Modular covariance for photons and gravitons in a Casimir box

The Casimir effect consists in a force between two conducting plates separated by a small distance due to the non-vanishing vacuum expectation value of the energy of the electromagnetic field. At finite temperature, the partition function of the system is characterized by an inversion symmetry, relating the low-temperature/small-separation regime to the high-temperature/large-separation one. I will show how such symmetry may be enhanced to full modular covariance when defining a suitable modular parameter. 

At low temperature, the leading contribution to the entropy scales like the area of the plates and originates from photons oscillating parallel to the plates. I will discuss how these modes are related to the non-trivial boundary conditions imposed on the fields at the plates and how, choosing closely related "perfectly conducting" conditions in linearized gravity, all the above results extend directly from photons to gravitons.

Zoom Link: https://pitp.zoom.us/j/97716816516?pwd=SUVacU5ob0tySWUrUUwyKzY0ZFNRZz09