Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2006-05-19
AnnalsPhys.322:236-285,2007
Physics
High Energy Physics
High Energy Physics - Theory
68 pp
Scientific paper
10.1016/j.aop.2006.07.014
We develop a group-theoretical approach to the formulation of generalized abelian gauge theories, such as those appearing in string theory and M-theory. We explore several applications of this approach. First, we show that there is an uncertainty relation which obstructs simultaneous measurement of electric and magnetic flux when torsion fluxes are included. Next we show how to define the Hilbert space of a self-dual field. The Hilbert space is Z2-graded and we show that, in general, self-dual theories (including the RR fields of string theory) have fermionic sectors. We indicate how rational conformal field theories associated to the two-dimensional Gaussian model generalize to (4k+2)-dimensional conformal field theories. When our ideas are applied to the RR fields of string theory we learn that it is impossible to measure the K-theory class of a RR field. Only the reduction modulo torsion can be measured.
Freed Daniel S.
Moore Gregory W.
Segal Graeme
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