TY - JOUR

T1 - Unified geometry of antisymmetric tensor gauge fields and gravity

AU - Freund, Peter G.C.

AU - Nepomechie, Rafael I.

N1 - Funding Information:
In sect. 3 we find the geometric origin of the lagrangians of antisymmetric tensor fields in interaction with gravity and a scalar field, as encountered in supergravity. Thus the U(1) bundle over loop space f~lM is endowed with a Kaluza-Jordan-type metric [5], and a suitably regularized scalar curvature of the bundle is used as a lagrangian. This, when integrated over the portion of the bundle that lies over the point-like loops in f~lM (its base space), reproduces the Bose part of the N--1 supergravity action in ten dimensions. Since the same action can also be obtained in * Work supported in part by the NSF: Grant no. PHY-78-23669. i National Science Foundation Predoctoral Fellow.
Copyright:
Copyright 2014 Elsevier B.V., All rights reserved.

PY - 1982/6/7

Y1 - 1982/6/7

N2 - Vector gauge fields are known to be related to connections on principal fibre bundles P(M,G) over space-time M. Here we relate abelian antisymmetric tensor gauge fields of rank r to constrained connections on P(Ωr-1M,U(1)), the U(1) bundles over the space of all (r-1)-dimensional closed submanifolds of M. In particular, the Kalb-Ramond field (r=2) is seen as such a connection on the bundle over the space of all loops in space-time. Moreover, a Kaluza-Jordan construction on P(Ω1M,U(1)) leads to the bosonic sector of the N = 1 supergravity action in ten dimensions. This result is highly reminiscent of the α′→ 0 limit of the closed string dual model.

AB - Vector gauge fields are known to be related to connections on principal fibre bundles P(M,G) over space-time M. Here we relate abelian antisymmetric tensor gauge fields of rank r to constrained connections on P(Ωr-1M,U(1)), the U(1) bundles over the space of all (r-1)-dimensional closed submanifolds of M. In particular, the Kalb-Ramond field (r=2) is seen as such a connection on the bundle over the space of all loops in space-time. Moreover, a Kaluza-Jordan construction on P(Ω1M,U(1)) leads to the bosonic sector of the N = 1 supergravity action in ten dimensions. This result is highly reminiscent of the α′→ 0 limit of the closed string dual model.

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U2 - 10.1016/0550-3213(82)90356-X

DO - 10.1016/0550-3213(82)90356-X

M3 - Article

AN - SCOPUS:0000346238

VL - 199

SP - 482

EP - 494

JO - Nuclear Physics B

JF - Nuclear Physics B

SN - 0550-3213

IS - 3

ER -