Elden Loomes | Searcharxiv

arXiv2026

Quantum (non)equivalence of dual massive $p$-form gauge theories

Gauge theories of massive $p$-forms are connected by various dualities, which hold classically but may be broken at the quantum level. One example is the $BF$ theory of topologically coupled $p$- and $(d-p-1)$-forms in $d$ dimensions, where the coupling between forms results in a manifestly gauge invariant mass term for either form when the other is integrated out classically. We perform the path integral quantisation of this theory; by integrating out one of the forms, the resulting determinants are sensitive to the topology of spacetime, and counterterms must be introduced to renormalise their divergences. We compute these determinants in terms of the topological numbers of spacetime, showing explicitly how the quantum duality of the massive theories is broken on topologically non-trivial backgrounds. This is directly related to the quantum breaking of the massless duality between the form that was integrated out and the longitudinal modes of its partner. In particular, the difference of counterterms is proportional to the Euler characteristic of spacetime. The existence of gravitational instantons suggests that these dualities may be broken even in Minkowski space in the presence of topological fluctuations.

hep-th↗

arXiv2026

Electromagnetic instantons and asymmetric Hawking radiation of black holes

We argue that the topological structure of Abelian gauge theories, such as Maxwell electrodynamics, in the background of a Euclidean Schwarzschild black hole manifests itself through an asymmetry in Hawking radiation. In particular, the topology of the black hole manifold, characterised by a non-contractible 2-sphere and Euler characteristic $\chi = 2$, admits non-trivial gauge-field configurations. These take the form of 2-form field strengths that are closed but not exact. From a topological perspective, such configurations are classified by the second cohomology group, which is isomorphic to $\mathbb{Z} \oplus \mathbb{Z}$, and are labelled by integer electric ($n$) and magnetic ($m$) charges, $(n,m)$. Self-dual ($n = m$) and anti-self-dual ($n = -m$) dyonic configurations carry vanishing Euclidean energy and are fully compatible with the Euclidean Schwarzschild geometry. More general dyonic configurations, by contrast, are interpreted as off-shell Euclidean field configurations. Nevertheless, both classes contribute to the thermal equilibrium vacuum and to finite-temperature correlation functions in the corresponding Lorentzian framework. Furthermore, because of the non-trivial topology, the electromagnetic $\theta_{\rm EM}$-term contributes to the physical observables. In particular, it sources $CP$-asymmetric Hawking radiation, observable as an imbalance between left- and right-polarised photons in the emission spectrum. We briefly discuss some implications of this phenomenon.

hep-th↗