Chiral theories of class S

Abstract

We study a class of four-dimensional N=1 superconformal field theories obtained from the six-dimensional (1,0) theory, on M5-branes on C^2/Z_k orbifold singularity, compactified on a Riemann surface. This produces various quiver gauge theories whose matter contents are chiral. We classify the building blocks associated to pairs-of-pants, and study the gauging of them as the gluing of punctures. The Riemann surface picture makes the duality invariance of the resulting quiver theories manifest: the theories associated to the same Riemann surface flow to the same nontrivial infrared fixed point. We explicitly check this from the 't Hooft anomalies of the global symmetries and central charges.

33 pages, 20 figures; v2: a discussion on the central charges in the case with U(1) curvatures in section 5.2 is corrected

References in corpus (10)

• 6d Conformal Matter
• Dimer models and toric diagrams
• Four-Dimensional SCFTs from M5-Branes
• Geometric Engineering, Mirror Symmetry and 6d (1,0) -> 4d, N=2
• Quiver Tails and N=1 SCFTs from M5-branes
• Charting Class ${\mathcal{S}}_k$ Territory
• Brane Tilings and Specular Duality
• N=1 theories of class S_k
• 6d $\mathcal{N}=(1,0)$ theories on $T^2$ and class S theories: part I
• Infinitely many N=1 dualities from $m+1-m=1$

Cited by in corpus (22)

• 6d SCFTs, 5d Dualities and Tao Web Diagrams
• Compactification of 6d minimal SCFTs on Riemann surfaces
• 4D Gauge Theories with Conformal Matter
• A slow review of the AGT correspondence
• From 6d flows to 4d flows
• AdS5 compactifications with punctures in massive IIA supergravity
• From 6D SCFTs to Dynamic GLSMs
• M5-branes Probing Flux Backgrounds
• S-duality in $\mathcal{N}=1$ orientifold SCFTs
• On the torus compactifications of $Z_2$ orbifolds of E-string theories
• Surface defects as transfer matrices
• 2D CFT blocks for the 4D class ${\mathcal{S}}_k$ theories
• Structure of Anomalies of 4d SCFTs from M5-branes, and Anomaly Inflow
• De Sitter Uplift with Dynamical Susy Breaking
• 4d N=1 from 6d N=(1,0) on a torus with fluxes
• The Coulomb and Higgs Branches of $\mathcal{N}=1$ Theories of Class ${\mathcal{S}}_k$
• Superconformal index with surface defects for class ${\mathcal{S}}_k$
• D-brane Instantons as Gauge Instantons in Orientifolds of Chiral Quiver Theories
• Universal consistent truncation for 6d/7d gauge/gravity duals
• Strongly coupled phases of $\mathcal{N}=1$ S-duality
• Hilbert Series of Bipartite Field Theories
• Aspects of 4d supersymmetric dynamics and geometry