The Hilbert series of U/SU SQCD and Toeplitz Determinants

Details The Hilbert series of U/SU SQCD and Toeplitz Determinants The Hilbert series of U/SU SQCD and Toeplitz Determinants

2011-04-11

arxiv.org/abs/1104.2045v2

Nucl.Phys.B850:553-593,2011

Physics

High Energy Physics

High Energy Physics - Theory

49 pages, 6 figures. Version 2: references added

Scientific paper

10.1016/j.nuclphysb.2011.05.012

We present a new technique for computing Hilbert series of N=1 supersymmetric QCD in four dimensions with unitary and special unitary gauge groups. We show that the Hilbert series of this theory can be written in terms of determinants of Toeplitz matrices. Applying related theorems from random matrix theory, we compute a number of exact Hilbert series as well as asymptotic formulae for large numbers of colours and flavours -- many of which have not been derived before.

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