Higher Connection in Open String Field Theory

TL;DR

This paper introduces a new 2-form connection in open string field theory, leading to novel gauge-invariant observables analogous to Berry phases, and explores its relation to the Kalb-Ramond B-field.

Contribution

It defines a higher connection and holonomy in string field theory, connecting it to the B-field and higher Berry phases, which is a novel conceptual development.

Findings

Defined a 2-form connection using star product and integration.

Introduced higher holonomies and 3-form curvature as new observables.

Proposed a link between the 2-form connection and the Kalb-Ramond B-field.

Abstract

We define a 2-form connection in the space of classical solutions of the bosonic open string field theory, using the open string star product and integration. The corresponding higher holonomies and the 3-form curvature are new observables invariant under the infinite-dimensional gauge algebra of open string field theory. The definition is analogous to that of Berry phase in quantum mechanics and is motivated by recent studies on higher Berry phase in condensed matter physics and quantum field theory. We suggest identifying this 2-form connection with the Kalb-Ramond $B$-field of the closed string background at least in favorable situations. Also discussed are sigma models whose target space is the moduli space of conformal boundary conditions of a two-dimensional CFT with the $B$-field given by a cousin of this 2-form connection.