Non-Linear Field Equation from Boundary State Formalism

Abstract

Boundary interactions of closed-string with open-strings are examined intended to provide a constructive formulation of boundary string field theory. As an illustration, we consider the BPS $D$-brane of the type II superstring in a constant NS-NS two-form background, and study the boundary interaction with arbitrary configurations of gauge field on the brane. The boundary interaction is presented, within the world-sheet cut-off theories, as an off-shell boundary state in the closed-string Hilbert space. It is regarded as a closed-string theoretical counterpart of the Wilson loop in the world-volume gauge theory. We show that the action of the closed-string BRST operator on the boundary state is translated into the non-linear BRST transformation of the open-string fields on the world-volume. In particular, the BRST invariance condition at the ${\alpha }^{\prime }$-order becomes the non-linear equation of motion for the non-commutative gauge theory. The action of the closed-string BRST operator on the boundary state is also shown to be identified with the beta functions of the world-sheet renormalization group flow.

51 pages, 3 figures, minor changes, references added

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• On Background Independent Open-String Field Theory
• Some Computations in Background Independent Open-String Field Theory
• Wilson Loops in Noncommutative Yang Mills
• On the Problems with Background Independence in String Theory
• Role of Short Distance Behavior in Off-Shell Open-String Field Theory
• Classical Open-String Field Theory ; $A_{\infty }$-Algebra, Renormalization Group and Boundary States
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Cited by in corpus (4)

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• Nonabelian 2-forms and loop space connections from SCFT deformations
• Super-Pohlmeyer invariants and boundary states for non-abelian gauge fields
• Boundary state of multiple D0-branes and closed string coupling