Counting chiral primaries in N=1 d=4 superconformal field theories

Details Counting chiral primaries in N=1 d=4 superconformal field theories Counting chiral primaries in N=1 d=4 superconformal field theories

2005-10-07

arxiv.org/abs/hep-th/0510060v2

Nucl.Phys. B747 (2006) 329-353

Physics

High Energy Physics

High Energy Physics - Theory

34 pages, significant revision

Scientific paper

10.1016/j.nuclphysb.2006.03.037

I derive a procedure to count chiral primary states in N=1 superconformal field theories in four dimensions. The chiral primaries are counted by putting the N=1 field theory on S^3 X R. I also define an index that counts semi-short multiplets of the superconformal theory. I construct N=1 supersymmetric Lagrangians on S^3 X R for theories which are believed to flow to a conformal fixed point in the IR. For ungauged theories I reduce the field theory to a supersymmetric quantum mechanics, whereas for gauge theories I use chiral ring arguments. I count chiral primaries for SU(2) SYM with three flavors and its Seiberg dual. Those two results agree provided a new chiral ring relation holds.

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