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Higher Connection in Open String Field Theory

Yichul Choi

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.

Higher Connection in Open String Field Theory

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 -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 -field given by a cousin of this 2-form connection.
Paper Structure (8 sections, 47 equations, 2 figures)

This paper contains 8 sections, 47 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Open string field theory
  3. 2-form connection
  4. Definition and basic properties
  5. Marginal solutions
  6. Another version
  7. Sigma models on boundary conformal manifolds
  8. Discussion

Figures (2)

  • Figure 1: A typical element of $\mathcal{A}$ is prepared by a path integral on a unit half-disk with operator insertions. It is convenient to map to the sliver frame shown in right. In both cases, along the real line we impose the reference boundary condition $\mathcal{B}$. Along the dotted lines the boundary condition is unspecified.
  • Figure 2: In the sliver frame, the star product $\Psi_1 * \Psi_2$ is obtained by a path integral on a half-infinite strip which is obtained by gluing the two half-infinite strips for $\Psi_1$ and $\Psi_2$. More complicated operator insertions are also possible.