Phase transitions in 3D gravity and fractal dimension
| Autor: | Henry Maxfield, Alexander Maloney, Xi Dong, Shaun Maguire |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
High Energy Physics - Theory
Nuclear and High Energy Physics Scalar (mathematics) Boundary (topology) FOS: Physical sciences General Relativity and Quantum Cosmology (gr-qc) AdS-CFT Correspondence Conformal and W Symmetry 01 natural sciences General Relativity and Quantum Cosmology Mathematics - Geometric Topology 0103 physical sciences FOS: Mathematics lcsh:Nuclear and particle physics. Atomic energy. Radioactivity 010306 general physics Mathematical physics Physics Conformal Field Theory 010308 nuclear & particles physics Conformal field theory Geometric Topology (math.GT) Moduli space AdS/CFT correspondence High Energy Physics - Theory (hep-th) Hausdorff dimension lcsh:QC770-798 Critical dimension Scalar field |
| Zdroj: | Journal of High Energy Physics, Vol 2018, Iss 5, Pp 1-41 (2018) Journal of High Energy Physics |
| ISSN: | 1029-8479 |
| Popis: | 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 AdS3. This is in addition to the first order Hawking-Page-like phase transitions between different locally AdS3 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 AdS3, 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. |
| Databáze: | OpenAIRE |
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