Cardy states, factorization and idempotency in closed string field theory

TL;DR

This paper demonstrates that boundary states in closed string field theory satisfy a universal nonlinear equation derived from boundary conformal field theory principles, linking open and closed string sectors and exploring properties of the star product.

Contribution

It generalizes previous flat background results to generic backgrounds, establishing a universal nonlinear equation for boundary states and analyzing the star product with B-field effects.

Findings

Boundary states satisfy a universal nonlinear equation in closed string field theory.

The equation encodes open string information via a regularization linked to the Cardy condition.

A non-associative, commutative product (Strachan product) emerges in the Seiberg-Witten limit.

Abstract

We show that boundary states in the generic on-shell background satisfy a universal nonlinear equation of closed string field theory. It generalizes our previous claim for the flat background. The origin of the equation is factorization relation of boundary conformal field theory which is always true as an axiom. The equation necessarily incorporates the information of open string sector through a regularization, which implies the equivalence with Cardy condition. We also give a more direct proof by oscillator representations for some nontrivial backgrounds (torus and orbifolds). Finally we discuss some properties of the closed string star product for non-vanishing $B$ field and find that a commutative and non-associative product (Strachan product) appears naturally in Seiberg-Witten limit.