4D Gauge Theories with Conformal Matter

TL;DR

The paper develops 4D N=1 quiver-like gauge theories in which links are 4D conformal matter arising from compactifications of 6D conformal matter on curved surfaces with flavor fluxes, and provides a detailed F-theory realization via elliptically fibered Calabi–Yau fourfolds. It combines a bottom-up field-theoretic analysis—formulating beta-function constraints, conformal windows, and confinement mechanisms for SQCD-like theories with CM links—with a top-down string-theory construction that encodes gauge groups, matter, and Yukawas at brane intersections and triple intersections, and accounts for quantum corrections to moduli spaces. The work explores quiver networks and Yukawa interactions across multiple CM sectors, including exceptional gauge groups and CM on higher-genus curves, and demonstrates how instanton effects can lift moduli or drive conformal fixed points in the IR. Together, these results reveal a rich landscape of 4D strongly coupled dynamics engineered from 6D CM and provide a platform for further string-theoretic calculations, dualities, and extensions to other dimensions.

Abstract

One of the hallmarks of 6D superconformal field theories (SCFTs) is that on a partial tensor branch, all known theories resemble quiver gauge theories with links comprised of 6D conformal matter, a generalization of weakly coupled hypermultiplets. In this paper we construct 4D quiverlike gauge theories in which the links are obtained from compactifications of 6D conformal matter on Riemann surfaces with flavor symmetry fluxes. This includes generalizations of super QCD with exceptional gauge groups and quarks replaced by 4D conformal matter. Just as in super QCD, we find evidence for a conformal window as well as confining gauge group factors depending on the total amount of matter. We also present F-theory realizations of these field theories via elliptically fibered Calabi-Yau fourfolds. Gauge groups (and flavor symmetries) come from 7-branes wrapped on surfaces, conformal matter localizes at the intersection of pairs of 7-branes, and Yukawas between 4D conformal matter localize at points coming from triple intersections of 7-branes. Quantum corrections can also modify the classical moduli space of the F-theory model, matching expectations from effective field theory.

Figures (12)

• Figure 1: Examples of quiver gauge theories with conformal matter. Here, each line with "CM" indicates 4D $\mathcal{N} = 2$$G \times G$ conformal matter, namely 6D $G \times G$ conformal matter compactified on a $T^2$.
• Figure 2: The initally blown up $E_6$--$E_6$--$E_6$ Yukawa point.
• Figure 3: The fully blown up $E_6$--$E_6$--$E_6$ Yukawa point.
• Figure 4: The initially blown up $E_7$--$E_7$--$E_7$ Yukawa point.
• Figure 5: The fully blown up $E_7$--$E_7$--$E_7$ Yukawa point.