Sub-leading structures in superconformal indices: subdominant saddles and logarithmic contributions

Abstract

We systematically study various sub-leading structures in the superconformal index of $$ \mathcal{N} $$ N = 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 $$ \mathcal{N} $$ N = 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 AdS5 black holes and could be tested by low-energy IIB supergravity.

The SCI of $$ \mathcal{N} $$ = 4 USp(2Nc) and SO(Nc) SYM as a matrix integral

“…We find the expected log 2 and log 4 corrections to the (logarithm of the) SCI. As already noted in [25], we find that expanding the index in the Cardy-like limit one recovers a matrix integral that coincides with the three-sphere partition function of a 3d pure Chern-Simons (CS) theory. In the cases at hand the CS theories have gauge group…”

“…An interesting direction regards the calculation of subleading effects that correct the index. Such corrections have been studied in large detail in [25] for N = 4 SU(N c ) SYM and for the generalization to N = 1 gauge theories representing a stack of D3-branes probing a toric Calabi-Yau threefold singularity. The calculation has been carried out both in the Cardy-like limit, using a saddle point approximation to the matrix integral, and in the BAE approach, finding agreement between the two descriptions at large N c .…”

Superconformal index of low-rank gauge theories via the Bethe Ansatz

“…From it, one can extract the Bekenstein-Hawking entropy, but also find hints of new physics. For instance, one can compute perturbative corrections expected to come from higher-derivative terms [42], as well as non-perturbative corrections coming from Euclidean complex saddles of the gravitational action [51,52] (thus highlighting the importance of Euclidean complex saddles [20]) and corrections expected from D-branes.…”

New AdS2 backgrounds and $$ \mathcal{N} $$ = 4 conformal quantum mechanics

“…More generally, it would be interesting to apply exact calculation techniques to our quiver quantum mechanics in order to understand the properties of the SCQM in the infrared. Related to this is the possibility of learning about supergravity using exact results, along the lines of [114].…”