2017/12/31 by Stefan Forste, Stefan Förste, Joshua Kames-King +1
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Boundary (topology) #Boundary value problem #Cosmology and Gravitation Theories #Curvature #Dual (grammatical number) #Geometry and complex manifolds #Gravitation #Holography #Syk #cond-mat.str-el #hep-th
paper · pdf · doi:10.1007/jhep03(2018)028
22 pages,v2 references added, typos corrected
openalex created_date 2018/01/05 · arxiv created 2018/01/09 · openalex publication_date 2018/03/01 · arxiv updated 2018/04/04 · openalex updated_date 2026/08/05
A bstract The gravitational part of the holographic dual to the SYK model has been conjectured to be Jackiw-Teitelboim (JT) gravity. In this paper we construct an AdS 2 background in N=(2, 2) <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> <mml:mo>=</mml:mo> <mml:mfenced> <mml:mrow> <mml:mn>2</mml:mn> <mml:mo>,</mml:mo> <mml:mspace/> <mml:mn>2</mml:mn> </mml:mrow> </mml:mfenced> </mml:math> JT gravity and show that the gravitational dynamics are — as in the N=0 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> </mml:math> and N=1 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> </mml:math> cases — fully captured by the extrinsic curvature as an effective boundary action. This boundary term is given by the super-Schwarzian of the N=2 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> <mml:mo>=</mml:mo> <mml:mn>2</mml:mn> </mml:math> SYK model, thereby providing further evidence of the JT/SYK duality. The chirality of this SYK model is reproduced by the inherent chirality of axial N=(2, 2) <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> <mml:mo>=</mml:mo> <mml:mfenced> <mml:mrow> <mml:mn>2</mml:mn> <mml:mo>,</mml:mo> <mml:mspace/> <mml:mn>2</mml:mn> </mml:mrow> </mml:mfenced> </mml:math> supergravity.