Nonrenormalization theorem for N = (4, 4) interface entropy

Creators: Karch, Andreas¹; Ooguri, Hirosi²; Wang, Mianqi¹

1. The University of Texas at Austin
2. California Institute of Technology

Abstract

We derive a formula for the half-BPS interface entropy between any pair of N = (4, 4) theories on the same conformal manifold. This generalizes the diastasis formula derived in [1] for = (2, 2) theories, which is restricted to the conformal submanifolds generated by either chiral or twisted chiral multiples of = (2, 2) supersymmetry. To derive the N = (4, 4) formula, we use the fact that the conformal manifold of N = (4, 4) theories is symmetric and quaternionic-Kähler and that its isotropy group contains the SU(2) ⊗ SU(2) external automorphism of the N = (4, 4) superconformal algebra. As an application of the formula, we prove a supersymmetric non-renormalization theorem, which explains the observation in [2] that the interface entropy for half-BPS Janus solutions in type IIB supergravity on AdS₃ × S³ × T⁴ coincides with the corresponding quantity in their free conformal field limits.

Copyright and License

© The Authors. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

Article funded by SCOAP3.

Acknowledgement

We thank Paul Aspinwall, Sergio Cecotti, Michael Gutperle, and Ling-Yan Hung for discussion. We also thank Costas Bachas, Ilka Brunner, and Michael Gutperle for their comments on the draft of this paper. AK and MW are supported in part by the U.S. Department of Energy, Office of High Energy Physics, under Grant No. DE-SC0022021 and a grant from the Simons Foundation (Grant 651678, AK). HO is supported in part by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award Number DE-SC0011632, the Simons Investigator Award (MP-SIP-00005259), and JSPS Grants-in-Aid for Scientific Research 23K03379. His work was performed in part at the Kavli Institute for the Physics and Mathematics of the Universe at the University of Tokyo, which is supported by the World Premier International Research Center Initiative, MEXT, Japan, and at the Aspen Center for Physics, which is supported by NSF grant PHY-1607611.

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