Phases of QCD$_3$ from Non-SUSY Seiberg Duality and Brane Dynamics

TL;DR

This work provides a non-supersymmetric Seiberg duality framework for orientifold QCD$_3$ with USp gauge groups by embedding the theory in a type IIB brane setup and deriving a magnetic dual. The duality organizes IR phases: 3d bosonization arises from magnetic squark condensation, while dynamical symmetry breaking emerges in regions where the magnetic squarks condense partially or fully; string theory brane dynamics interpret these transitions via open-string tachyon condensation and brane reconnection. The analysis connects the Komargodski–Seiberg flavor-breaking scenario to a UV-complete dual description and clarifies the role of the Wilson–Fisher fixed point in the bosonized phase, with a complementary discussion of massive-squark and potential IR CFT regimes at large flavor number. The results extend the understanding of 3d YM-CS theories with fundamental matter, offer a UV perspective on 3d bosonization, and outline open directions for unitary groups and broader gauge families.

Abstract

We consider a non-supersymmetric USp Yang-Mills Chern-Simons gauge theory coupled to fundamental flavours. The theory is realised in type IIB string theory via an embedding in a Hanany-Witten brane configuration which includes an orientifold and anti-branes. We argue that the theory admits a magnetic Seiberg dual. Using the magnetic dual we identify dynamics in field theory and brane physics that correspond to various phases, obtaining a better understanding of 3d bosonization and dynamical breaking of flavour symmetry in USp QCD$_3$ theory. In field theory both phases correspond to magnetic 'squark' condensation. In string theory they correspond to open string tachyon condensation and brane reconnection. We also discuss other phases where the magnetic 'squark' is massive. Finally, we briefly comment on the case of unitary gauge groups.

Figures (7)

• Figure 1: Diagram A represents the phases of QCD$_3$ anticipated by Komargodski:2017keh. Region I is the phase of bosonization, region II the phase of symmetry breaking and region III a phase with an IR CFT description. The curve separating the regions II and III occurs at some $N_*$ which is potentially a function of both $\kappa$ and $N_c$. The wiggly features of this curve are not a statement about its actual shape, but rather a symbolic depiction of our ignorance about its precise form. A constraint on the shape of this curve was determined in Ref. Komargodski:2017keh. Diagram B represents the phases of orientifold QCD$_3$ that arise naturally (under a certain set of assumptions) from the magnetic description of the theory. With the exception of the region $\kappa<-N_f$ where no Seiberg duality is available the remaining regions I, II/II$'$ and III, are expected to describe the same IR physics as the corresponding regions in diagram A.
• Figure 2: The electric theory. It is a non-supersymmetric $USp(2N_c)$ Yang-Mills theory with a level $2k$ Chern-Simons term and $2N_f$ flavours.
• Figure 3: The magnetic theory. It is a non-supersymmetric $USp(2N_f+2k-2N_c+2)$ Yang-Mills theory with a level $-2k$ Chern-Simons term.
• Figure 4: Perturbative contributions to a scalar mass.
• Figure 5: A realisation of the bosonized phase in the magnetic theory. $N_f$ flavor branes reconnect with color branes. The gauge group is $USp(2\kappa)$.