Nonrenormalization Theorem for ${\cal N}=(4,4)$ Interface Entropy
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| Format: | Preprint |
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2025
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| author | Karch, Andreas Ooguri, Hirosi Wang, Mianqi |
| author_facet | Karch, Andreas Ooguri, Hirosi Wang, Mianqi |
| contents | We derive a formula for the half-BPS interface entropy between any pair of ${\cal N}=(4,4)$ theories on the same conformal manifold. This generalizes the diastasis formula derived in arXiv:1311.2202 for ${\cal N}=(2,2)$ theories, which is restricted to the conformal submanifolds generated by either chiral or twisted chiral multiples of ${\cal N}=(2,2)$ supersymmetry. To derive the ${\cal N}=(4,4)$ formula, we use the fact that the conformal manifold of ${\cal N}=(4,4)$ theories is symmetric and quaternionic-Kähler and that its isotropy group contains the $SU(2) \otimes SU(2)$ external automorphism of the ${\cal N}=(4,4)$ superconformal algebra. As an application of the formula, we prove a supersymmetric non-renormalization theorem, which explains the observation in arXiv:1005.4433 that the interface entropy for half-BPS Janus solutions in type IIB supergravity on ${\it AdS}_3 \times S^3 \times T^4$ coincides with the corresponding quantity in their free conformal field limits. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2502_06928 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Nonrenormalization Theorem for ${\cal N}=(4,4)$ Interface Entropy Karch, Andreas Ooguri, Hirosi Wang, Mianqi High Energy Physics - Theory We derive a formula for the half-BPS interface entropy between any pair of ${\cal N}=(4,4)$ theories on the same conformal manifold. This generalizes the diastasis formula derived in arXiv:1311.2202 for ${\cal N}=(2,2)$ theories, which is restricted to the conformal submanifolds generated by either chiral or twisted chiral multiples of ${\cal N}=(2,2)$ supersymmetry. To derive the ${\cal N}=(4,4)$ formula, we use the fact that the conformal manifold of ${\cal N}=(4,4)$ theories is symmetric and quaternionic-Kähler and that its isotropy group contains the $SU(2) \otimes SU(2)$ external automorphism of the ${\cal N}=(4,4)$ superconformal algebra. As an application of the formula, we prove a supersymmetric non-renormalization theorem, which explains the observation in arXiv:1005.4433 that the interface entropy for half-BPS Janus solutions in type IIB supergravity on ${\it AdS}_3 \times S^3 \times T^4$ coincides with the corresponding quantity in their free conformal field limits. |
| title | Nonrenormalization Theorem for ${\cal N}=(4,4)$ Interface Entropy |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2502.06928 |