Conformal symmetry and supersymmetry in Rindler space

TL;DR

This paper investigates how conformal symmetry and supersymmetry behave in two-dimensional Rindler space, revealing their transformations and anomaly cancellations, which are crucial for understanding the equivalence of inertial and accelerated frames in quantum field theory.

Contribution

It constructs explicit transformations of fields and analyzes anomaly cancellations for conformal and supersymmetric theories in Rindler space, extending understanding of symmetries in accelerated frames.

Findings

Transformations of massless scalars and spinors in Rindler space are explicitly derived.

Anomaly cancellation requires theories with string-theoretic particle spectra.

Results support the equivalence of Minkowski and Rindler frame theories under certain conditions.

Abstract

This paper addresses the fate of extended space-time symmetries, in particular conformal symmetry and supersymmetry, in two-dimensional Rindler space-time appropriate to a uniformly accelerated non-inertial frame in flat 1+1-dimensional space-time. Generically, in addition to a conformal co-ordinate transformation, the transformation of fields from Minkowski to Rindler space is accompanied by local conformal and Lorentz transformations of the components, which also affect the Bogoliubov transformations between the associated Fock spaces. I construct these transformations for massless scalars and spinors, as well as for the ghost and super-ghost fields necessary in theories with local conformal and supersymmetries, as arising from coupling to 2-D gravity or supergravity. Cancellation of the anomalies in Minkowski and in Rindler space requires theories with the well-known critical spectrum of particles arising in string theory in the limit of infinite strings, and is relevant for the equivalence of Minkowski and Rindler frame theories.