書誌事項
- 公開日
- 2018-05
- 権利情報
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- https://creativecommons.org/licenses/by/4.0/
- https://creativecommons.org/licenses/by/4.0/
- DOI
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- 10.1007/jhep05(2018)080
- 公開者
- Springer Science and Business Media LLC
説明
<jats:title>A<jats:sc>bstract</jats:sc> </jats:title> <jats:p>We show that for three dimensional gravity with higher genus boundary conditions, if the theory possesses a sufficiently light scalar, there is a second order phase transition where the scalar field condenses. This three dimensional version of the holographic superconducting phase transition occurs even though the pure gravity solutions are locally AdS<jats:sub>3</jats:sub>. This is in addition to the first order Hawking-Page-like phase transitions between different locally AdS<jats:sub>3</jats:sub> handlebodies. This implies that the Rényi entropies of holographic CFTs will undergo phase transitions as the Rényi parameter is varied, as long as the theory possesses a scalar operator which is lighter than a certain critical dimension. We show that this critical dimension has an elegant mathematical interpretation as the Hausdorff dimension of the limit set of a quotient group of AdS<jats:sub>3</jats:sub>, and use this to compute it, analytically near the boundary of moduli space and numerically in the interior of moduli space. We compare this to a CFT computation generalizing recent work of Belin, Keller and Zadeh, bounding the critical dimension using higher genus conformal blocks, and find a surprisingly good match.</jats:p>
収録刊行物
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- Journal of High Energy Physics
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Journal of High Energy Physics 2018 (5), 080-, 2018-05
Springer Science and Business Media LLC