We consider the partition function for a matrix model with a global unitary invariant energy function. We show that the averages over the partition function of global unitary invariant trace polynomials of the matrix variables are the same when calculated with any choice of a global unitary fixing, while averages of such polynomials without a trace define matrix-valued correlation functions, that depend on the choice of unitary fixing. The unitary fixing is formulated within the standard Faddeev-Popov framework, in which the squared Vandermonde determinant emerges as a factor of the complete Faddeev-Popov determinant. We give the ghost representation for the FP determinant, and the corresponding BRST invariance of the unitary-fixed partition function. The formalism is relevant for deriving Ward identities obeyed by matrix-valued correlation functions.
|Number of pages||9|
|Journal||Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics|
|State||Published - 18 Sep 2003|
Bibliographical noteFunding Information:
This work was supported in part by the Department of Energy under Grant #DE-FG02-90ER40542. We wish to thank Herbert Neuberger and Steven Weinberg for useful discussions.