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Topological Structures in String Theory

Graeme Segal
Philosophical Transactions: Mathematical, Physical and Engineering Sciences
Vol. 359, No. 1784, Topological Methods in the Physical Sciences (Jul. 15, 2001), pp. 1389-1398
Published by: Royal Society
Stable URL: http://www.jstor.org/stable/3066340
Page Count: 10
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Topological Structures in String Theory
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Abstract

In string theory space-time comes equipped with an additional geometric structure called a B-field or 'gerbe'. I describe this structure, mention its relationship with non-commutative geometry, and explain how to use the B-field to define a twisted version of the K-theory of space-time. String-theoretical space-time can contain topologically non-trivial dynamical structures called D-branes. These are simply accounted for in the framework of conformal field theory. In a highly simplified limiting case-topological field theory with a finite gauge group-the D-branes naturally represent elements of the twisted K-theory of space-time: the K-theory class is the 'charge' of the D-brane.

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