The SUSY index beyond the Cardy limit

We evaluate the superconformal index of 4d $$ \mathcal{N} $$ N = 4 SYM with gauge algebra so(2Nc + 1) in the Cardy-like limit. We then study the relation with the results obtained for the S-dual usp(2Nc), discussing the fate of S-duality in different regions of charges. We find that S-duality is preserved thanks to a non-trivial integral identity that relates the three sphere partition functions of pure 3d Chern-Simons gauge theories.

S-duality in the Cardy-like limit of the superconformal index

Amariti,

Zanetti

2024

Large black hole entropy from the giant brane expansion

Beccaria,

Cabo-Bizet

2024

We show that the Bekenstein-Hawking entropy of large supersymmetric black holes in AdS5 × S5 emerges from remarkable cancellations in the giant graviton expansions recently proposed by Imamura, and Gaiotto and Lee, independently. A similar cancellation mechanism is shown to happen in the exact expansion in terms of free fermions recently put-forward by Murthy. These two representations can be understood as sums over independent systems of giant D3-branes and free fermions, respectively. At large charges, the free energy of each independent system localizes to its asymptotic expansion near the leading singularity. The sum over the independent systems maps their localized free energy to the localized free energy of the superconformal index of U(N) $$\mathcal{N}$$ = 4 SYM. This result constitutes a non-perturbative test of the giant graviton expansion valid at any value of N. Moreover, in the holographic scaling limit N → ∞ at fixed ratio $$\frac{{\text{Entropy}}}{{N}^{2}}$$, it recovers the 1/16 BPS black hole entropy by a saddle-point approximation of the giant graviton expansion.

Large N universality of 4d $$ \mathcal{N} $$ = 1 superconformal index and AdS black holes

Choi,

Kim,

Song

2024

We study the large N limit of the matrix models associated with the superconformal indices of four-dimensional $$ \mathcal{N} $$ N = 1 superconformal field theories. We find that for a large class of $$ \mathcal{N} $$ N = 1 superconformal gauge theories, the superconformal indices in the large N limit of such theories are dominated by the ‘parallelogram’ saddle, providing O(N2) free energy for the generic value of chemical potentials. This saddle corresponds to BPS black holes in AdS5 whenever a holographic dual description is available. Our saddle applies to a large class of gauge theories, including ADE quiver gauge theories, and the theories with rank-2 tensor matters. Our analysis works for most $$ \mathcal{N} $$ N = 1 superconformal gauge theories that admit a suitable large N limit while keeping the flavor symmetry fixed. We also find ‘multi-cut’ saddle points, which correspond to the orbifolded Euclidean black holes in AdS5.