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Gauge invariant and gauge fixed D-brane actions

Dec, 1996

34 pages

Published in:

Nucl.Phys.B 495 (1997) 99-126

e-Print:

hep-th/9612080 [hep-th]

DOI:

10.1016/S0550-3213(97)00180-6

Report number:

CALT-68-2088

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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

\theta_1

and

\theta_2

, and a U(1) gauge field

A_{\mu}

. 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

\lambda

and the U(1) gauge field

A_{\mu}

. 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

\lambda

is the Goldstone fermion. The gauge-fixed supersymmetric D-brane theories with

p<9

can be obtained from the 10d one by dimensional reduction.

Note:

33 pages, latex, no figures; revised as requested by referee

11.10.Kk
11.25.Pm
I 1.27.+d
Born-Infeld theory
D-branes
Superstring theory
membrane model: p-brane
supersymmetry: superfield
space-time
dimension: 10

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