Three-dimensional dualities with bosons and fermions

TL;DR

The paper presents a broad framework of non-supersymmetric IR dualities in three-dimensional Chern-Simons-matter theories with bosons and fermions in the fundamental representation across SU, U, USp, and SO gauge groups. By varying two relevant mass parameters, it reveals intricate phase diagrams with lines of critical behavior and multicritical fixed points, and it predicts emergent IR symmetries and time-reversal invariance in certain regimes. Extensive cross-checks include coupling to background fields, mapping of monopole and baryon operators, and consistency under RG flows and level-rank dualities. The work also derives new Abelian dualities, illustrates them with concrete examples, and discusses potential extensions to quantum phases beyond the classical phase-diagram analysis.

Abstract

We propose new infinite families of non-supersymmetric IR dualities in three space-time dimensions, between Chern-Simons gauge theories (with classical gauge groups) with both scalars and fermions in the fundamental representation. In all cases we study the phase diagram as we vary two relevant couplings, finding interesting lines of phase transitions. In various cases the dualities lead to predictions about multi-critical fixed points and the emergence of IR quantum symmetries. For unitary groups we also discuss the coupling to background gauge fields and the map of simple monopole operators.

Figures (9)

• Figure 1: Masks for the phases of the various dualities. The phases in circles are either fully gapped (possibly with topological order) or contain Goldstone bosons. The thick blue lines correspond to the tuning of one mass parameter that conjecturally yields extra massless matter. The shaded circle in the middle covers the detailed structure of the phase diagram around the origin, which we do not know precisely.
• Figure 2: $\qquad O(2)$ WF $\times$$\psi$$\qquad\longleftrightarrow\qquad$$U(2)_{-1/2}$ with $\phi,\psi$. $\quad$ Phase diagram.
• Figure 3: $\qquad SU(2)_{1/2}$ with $\phi, \psi$$\qquad\longleftrightarrow\qquad$$U(1)_{-3/2}$ with $\phi,\psi$$\times\, U(1)_1$. $\;$ Phase diagram. On both sides we emphasized an emergent time-reversal symmetry (with an anomaly) with respect to the dashed line.
• Figure 4: $\qquad U(1)_{3/2}$ with $\phi,\psi$$\qquad\longleftrightarrow\qquad$$U(1)_{-3/2}$ with $\phi,\psi$$\times\, U(1)_1$. $\quad$ Phase diagram. We emphasized a quantum time-reversal symmetry (with an anomaly) with respect to the dashed line.
• Figure 5: $\qquad U(1)_{-1/2}$ with $\phi,\psi$$\qquad\text{vs.}\qquad$$U(1)_{1/2}$ with $\phi,\psi$$\times\,U(-1)_1$. $\;$ Phase diagrams. The two theories are not dual as the phases do not match (the two theories are mapped into each other by time reversal). However each diagram is symmetric with respect to the dashed line, due to a self-duality.