String theory and noncommutative geometry

Seiberg, Nathan; Witten, Edward

doi:10.1088/1126-6708/1999/09/032

String theory and noncommutative geometry

Aug, 1999

99 pages

Published in:

JHEP 09 (1999) 032

e-Print:

hep-th/9908142 [hep-th]

DOI:

10.1088/1126-6708/1999/09/032

Report number:

IASSNS-HEP-99-74

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Abstract:

We extend earlier ideas about the appearance of noncommutative geometry in string theory with a nonzero B-field. We identify a limit in which the entire string dynamics is described by a minimally coupled (supersymmetric) gauge theory on a noncommutative space, and discuss the corrections away from this limit. Our analysis leads us to an equivalence between ordinary gauge fields and noncommutative gauge fields, which is realized by a change of variables that can be described explicitly. This change of variables is checked by comparing the ordinary Dirac-Born-Infeld theory with its noncommutative counterpart. We obtain a new perspective on noncommutative gauge theory on a torus, its T-duality, and Morita equivalence. We also discuss the D0/D4 system, the relation to M-theory in DLCQ, and a possible noncommutative version of the six-dimensional (2,0) theory.

Note:

100 pages, sorry. Clarifications added, trivial misprints fixed and references added Report-no: IASSNS-HEP-99/74 Journal-ref: JHEP 9909 (1999) 032

string model
supersymmetry
differential geometry: noncommutative
gauge field theory: Yang-Mills
Born-Infeld model
soliton: BPS
duality
membrane model
bibliography

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