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- W1946703250 abstract "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 $mathbb{T}^2times mathbb{R}^{d-1}$ transforms as the absolute value of a non-holomorphic modular form of weight $d-1$, 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 $mathcal{N}=4$ 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." @default.
- W1946703250 created "2016-06-24" @default.
- W1946703250 creator A5050827035 @default.
- W1946703250 date "2016-06-20" @default.
- W1946703250 modified "2023-10-18" @default.
- W1946703250 title "Modular forms and a generalized Cardy formula in higher dimensions" @default.
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- W1946703250 doi "https://doi.org/10.1103/physrevd.93.126005" @default.
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