Exotic gravity theory in loop space

TL;DR

This paper explores an exotic superconformal gravity theory in six dimensions within loop space, reinterpreting gravitational potentials and curvature as ultra-local geometric objects on loop space, extending previous formulations.

Contribution

It introduces a novel reinterpretation of an exotic gravity theory in loop space, focusing on its bosonic sector and connecting it to ultra-local geometric structures.

Findings

Reinterpreted exotic gravitational potential as an ultra-local metric

Expressed curvature in loop space as an ultra-local curvature

Extended the analogy between two-form fields and gravitational structures

Abstract

An exotic linearised theory of superconformal gravity in D = 6, (4,0) superspace, proposed by C. Hull, is discussed in loop space with focus on its bosonic sector. Pursuing an analogy to the loop space version of the system of a two form B and its field strength H, we show that the exotic linearised gravitational potential C and curvature G can be reinterpreted as an ultra-local (linearised) metric and curvature on loop space.