2015/08/31 by Edgar Shaghoulian · 1 citation
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Casimir effect #Conformal map #Conformal symmetry #Cosmology and Gravitation Theories #Gauge theory #Geometry #Holomorphic function #Lorentz covariance #Lorentz transformation #Mathematical physics #Mathematics #Physics #Pure mathematics #Quantum Electrodynamics and Casimir Effect #Quantum mechanics #Scalar (mathematics) #Scalar field #Torus #cond-mat.str-el #hep-th #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1103/physrevd.93.126005
published as Phys. Rev. D 93, 126005 (2016) · v3 typo fixed; v2 discussion clarified and appendix added; 9 pages
openalex publication_date 2016/06/20 · arxiv created 2016/11/23 · arxiv updated 2016/11/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
We derive a formula which applies to conformal field theories on a spatial torus and gives the asymptotic density of states solely in terms of the vacuum energy on a parallel plate geometry. The formula follows immediately from global scale and Lorentz invariance, but to our knowledge has not previously been made explicit. It can also be understood from the fact that log Z on \mathbbT2\ifmmode×\else\texttimes\fiℝ^d\ensuremath-1 transforms as the absolute value of a nonholomorphic modular form of weight d\ensuremath-1, which we show. The results are extended to theories which violate Lorentz invariance and hyperscaling but maintain a scaling symmetry. The formula is checked for the cases of a free scalar, free Maxwell gauge field, and free N=4 super Yang-Mills. The case of a Maxwell gauge field gives Casimir's original calculation of the electromagnetic force between parallel plates in terms of the entropy of a photon gas.