Sub-leading structures in superconformal indices: subdominant saddles and logarithmic contributions
Alfredo González Lezcano, Junho Hong, James T. Liu, Leopoldo A. Pando Zayas
Abstract
A bstract We systematically study various sub-leading structures in the superconformal index of $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 4 supersymmetric Yang-Mills theory with SU( N ) gauge group. We concentrate in the superconformal index description as a matrix model of elliptic gamma functions and in the Bethe-Ansatz presentation. Our saddle-point approximation goes beyond the Cardy-like limit and we uncover various saddles governed by a matrix model corresponding to SU( N ) Chern-Simons theory. The dominant saddle, however, leads to perfect agreement with the Bethe-Ansatz approach. We also determine the logarithmic correction to the superconformal index to be log N , finding precise agreement between the saddle-point and Bethe-Ansatz approaches in their respective approximations. We generalize the two approaches to cover a large class of 4d $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 1 superconformal theories. We find that also in this case both approximations agree all the way down to a universal contribution of the form log N . The universality of this last result constitutes a robust signature of this ultraviolet description of asymptotically AdS 5 black holes and could be tested by low-energy IIB supergravity.