Semi-Chiral Operators in 4d $\mathcal{N}=1$ Gauge Theories

Abstract

We discuss the properties of quarter-BPS local operators in four dimensional $\mathcal{N}=1$ supersymmetric Yang-Mills theory using the formalism of holomorphic twists. We study loop corrections both to the space of local operators and to algebraic operations which endow the twisted theory with an infinite symmetry algebra. We classify all single-trace quarter-BPS operators in the planar approximation for $SU(N)$ gauge theory and propose a holographic dual description for the twisted theory. We classify perturbative quarter-BPS operators in $SU(2)$ and $SU(3)$ gauge theories with sufficiently small quantum numbers and discuss possible non-perturbative corrections to the answer. We set up analogous calculations for some theories with matter.

v1:55+20 pages, 61 footnotes, comments welcome; v2: published version

References in corpus (5)

• Applications of the Superconformal Index for Protected Operators and q-Hypergeometric Identities to N=1 Dual Theories
• Field Algebras
• Localization on Hopf surfaces
• Comments on 1/16 BPS Quantum States and Classical Configurations
• From Rigid Supersymmetry to Twisted Holomorphic Theories

Cited by in corpus (7)

• Twisted holography on AdS${}_3\times S^3\times K3$ & the planar chiral algebra
• Witten index of BMN matrix quantum mechanics
• Loop Corrected Supercharges from Holomorphic Anomalies
• Holomorphic field theories and higher algebra
• BV Formalism and Partition Functions
• Schur Connections: Chord Counting, Line Operators, and Indices
• Integrable models from 4d holomorphic BF theory