2016/05/19 by Arash Arabi Ardehali, Ardehali, Arash Arabi · 1 citation
Mathematics · Physics and Astronomy · #Anomaly (physics) #Black Holes and Theoretical Physics #Class (philosophy) #FOS: Physical sciences #Gauge (firearms) #Gauge theory #High Energy Physics - Theory (hep-th) #Limit (mathematics) #Mathematical Physics (math-ph) #Mathematical analysis #Mathematical physics #Mathematics #Particle physics theoretical and experimental studies #Physics #Pure mathematics #Quantum Chromodynamics and Particle Interactions #Quantum mechanics #Quiver #Theoretical physics #hep-th #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.1605.06100
66+11 pages; PhD thesis; largely based on (and hence text overlap with) arXiv:1407.6024, arXiv:1411.5028, arXiv:1502.07737, arXiv:1512.03376
arxiv created 2016/05/19 · openalex publication_date 2016/05/19 · arxiv updated 2016/05/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The superconformal index of a typical Lagrangian 4d SCFT is given by a special function known as an elliptic hypergeometric integral (EHI). The high-temperature limit of the index corresponds to the hyperbolic limit of the EHI. The hyperbolic limit of certain special EHIs has been analyzed by Eric Rains around 2006; extending Rains's techniques, we discover a surprisingly rich structure in the high-temperature limit of a (rather large) class of EHIs that arise as the superconformal index of unitary Lagrangian 4d SCFTs with non-chiral matter content. Our result has implications for N=1 dualities, the AdS/CFT correspondence, and supersymmetric gauge dynamics on R3× S1. We also investigate the high-temperature asymptotics of the large-N limit of the superconformal index of a class of holographic 4d SCFTs (described by toric quiver gauge theories with SU(N) nodes). We show that from this study a rather general solution to the problem of holographic Weyl anomaly in AdS5/CFT4 at the subleading order (in the 1/N expansion) emerges. Most of this dissertation is based on published works by Jim Liu, Phil Szepietowski, and the author. We include here a few previously unpublished results as well, one of which is the high-temperature asymptotics of the superconformal index of puncture-less SU(2) class-S theories.