Gauged fermionic matrix quantum mechanics
arXiv:1903.01628 · doi:10.1007/JHEP03(2019)185
Abstract
We consider the gauged free fermionic matrix model, for a single fermionic matrix. In the large limit this system describes a chiral fermion in dimensions. The Gauss' law constraint implies that to obtain a physical state, indices of the fermionic matrices must be fully contracted, to form a singlet. There are two ways in which this can be achieved: one can consider a trace basis formed from products of traces of fermionic matrices or one can consider a Schur function basis, labeled by Young diagrams. The Schur polynomials for the fermions involve a twisted character, as a consequence of Fermi statistics. The main result of this paper is a proof that the trace and Schur bases coincide up to a simple normalization coefficient that we have computed.
20 pages
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