Find closed forms for finite-temperature monodromy-defect one-point functions

Obtain compact closed-form expressions for the finite-temperature one-point functions of |\Phi|^2 and the conserved U(1) current in the free scalar theory with a monodromy defect, including the contributions of the admissible singular modes.

Background

The monodromy-defect one-point functions are represented by sums over thermal images and, in even dimensions, by rapidly convergent integral representations. The regular-mode contributions are numerically tractable, while the singular-mode contributions are subject to infrared convergence restrictions on the monodromy parameter.

A closed form would make the analytic dependence on the thermal cross-ratio, monodromy parameter, and singular-mode couplings more transparent and would facilitate systematic analysis of the associated thermal defect data.

References

Computing the integrals for m\neq0 is challenging and we have not been able to find a closed form expression that captures the full correlator at arbitrary transverse distance \rho valid for any d.

— Boundaries and defects in conformal field theories at finite temperature  (2609.38130 - Artico et al., 29 Sep 2026) in Section 5, subsections “Thermal one-point function of |\Phi|^2” and “Thermal one-point function of J_\mu”