theories can be identified through an index theorem, which is a higher-spin extension of the Hirzebruch-Riemann-Roch index theorem. We also discuss the anomaly cancellation mechanisms on twistor space to render anomalous theories quantum consistent at one loop.

Paper Structure

This paper contains 37 sections, 1 theorem, 157 equations, 1 figure, 6 tables.

Table of Contents

  1. Introduction
  2. Note added.
  3. Review
  4. Twistor geometry
  5. Higher-spin symmetry
  6. Holomorphic $\star$-product.
  7. Parent twistor BV actions
  8. Actions for chiral/self-dual higher-spin theories
  9. Parent twistor actions for chiral theories
  10. Twistor actions on the base.
  11. Summary.
  12. Parent twistor actions for self-dual theories
  13. Twistor actions on the base.
  14. Summary.
  15. BV-BRST formalism for holomorphic twistorial higher-spin theories
  16. ...and 22 more sections

Key Result

Theorem 4.1

All higher-spin theories that arise from the action eq:BV-action on twistor space with trivial index $\mathrm{Ind}(\bar{\mathcal{D}}_{\mathbb{V}})$ are anomaly-free at one loop.

Figures (1)

  • Figure 1: The Feynman wheel diagram associated with the gauge anomaly in $6d$.

Theorems & Definitions (1)

  • Theorem 4.1