Chiral--Maxwell Cavity EFT: Reduced Gauge-Mode Condensation and Quantum-Optics Limits

Abstract

We develop a finite-volume Chiral--Maxwell effective field theory in which a topologically nontrivial hadronic sector acts as a nonlinear medium for a reduced cavity gauge mode. Starting from the SU(2) nonlinear sigma model minimally coupled to Maxwell theory, we construct an equivariant low-mode sector that retains the topological charge structure while projecting the dynamics onto an effective 1+1 theory. Both mass-like scales in the reduced action are finite-volume kinematic gaps---arising from transverse winding energy and holonomy curvature, respectively---with no explicit symmetry breaking, in direct analogy with the Hosotani mechanism on compact cycles. Both gaps vanish in the infinite-volume limit, consistently with massless photons and pions in bulk ChPT. In one hierarchy, Coleman duality yields a gauge-invariant one-loop effective potential for the reduced gauge coordinate; we identify its domain of validity and establish that the locally stable nontrivial branch satisfies the EFT hierarchy condition. In the complementary hierarchy, integrating out the gauge mode produces a one-loop deformed sine-Gordon EFT for the chiral sector with a closed-form kink tension correction. Upon quantization, the reduced theory maps onto nonlinear cavity Hamiltonians whose trivial and locally condensed branches obey distinct selection rules, providing experimentally accessible diagnostics.

arXiv comment54 pages, 6 figures. Replaced with the version accepted in Eur. Phys. J. C: title, abstract, narrative, and references updated (reduced gauge-mode condensation). DOI: 10.1140/epjc/s10052-026-16250-6