Abstract
We provide a first principles derivation of the supersymmetric Casimir energy of \( \mathcal{N} \) = 1 SCFTs in four dimensions using the supercharge algebra on general conformal supergravity backgrounds that admit Killing spinors. The superconformal Ward identities imply that there exists a continuous family of conserved R-currents on supersymmetric backgrounds, as well as a continuous family of conserved currents for each conformal Killing vector. These continuous families interpolate between the consistent and covariant R-current and energy-momentum tensor. The resulting Casimir energy, therefore, depends on two continuous parameters corresponding to the choice of conserved currents used to define the energy and R-charge. This ambiguity is in addition to any possible scheme dependence due to local terms in the effective action. As an application, we evaluate the general expression for the supersymmetric Casimir energy we obtain on a family of backgrounds with the cylinder topology ℝ × S3 and admitting a single Majorana supercharge. Our result is a direct consequence of the supersymmetry algebra, yet it resembles more known expressions for the non-supersymmetric Casimir energy on such backgrounds and differs from the supersymmetric Casimir energy obtained from the zero temperature limit of supersymmetric partition functions. We defer a thorough analysis of the relation between these results to future work.
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Acknowledgments
The work of PP was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2023R1A2C1006975) and from the JRG Program at the APCTP through the Science and Technology Promotion Fund and Lottery Fund of the Korean Government. PP would like to thank the National and Kapodistrian University of Athens for the hospitality during the completion of this work. IP would like to thank the Isaac Newton Institute for Mathematical Sciences, Cambridge, for support and hospitality during the programme “Black holes: bridges between number theory and holographic quantum information” where work on this paper was undertaken. This work was supported by EPSRC grant no EP/R014604/1.
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Panopoulos, P., Papadimitriou, I. Supersymmetric Casimir energy on \( \mathcal{N} \) = 1 conformal supergravity backgrounds. J. High Energ. Phys. 2024, 29 (2024). https://doi.org/10.1007/JHEP04(2024)029
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DOI: https://doi.org/10.1007/JHEP04(2024)029