$$ \mathcal{N} $$ = 2 JT supergravity and matrix models
Gustavo J. Turiaci, Edward Witten
Abstract
A bstract Generalizing previous results for $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 0 and $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 1, we analyze $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 2 JT supergravity on asymptotically AdS 2 spaces with arbitrary topology and show that this theory of gravity is dual, in a holographic sense, to a certain random matrix ensemble in which supermultiplets of different R -charge are statistically independent and each is described by its own $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 2 random matrix ensemble. We also analyze the case with a time-reversal symmetry, either commuting or anticommuting with the R -charge. In order to compare supergravity to random matrix theory, we develop an $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 2 analog of the recursion relations for Weil-Petersson volumes originally discovered by Mirzakhani in the bosonic case.