2019/06/11 by Henry Maxfield · 1 citation
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #BTZ black hole #Black Holes and Theoretical Physics #Black hole (networking) #Gravitational singularity #Homogeneous space #Naked singularity #Noncommutative and Quantum Gravity Theories #Quantum #Quantum gravity #Semiclassical physics #Spin (aerodynamics) #hep-th
paper · pdf · doi:10.1007/jhep12(2019)003
arxiv created 2019/06/11 · openalex created_date 2019/06/27 · openalex publication_date 2019/12/01 · arxiv updated 2020/01/29 · openalex updated_date 2026/08/06
A bstract Any unitary compact two-dimensional CFT with c > 1 and no symmetries beyond Virasoro has a parametrically large density of primary states at large spin for h <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mi>h</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> > hextr <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mover> <mml:mi>h</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mtext>extr</mml:mtext> </mml:msub> </mml:math> ∼ (c-1)/(24) <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mfrac> <mml:mrow> <mml:mi>c</mml:mi> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> <mml:mn>24</mml:mn> </mml:mfrac> </mml:math> , of a universal form determined by modular invariance. By including the contribution of light primary operators and multi-twist composites constructed from them in the modular bootstrap, we find that hextr <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mover> <mml:mi>h</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mtext>extr</mml:mtext> </mml:msub> </mml:math> receives corrections in a large spin expansion, which we compute at finite c . The analysis uses a formulation of the modular S-transform as a Fourier transform acting on the density of primary states. For theories with gravitational duals, hextr <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mover> <mml:mi>h</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mtext>extr</mml:mtext> </mml:msub> </mml:math> is interpreted as the extremality bound of rotating BTZ black holes, receiving quantum corrections which we compute at one loop by prohibiting naked singularities in the quantum-corrected geometry. This gravity result is reproduced by modular bootstrap in a semiclassical c → ∞ limit.