Constant field strengths on T^{2n}

TL;DR

The paper addresses fluctuations around constant diagonal field strengths in $U(N)$ Yang–Mills on even-dimensional tori $T^{2n}$, extending Van Baal's $T^4$ results. It develops a dimensional reduction to a low-energy theory and diagonalizes the mass operators by exploiting a complex structure, ultimately expressing the spectrum and eigenfunctions in terms of theta functions on $T^{2n}$. A comprehensive analysis of stability, supersymmetry, and the fermionic spectrum—including zeromodes and index-theory checks—provides a systematic framework for D-brane applications and string-theoretic contexts. The findings offer explicit fluctuation spectra for both bosonic and fermionic sectors and illuminate the role of fluxes in moduli counting, SUSY breaking, and potential black-hole entropy connections in higher-dimensional brane setups.

Abstract

We analyse field strength configurations in U(N) Yang-Mills theory on T^{2n} that are diagonal and constant, extending early work of Van Baal on T^4. The spectrum of fluctuations is determined and the eigenfunctions are given explicitly in terms of theta functions on tori. We show the relevance of the analysis to higher dimensional D-branes and discuss applications of the results in string theory.