We derive a formula for the half-BPS interface entropy between any pair of <InlineEquation ID="IEq2"> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="script">N</mi> </math></EquationSource> <EquationSource Format="TEX">$ \mathcal{N} $</EquationSource> </InlineEquation> = (4, 4) theories on the same conformal manifold. This generalizes the diastasis formula derived in [1] for <InlineEquation ID="IEq3"> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="script">N</mi> </math></EquationSource> <EquationSource Format="TEX">$ \mathcal{N} $</EquationSource> </InlineEquation> = (2, 2) theories, which is restricted to the conformal submanifolds generated by either chiral or twisted chiral multiples of <InlineEquation ID="IEq4"> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="script">N</mi> </math></EquationSource> <EquationSource Format="TEX">$ \mathcal{N} $</EquationSource> </InlineEquation> = (2, 2) supersymmetry. To derive the <InlineEquation ID="IEq5"> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="script">N</mi> </math></EquationSource> <EquationSource Format="TEX">$ \mathcal{N} $</EquationSource> </InlineEquation> = (4, 4) formula, we use the fact that the conformal manifold of <InlineEquation ID="IEq6"> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="script">N</mi> </math></EquationSource> <EquationSource Format="TEX">$ \mathcal{N} $</EquationSource> </InlineEquation> = (4, 4) theories is symmetric and quaternionic-Kähler and that its isotropy group contains the SU(2) ⊗ SU(2) external automorphism of the <InlineEquation ID="IEq7"> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="script">N</mi> </math></EquationSource> <EquationSource Format="TEX">$ \mathcal{N} $</EquationSource> </InlineEquation> = (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.

Nonrenormalization theorem for $ \mathcal{N} $ = (4, 4) interface entropy

期刊论文
出版模式：

开放获取
发表日期：

2025年7月8日

查看全文

Andreas Karch,
Hirosi Ooguri,
Mianqi Wang

摘要

We derive a formula for the half-BPS interface entropy between any pair of $N$ $ \mathcal{N} $ = (4, 4) theories on the same conformal manifold. This generalizes the diastasis formula derived in [1] for $N$ $ \mathcal{N} $ = (2, 2) theories, which is restricted to the conformal submanifolds generated by either chiral or twisted chiral multiples of $N$ $ \mathcal{N} $ = (2, 2) supersymmetry. To derive the $N$ $ \mathcal{N} $ = (4, 4) formula, we use the fact that the conformal manifold of $N$ $ \mathcal{N} $ = (4, 4) theories is symmetric and quaternionic-Kähler and that its isotropy group contains the SU(2) ⊗ SU(2) external automorphism of the $N$ $ \mathcal{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.

Nonrenormalization theorem for \( \mathcal{N} \) = (4, 4) interface entropy

摘要