Topological gravity with exchange algebra

TL;DR

This paper constructs a topological gravity model derived from twisted (2,0) supergravity, revealing an infinite set of BRST invariant operators that form an exchange algebra related to quantum groups, differing from standard topological gravity.

Contribution

It introduces a novel topological gravity with an infinite tower of BRST invariant quantities satisfying a classical exchange algebra of OSp(2,2), which become quantum operators with braided correlations.

Findings

Infinite BRST invariant quantities form an OSp(2,2) multiplet.

These quantities satisfy a classical exchange algebra.

Quantum correlation functions exhibit braiding according to quantum OSp(2,2).

Abstract

A topological gravity is obtained by twisting the effective $(2,0)$ super\-gravity. We show that this topological gravity has an infinite number of BRST invariant quantities with conformal weight $0$. They are a tower of OSp$(2,2)$ multiplets and satisfy the classical exchange algebra of OSp$(2,2)$. We argue that these BRST invariant quantities become physical operators in the quantum theory and their correlation functions are braided according to the quantum OSp$(2,2)$ group. These properties of the topological effective gravity are not shared by the standard topological gravity.