Decomposition of BPS moduli spaces and asymptotics of supersymmetric partition functions

A Cardy-like regime of the four-dimensional superconformal index has been shown to be governed by ’t Hooft anomalies and to single out a large-N saddle carrying the Bekenstein-Hawking entropy of dual supersymmetric black holes in AdS5. For the universal index where no flavour fugacities are turned on, this correspondence has been improved by matching the first subleading corrections to the saddle-point action with the four-derivative corrections to the black hole action in minimal gauged supergravity, as well as the respective corrected entropies. Here, we extend this match by including flavour symmetries. We consider five-dimensional gauged supergravity with vector multiplet and four-derivative couplings, and provide an effective theory reproducing the ’t Hooft anomalies of the R- and flavour symmetries of generic holographic superconformal field theories at next-to-leading order in the large-N expansion. Then we focus on a specific model dual to ℂ3/ℤν quiver gauge theories, where the ’t Hooft anomaly coefficients receive simple but sufficiently generic corrections. In this model, we evaluate the four-derivative corrections to the on-shell action of the supersymmetric multi-charge black hole, showing agreement with the flavoured Cardy-like formula from the index. We give a prediction for the corrected entropy of the supersymmetric black hole and discuss the general validity of our results. Taking the limit of infinite AdS5 radius, we also obtain four-derivative corrections to the action and entropy of supersymmetric asymptotically flat black holes.

Section: The Multi-charge Cardy-like Formula From Equivariant Integra...mentioning

confidence: 99%

Higher-derivative corrections to flavoured BPS black hole thermodynamics and holography

Cassani,

Ruipérez,

Turetta

2024

“…See [49] for a review. A supersymmetric back- 14 See also [45] for related discussions. 15 Note that the superconformal index I and the partition function Z S 3 ×S 1 differs by a contribution which is known as the Casimir energy [46,47] log Z S 3 ×S 1 = −βEC + log I .…”

Section: Twisted S 3 × S 1 Supersymmetric Backgroundmentioning

confidence: 99%

Anomaly matching across dimensions and supersymmetric Cardy formulae

Ohmori

Tizzano

2022

’t Hooft anomalies are known to induce specific contributions to the effective action at finite temperature. We present a general method to directly calculate such contributions from the anomaly polynomial of a given theory, including a term which involves a U(1) connection for the thermal circle isometry. Based on this observation, we show that the asymptotic behavior of the superconformal index of 4d$$ \mathcal{N} $$ N = 1 theories on the “second sheet” can be calculated by integrating the anomaly polynomial on a particular background. The integration is then performed by an equivariant method to reproduce known results. Our method only depends on the anomaly polynomial and therefore the result is applicable to theories without known Lagrangian formulation. We also present a new formula that relates the behavior of 6d$$ \mathcal{N} $$ N = (1, 0) SCFTs on the second sheet to the anomaly polynomial.

Root of unity asymptotics for Schur indices of 4d Lagrangian theories

Eleftheriou

2023

The Schur index of a 4 dimensional $$ \mathcal{N} $$ N = 2 superconformal field theory counts (with sign) bosonic and fermionic states that preserve 4 supercharges. We consider the Schur indices of 4d $$ \mathcal{N} $$ N = 4 super Yang-Mills and $$ \mathcal{N} $$ N = 2 circular quiver gauge theories with gauge groups U(N) or SU(N). We calculate the exponentially dominant part of their asymptotic expansions as the index parameter q approaches any root of unity. We find that some of the indices exhibit “small” ($$ \mathcal{O} $$ O (N0) as N → ∞) exponential growth, which is much smaller than an $$ \mathcal{O} $$ O (N2) exponential growth of states that is indicative of a black hole. This implies that the indices do not capture a growth of states that would correspond to a supersymmetric black hole that preserves 4 supercharges in the holographic dual AdS theory. Interestingly, the exponentially dominant part in the Schur asymptotics we consider, depends on the parity of the rank N.