Character Expansions, Itzykson-Zuber Integrals, and the QCD Partition Function
A.B. Balantekin (Wisconsin U., Madison, Max-Planck-Institute,, Heidelberg)
TL;DR
This paper introduces a combinatorial formula for U(N) character expansions that simplifies complex group integrals, enabling quick calculations of integrals like the Itzykson-Zuber integral and QCD partition functions.
Contribution
It provides a novel combinatorial approach to generate U(N) character expansions, simplifying calculations of group integrals in quantum field theory.
Findings
Simplified calculation of the Itzykson-Zuber integral
Efficient computation of QCD finite volume partition functions
New combinatorial formula for U(N) character expansions
Abstract
A combinatorial formula to generate U(N) character expansions is presented. It is shown that the resulting character expansion formulas greatly simplify a number of problems where integrals over the group manifolds need to be calculated. Several examples are given, including direct and very quick calculations of the Itzykson-Zuber integral and the finite volume effective partition function of QCD in the sector with a given topological charge.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.