$U(1)$--Extended Gauge Algebras in $p$-Loop Space

Details $U(1)$--Extended Gauge Algebras in $p$-Loop Space $U(1)$--Extended Gauge Algebras in $p$-Loop Space

1992-12-05

arxiv.org/abs/hep-th/9212037v1

Nucl.Phys. B398 (1993) 343-358

Physics

High Energy Physics

High Energy Physics - Theory

13 pages, UG-5/92; CTP-TAMU-63/92; DAMTP/R-92/32; Imperial/TP/91-92/30; SISSA 157/92/EP

Scientific paper

10.1016/0550-3213(93)90113-4

We consider, for $p$ odd, a $p$--brane coupled to a $(p+1)$th rank background antisymmetric tensor field and to background Yang-Mills (YM) fields {\it via} a Wess-Zumino term. We obtain the generators of antisymmetric tensor and Yang-Mills gauge transformations acting on $p$--brane wavefunctionals (functions on `$p$-loop space'). The Yang-Mills generators do not form a closed algebra by themselves; instead, the algebra of Yang-Mills and antisymmetric tensor generators is a $U(1)$ extension of the usual algebra of Yang-Mills gauge transformations. We construct the $p$-brane's Hamiltonian and thereby find gauge-covariant functional derivatives acting on $p$--brane wavefunctionals that commute with the YM and $U(1)$ generators.

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