A universal nonlinear relation among boundary states in closed string field theory

TL;DR

This paper reveals a universal nonlinear relation among boundary states in closed string field theory, applicable to various D-branes, and provides a background-independent formulation that clarifies the geometric nature of this relation.

Contribution

It introduces a background-independent, conformal field theory-based formulation of the boundary state relation, generalizes previous work, and analytically determines the universal coefficient.

Findings

Boundary states satisfy a universal nonlinear idempotency relation.

The relation holds for various D-branes, including infinitesimally deformed ones.

The coefficient of the relation is analytically determined and shown to be universal.

Abstract

We show that the boundary states satisfy a nonlinear relation (the idempotency equation) with respect to the star product of closed string field theory. This relation is universal in the sense that various D-branes, including the infinitesimally deformed ones, satisfy the same equation, including the coefficient. This paper generalizes our analysis (hep-th/0306189) in the following senses. (1) We present a background-independent formulation based on conformal field theory. It illuminates the geometric nature of the relation and allows us to more systematically analyze the variations around the D-brane background. (2) We show that the Witten-type star product satisfies a similar relation but with a more divergent coefficient. (3) We determine the coefficient of the relation analytically. The result shows that the alpha parameter can be formally factored out, and the relation becomes universal. We present a conjecture on vacuum theory based on this computation.