The Romelsberger Index, Berkooz Deconfinement, and Infinite Families of Seiberg Duals

Abstract

Romelsberger's index has been argued to be an RG-invariant and, therefore, Seiberg-duality-invariant object that counts protected operators in the IR SCFT of an N=1 theory. These claims have so far passed all tests. In fact, it remains possible that this index is a perfect discriminant of duality. The investigation presented here bolsters such optimism. It is shown that the conditions of total ellipticity, which are needed for the mathematical manifestation of duality, are equivalent to the conditions ensuring non-anomalous gauge and flavor symmetries and the matching of (most) 't Hooft anomalies. Further insights are gained from an analysis of recent results by Craig, et al. It is shown that a non-perturbative resolution of an apparent mismatch of global symmetries is automatically accounted for in the index. It is then shown that through an intricate series of dynamical steps, the index not only remains fixed, but the only integral relation needed is the one that gives the "primitive" Seiberg dualities, perhaps hinting that the symmetry at the core is fundamental rather than incidental.

47 pages; some typos corrected

References in corpus (10)

• Rigid Supersymmetric Theories in Curved Superspace
• Applications of the Superconformal Index for Protected Operators and q-Hypergeometric Identities to N=1 Dual Theories
• Counting Gauge Invariants: the Plethystic Program
• Superconformal indices for N=1 theories with multiple duals
• On the Superconformal Index of N=1 IR Fixed Points: A Holographic Check
• On the ISS model of dynamical SUSY breaking
• Supersymmetric dualities beyond the conformal window
• Charging the Superconformal Index
• Phases of N=1 supersymmetric chiral gauge theories
• New dynamics and dualities in supersymmetric chiral gauge theories

Cited by in corpus (8)

• Elliptic hypergeometric integrals and 't Hooft anomaly matching conditions
• On a modular property of N=2 superconformal theories in four dimensions
• Vanishing superconformal indices and the chiral symmetry breaking
• New N=1 dualities from orientifold transitions - Part I: Field Theory
• A new pentagon identity for the tetrahedron index
• Extended global symmetries for 4d N=1 SQCD theories
• Integral pentagon relations for 3d superconformal indices
• 4d $\mathcal{N}=1$ quiver gauge theories and the ${\mathrm{A}}_{\mathrm{n}}$ Bailey lemma