Fusion, Crossing and Monodromy in Conformal Field Theory Based on $SL(2)$ Current Algebra with Fractional Level

Details Fusion, Crossing and Monodromy in Conformal Field Theory Based on $SL(2)$ Current Algebra with Fractional Level Fusion, Crossing and Monodromy in Conformal Field Theory Based on $SL(2)$ Current Algebra with Fractional Level

1996-07-16

arxiv.org/abs/hep-th/9607129v1

Nucl.Phys. B481 (1996) 577-624

Physics

High Energy Physics

High Energy Physics - Theory

42 Pages, LaTeX, uses pictex.sty, alternatively prepictex.tex, pictex.tex, postpictex.tex

Scientific paper

10.1016/S0550-3213(96)00506-8

Based on our earlier work on free field realizations of conformal blocks for conformal field theories with $SL(2)$ current algebra and with fractional level and spins, we discuss in some detail the fusion rules which arise. By a careful analysis of the 4-point functions, we find that both the fusion rules previously found in the literature are realized in our formulation. Since this is somewhat contrary to our expectations in our first work based on 3-point functions, we reanalyse the 3-point functions and come to the same conclusion. We compare our results on 4-point conformal blocks in particular with a different realization of these found by O. Andreev, and we argue for the equivalence. We describe in detail how integration contours have to be chosen to obtain convenient bases for conformal blocks, both in his and in our own formulation. We then carry out the rather lengthy calculation to obtain the crossing matrix between s- and t-channel blocks, and we use that to determine the monodromy invariant 4-point greens functions. We use the monodromy coefficients to obtain the operator algebra coefficients for theories based on admissible representations.

Affiliated with

Also associated with

No associations

Rating

Fusion, Crossing and Monodromy in Conformal Field Theory Based on $SL(2)$ Current Algebra with Fractional Level does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Fusion, Crossing and Monodromy in Conformal Field Theory Based on $SL(2)$ Current Algebra with Fractional Level, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Fusion, Crossing and Monodromy in Conformal Field Theory Based on $SL(2)$ Current Algebra with Fractional Level will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-434816