A note on Faddeev--Popov action for doubled-yet-gauged particle and graded Poisson geometry

TL;DR

This paper explores the BRST formulation of a doubled, gauged particle action and connects it with graded Poisson geometry, revealing quantum corrections involving the dilaton that relate to Double Field Theory symmetries.

Contribution

It demonstrates the equivalence of the BRST formulation of a doubled, gauged particle with graded Poisson geometry and derives quantum corrections involving the dilaton.

Findings

BRST formulation matches graded Poisson geometry

Quantum corrections involve the dilaton

Connections to Double Field Theory symmetries

Abstract

The section condition of Double Field Theory has been argued to mean that doubled coordinates are gauged: a gauge orbit represents a single physical point. In this note, we consider a doubled and at the same time gauged particle action, and show that its BRST formulation including Faddeev--Popov ghosts matches with the graded Poisson geometry that has been recently used to describe the symmetries of Double Field Theory. Besides, by requiring target spacetime diffeomorphisms at the quantum level, we derive quantum corrections to the classical action involving dilaton, which might be comparable with the Fradkin--Tseytlin term on string worldsheet.