Microstate counting via Bethe Ansätze in the 4d N = 1 superconformal index

• Published in: The journal of high energy physics Vol. 2020; no. 3
• Main Authors: Lezcano, Alfredo González, Pando Zayas, Leopoldo A.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.03.2020; Springer Nature B.V
• Subjects: Black holes; Branes; Classical and Quantum Gravitation; Cones; Elementary Particles; Entropy; Gauge theory; High energy physics; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; String Theory; Theoretical physics; Black Holes in String Theory; AdS-CFT Correspondence; Supersymmetric Gauge Theory
• ISSN: 1029-8479
• DOI: 10.1007/JHEP03(2020)088

A bstract We study the superconfomal index of four-dimensional toric quiver gauge theories using a Bethe Ansatz approach recently applied by Benini and Milan. Relying on a particular set of solutions to the corresponding Bethe Ansatz equations we evaluate the superconformal index in the large N limit, thus avoiding to take any Cardy-like limit. We present explicit results for theories arising as a stack of N D3 branes at the tip of toric Calabi-Yau cones: the conifold theory, the suspended pinch point gauge theory, the first del Pezzo theory and Y p,q quiver gauge theories. For a suitable choice of the chemical potentials of the theory we find agreement with predictions made for the same theories in the Cardy-like limit. However, for other regions of the domain of chemical potentials the superconformal index is modified and consequently the associated black hole entropy receives corrections. We work out explicitly the simple case of the conifold theory.