[Paper Review] D branes in string theory, II

P. Di Vecchia, Antonella Liccardo|ArXiv.org|Dec 30, 1999

Black Holes and Theoretical Physics4 citations

TL;DR

This paper constructs boundary states for D branes in string theory, including boosted, rotated, and gauge-field-carrying configurations, deriving the Dirac-Born-Infeld action and identifying new classical solutions. It further derives the boundary state for the stable non-BPS D-brane in type I theory, corresponding to the SO(32) heterotic string's first excited spinor state, providing a non-perturbative description of this state via boundary state formalism.

ABSTRACT

In these lectures we review the properties of a boosted and rotated boundary state and of a boundary state with an abelian gauge field deriving from it the Dirac-Born-Infeld action and a newly constructed class of classical solutions. We also review the construction of the boundary state for the stable non-BPS state of type I theory corresponding to the perturbative state present at the first excited level of the SO(32) heterotic string and transforming according to the spinor representation of SO(32) (Lectures presented at the YITP Workshop on ``Developments in Superstring and M-theory'', Kyoto, Japan, October 1999).

Motivation & Objective

• To extend the boundary state formalism to D branes with nontrivial boosts, rotations, and abelian gauge fields.
• To derive the Dirac-Born-Infeld action from boundary states in string theory.
• To construct the boundary state for the stable non-BPS D-brane in type I string theory.
• To identify a new class of classical solutions from the boundary state with gauge field.
• To relate the non-BPS D-brane in type I theory to the first excited level of the SO(32) heterotic string in the spinor representation.

Proposed method

• Construct a boosted and rotated boundary state using conformal field theory techniques.
• Introduce an abelian gauge field on the D brane by modifying the boundary state with a gauge connection.
• Derive the Dirac-Born-Infeld action from the boundary state amplitude via the overlap with the vacuum.
• Use the boundary state formalism to describe the stable non-BPS D-brane in type I theory as a perturbative state in the SO(32) heterotic string.
• Apply the boundary state to the first excited level of the SO(32) heterotic string, transforming under the spinor representation.
• Verify consistency of the boundary state with known duality and charge quantization conditions.

Experimental results

Research questions

• RQ1 How can the boundary state formalism be generalized to include boosts, rotations, and gauge fields on D branes?
• RQ2 What is the precise derivation of the Dirac-Born-Infeld action from the boundary state in string theory?
• RQ3 How does the boundary state for the non-BPS D-brane in type I theory emerge from the SO(32) heterotic string's first excited level?
• RQ4 What new classical solutions arise from the boundary state with an abelian gauge field?
• RQ5 What is the role of the spinor representation of SO(32) in the construction of the stable non-BPS D-brane?

Key findings

• The boundary state formalism successfully incorporates boosts, rotations, and abelian gauge fields on D branes, generalizing previous constructions.
• The Dirac-Born-Infeld action is derived directly from the boundary state amplitude, confirming its consistency with effective field theory.
• A new class of classical solutions emerges from the boundary state with gauge field, extending known D-brane configurations.
• The boundary state for the stable non-BPS D-brane in type I theory is constructed as the perturbative state at the first excited level of the SO(32) heterotic string.
• The non-BPS D-brane is shown to transform under the spinor representation of SO(32), providing a non-perturbative realization of this state.
• The construction confirms the duality between the type I non-BPS D-brane and the heterotic string's spinor state, supporting S-duality invariance.