Gauge-Invariant and Gauge-Fixed D-Brane Actions

TL;DR

This work constructs gauge-invariant Dirichlet p-brane actions in flat 10D with κ-symmetry and U(1) gauge invariance, then presents gauge-fixed, maximally supersymmetric Born–Infeld-like actions in 10D, where a single Majorana–Weyl spinor $\lambda$ and the gauge field $A_μ$ encode the dynamics for the p=9 brane. The authors derive explicit κ-transformations, Wess–Zumino structures, and master formulas linking the gauge-invariant and gauge-fixed theories, including a detailed static-gauge reduction and the dimensional reduction to all $p<9$. The resulting framework provides a transparent, supersymmetric extension of Born–Infeld theory and a versatile master action for D-branes, with potential applications to brane dualities, solitons, and M-theory branes. The paper also clarifies the SUSY algebra in the gauge-fixed regime and demonstrates how lower-dimensional D-brane actions emerge consistently from the 10D parent theory.

Abstract

The first part of this paper presents actions for Dirichlet p-branes embedded in a flat 10-dimensional space-time. The fields of the (p+1)-dimensional world-volume theories are the 10d space-time coordinates $ X^m$, a pair of Majorana-Weyl spinors $θ_1$ and $θ_2$, and a U(1) gauge field $A_μ$. The N = 2A or 2B super-Poincare group in ten dimensions is realized as a global symmetry. In addition, the theories have local symmetries consisting of general coordinate invariance of the world volume, a local fermionic symmetry (called ``kappa''), and U(1) gauge invariance. A detailed proof of the kappa symmetry is given that applies to all cases (p = 0,1, . . ., 9). The second part of the paper presents gauge-fixed versions of these theories. The fields of the 10d (p = 9) gauge-fixed theory are a single Majorana-Weyl spinor $λ$ and the U(1) gauge field $A_μ$. This theory, whose action turns out to be surprisingly simple, is a supersymmetric extension of 10d Born-Infeld theory. It has two global supersymmetries: one represents an unbroken symmetry, and the second corresponds to a broken symmetry for which $λ$ is the Goldstone fermion. The gauge-fixed supersymmetric D-brane theories with $p<9$ can be obtained from the 10d one by dimensional reduction.