Connecting the chiral and heavy quark limits: full mass dependence of fermion determinant in an instanton background

DOI10.1088/0305-4470/39/21/S19zbMATH Open1094.81514arXivhep-th/0511181MaRDI QIDQ5478493

Publication date: 13 July 2006

Published in: Journal of Physics A: Mathematical and General (Search for Journal in Brave)

Abstract: This talk reports work done in collaboration with Jin Hur, Choonkyu Lee and Hyunsoo Min concerning the computation of the precise mass dependence of the fermion determinant for quarks in the presence of an instanton background. The result interpolates smoothly between the previously known chiral and heavy quark limits of extreme small and large mass. The computational method makes use of the fact that the single instanton background has radial symmetry, so that the computation can be reduced to a sum over partial waves of logarithms of radial determinants, each of which can be computed numerically in an efficient manner using a theorem of Gelfand and Yaglom. The bare sum over partial waves is divergent and must be regulated and renormalized. We use the angular momentum cutoff regularization and renormalization scheme. Our results provide an extension of the Gelfand-Yaglom result to higher dimensional separable differential operators. I also comment on the application of this approach to a wide variety of fluctuation determinant computations in quantum field theory.

Full work available at URL: https://arxiv.org/abs/hep-th/0511181

Mathematics Subject Classification ID

Strong interaction, including quantum chromodynamics (81V05) Perturbative methods of renormalization applied to problems in quantum field theory (81T15) PDEs in connection with quantum mechanics (35Q40)