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Phase transitions in 3D gravity and fractal dimension

2018; Springer Nature; Volume: 2018; Issue: 5 Linguagem: Inglês

10.1007/jhep05(2018)080

1127-2236

Xi Dong, Shaun Maguire, Alexander Maloney, Henry Maxfield,

Noncommutative and Quantum Gravity Theories

A bstract 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 3 . This is in addition to the first order Hawking-Page-like phase transitions between different locally AdS 3 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 3 , 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.