Light-cone supersymmetry and D-branes

TL;DR

The paper develops a light-cone formulation for D-brane boundary states in type II strings, preserving half the spacetime supersymmetry and rendering p-branes as (p+1)-instantons with boundary condensates that yield Born–Infeld–type worldvolume actions. It provides explicit SO(8) rotation constructions of boundary states, connects zero-mode couplings to NS–NS and RR massless fields with linearized D-brane sources, and matches these to black p-brane solutions in the appropriate limit. Inter-brane interactions are computed via cylinder diagrams, revealing SUSY-preserving cancellations for BPS configurations and detailing the preserved-supersymmetry fractions across parallel, intersecting, and orthogonal two- and multi-brane systems, including D-instanton, D-string, and D3/D5/D7 cases. The work also analyzes boundary condensates’ RR couplings through Chern–Simons terms and Born–Infeld actions, and derives Ward identities for spontaneously broken space-time SUSY, showing how nonlinear SUSY relations constrain amplitudes with soft fermions. Overall, the paper unifies boundary-state techniques, Born–Infeld dynamics, and SUSY breaking in a light-cone framework for D-branes, clarifying both linearized bulk couplings and nonlinear symmetry structures.

Abstract

$D$-brane boundary states for type II superstrings are constructed by enforcing the conditions that preserve half of the space-time supersymmetry. A light-cone coordinate frame is used where time is identified as one of the coordinates transverse to the brane's (euclidean) world-volume so that the $p$-brane is treated as a $(p+1)$-instanton. The boundary states have the superspace interpretation of top or bottom states in a light-cone string superfield. The presence of a non-trivial open-string boundary condensate give rise to the familiar $D$-brane source terms that determine the (linearized) Born--Infeld-like effective actions for $p$-branes and the (linearized) equations of motion for the massless fields implied by the usual $p$-brane ansatze. The `energy' due to closed string exchange between separate $D$-branes is calculated (to lowest order in the string coupling) in situations with pairs of parallel, intersecting as well as orthogonal branes -- in which case the unbroken supersymmetry may be reduced. Configurations of more than two branes are also considered in situations in which the supersymmetry is reduced to $1/8$ or $1/16$ of the full amount. The Ward identities resulting from the non-linearly realized broken space-time supersymmetry in the presence of a $D$-brane are also discussed.