F-Theory and N=1 SCFTs in Four Dimensions

TL;DR

This paper develops a geometric framework for obtaining four-dimensional N=1 SCFTs from compactifications of six-dimensional (1,0) theories using F-theory. By modeling the F-theory base as an ADE orbifold and implementing a two-step quotient by kernel and lifted determinant actions, it constructs a broad class of nontrivial 4d fixed points whose moduli spaces encode Riemann surface data and, in special ADE cases, the moduli of flat connections on Σ. It provides explicit constructions for A-type and D-type quotients, clarifying how Kodaira fibers and flavor symmetries arise from the quotient data, and it extends the program to N=1 via twisting, predicting moduli spaces governed by flat ADE connections on Σ. The work also outlines couplings to N=3 theories, suggesting rich interplays among different classes of non-Lagrangian SCFTs with moduli controlled by geometric and topological data of Σ and ADE structures.

Abstract

Using the F-theory realization, we identify a subclass of 6d (1,0) SCFTs whose compactification on a Riemann surface leads to N = 1 4d SCFTs where the moduli space of the Riemann surface is part of the moduli space of the theory. In particular we argue that for a special case of these theories (dual to M5 branes probing ADE singularities), we obtain 4d N = 1 theories whose space of marginal deformations is given by the moduli space of flat ADE connections on a Riemann surface.

Figures (5)

• Figure 1: Quotients along curves of fixed points. The long vertical curve is the quotient before resolution.
• Figure 2: The quotients $A_{k+1}/\mathbb{Z}_k$, $k= 2, 3, 4, 5, 6$.
• Figure 3: The resolutions of $A_{k+1}/\mathbb{Z}_k$, $k=3,4,5,6$.
• Figure 4: The quotient $D_{q+2}/\mathbb{Z}_3$ and its resolution.
• Figure 5: Resolution graph of D-type singularity.