Chiral gauge dynamics and dynamical supersymmetry breaking

TL;DR

The paper analyzes a chiral $SU(2)$ gauge theory with a high-spin fermion in the $I=\frac{3}{2}$ representation and its ${\cal N}=1$ SUSY extension. By employing center-stabilizing deformations on $S^1\times\mathbb{R}^3$ and semiclassical techniques, it identifies a novel magnetic-quintet confinement mechanism in the non-supersymmetric case while arguing that the supersymmetric version does not confine and likely flows to a conformal fixed point. The work also clarifies the microscopic origins of certain superpotentials in SQCD on the circle via modified monopole operators and introduces a 3d-CFT perspective for the origin of the 4d theory, including the role of anomaly matching and topological symmetries. Additionally, it introduces the exotic magnetic bion and draws parallels with monopole physics in condensed matter, highlighting a broader class of topological excitations shaping infrared dynamics.

Abstract

We study the dynamics of a chiral SU(2) gauge theory with a Weyl fermion in the I=3/2 representation and of its supersymmetric generalization. In the former, we find a new and exotic mechanism of confinement, induced by topological excitations that we refer to as magnetic quintets. The supersymmetric version was examined earlier in the context of dynamical supersymmetry breaking by Intriligator, Seiberg, and Shenker, who showed that if this gauge theory confines at the origin of moduli space, one may break supersymmetry by adding a tree level superpotential. We examine the dynamics by deforming the theory on S^1 x R^3, and show that the infrared behavior of this theory is an interacting CFT at small S^1. We argue that this continues to hold at large S^1, and if so, that supersymmetry must remain unbroken. Our methods also provide the microscopic origin of various superpotentials in SQCD on S^1 x R^3 - which were previously obtained by using symmetry and holomorphy - and resolve a long standing interpretational puzzle concerning a flux operator discovered by Affleck, Harvey, and Witten. It is generated by a topological excitation, a "magnetic bion", whose stability is due to fermion pair exchange between its constituents. We also briefly comment on composite monopole operators as leading effects in two dimensional anti-ferromagnets.

Figures (5)

• Figure 1: The figure describes the main idea of deformation theory. The A-path (split from y-axis for visual convenience) corresponds to pure YM theory. This theory undergoes a center symmetry changing transition when the radius is of order the inverse strong scale. The double-trace deformation can be used to stabilize the center symmetry down to arbitrarily small radius, along the B-path. The deformed YM theory (YM*) is continuously connected to pure YM on ${\mathbb R}^4$. The small-volume confined theory is amenable to non-perturbative semi-classical analysis, like supersymmetric theories. The dynamics of YM theories with vector-like or chiral fermions can be studied within this framework.
• Figure 2: A cartoon of the magnetic quintet in the chiral non-supersymmetric $SU(2)$ gauge theory with an $I=3/2$ representation fermion. It may be viewed as a composite of 3 BPS and 2 $\overline {\rm KK}$ monopoles. These excitations, all with magnetic charge +1, repel each other in the absence of fermionic zero modes. The fermion zero mode exchanges generate a five-body interaction which leads to the formation of the magnetic quintet. This is the leading cause of the mass gap and the bosonic operator allowed by the $({\mathbb Z}_5)_{*}$ symmetry. An analogous topological excitation is forbidden in the supersymmetric theory by a continuous $U(1)_{*}$ shift symmetry.
• Figure 3: (a) is the monopole operator ${\cal M}_1$, e.g., (\ref{['monopole2']}), (\ref{['monQCD']}) dictated by the index theorem. (b) is the Yukawa vertex. (c) is a modified monopole operator $\widetilde{\cal M}_{\rm 1}$ e.g, (\ref{['monopole2mod']}), (\ref{['monQCD2']}) obtained upon Yukawa contractions. Note that $\widetilde{\cal M}_{\rm 1}$ has exactly two fermionic zero modes and can thus contribute to the superpotential.
• Figure 4: The moduli space of the chiral supersymmetric $SU(2)$$I=3/2$ theory on ${\mathbb R}^3 \times S^1$, with Higgs branch parameterized by $u \in \mathbb C$, and a Coulomb branch parameterized by $Y$. In the semi-classical domain, $Y \sim e^{-\phi +i \sigma}$, where $(\phi, \sigma) \in (S^1/{\mathbb Z}_2) \times S^1$. The geometrized $\sigma$ rotation is the topological $U(1)_J$ symmetry. The fixed point of the ${\mathbb Z}_2$ action shown by red-dotted line is the center-symmetric configuration. On ${\mathbb R}^3$, $(S^1/{\mathbb Z}_2)$ is replaced by ${\mathbb R}^{+}$, as the $\phi$ direction decompactifies into a semi-infinite cylinder. In the ${\mathbb R}^4$ limit, the Coulomb branch shrinks to zero and only the Higgs branch survives.
• Figure 5: (a) is the monopole operator ${\cal M}$ (\ref{['monMaj']}) with two zero modes and charge normalized to $+1$. (b) is the magnetic bion operator (\ref{['bion']}), with no zero mode and charge $+2$. The latter is stable via a fermionic paring mechanism, which overcomes Coulomb repulsion between constituent monopoles.