Anomaly-free twistorial higher-spin theories

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.

💡 Research Summary

The paper investigates the quantum consistency of a broad class of bosonic holomorphic higher‑spin theories formulated on twistor space, using the Batalin‑Vilkovisky (BV) formalism. After a concise introduction to twistor geometry, the authors describe the complex projective three‑space ( \mathbb{CP}^3 ) and its open subset ( PT ) (the projective twistor space). Homogeneous coordinates ( Z^A=(\lambda_\alpha,\mu^{\dot\alpha}) ) are split into left‑ and right‑handed spinors, and the incidence relation ( \mu^{\dot\alpha}=x^{\alpha\dot\alpha}\lambda_\alpha ) identifies a four‑dimensional complexified spacetime as a moduli space of twistor lines.

A central ingredient is the holomorphic star‑product defined by an infinity twistor ( I_{AB} ). For vanishing cosmological constant (( \Lambda=0 )) the star‑product reduces to a simple Poisson bracket, and the associated higher‑spin algebra ( \mathfrak{hs}_\Lambda ) becomes the tensor product of two Weyl algebras, one for ( \lambda ) and one for ( \mu ).

The authors then construct “parent twistor” BV actions that generate a variety of chiral and self‑dual higher‑spin models after reduction to spacetime. The fundamental field is a (0,1)‑form connection \