Non-Supersymmetric Seiberg Duality, Orientifold QCD and Non-Critical Strings

TL;DR

The paper argues for a non-supersymmetric Seiberg-like electric–magnetic duality in orientifold QCD (OQCD) by defining electric theories with $U(N_c)$ gauge groups and fermions in (anti)symmetric representations, and magnetic duals with ranks $N_f-N_c\mp 4$. It embeds both sides in a tachyon-free non-critical Type 0$'$B string background, deriving duality via D-brane boundary/crosscap monodromies and showing anomaly matching. At large $N$ the duality follows from planar equivalence with ${\cal N}=1$ SQCD, while finite-$N$ evidence comes from anomaly checks and the string construction, plus a predicted conformal window: for OQCD-AS, ${3\over 2}N_c-{20\over 3}\le N_f\le 3N_c+{4\over 3}$, and for OQCD-S, ${3\over 2}N_c+{20\over 3}\le N_f\le 3N_c-{4\over 3}$, with $N_c>5$. The analysis also discusses moduli space lifting at finite $N$, the role of quartic couplings, and implications for IR dynamics, offering a concrete framework for non-supersymmetric dualities and their string-theoretic underpinnings.

Abstract

We propose an electric-magnetic duality and conjecture an exact conformal window for a class of non-supersymmetric U(N_c) gauge theories with fermions in the (anti)symmetric representation of the gauge group and N_f additional scalar and fermion flavors. The duality exchanges N_c with N_f -N_c \mp 4 leaving N_f invariant, and has common features with Seiberg duality in N=1 SQCD with SU or SO/Sp gauge group. At large N the duality holds due to planar equivalence with N=1 SQCD. At finite N we embed these gauge theories in a setup with D-branes and orientifolds in a non-supersymmetric, but tachyon-free, non-critical type 0B string theory and argue in favor of the duality in terms of boundary and crosscap state monodromies as in analogous supersymmetric situations. One can verify explicitly that the resulting duals have matching global anomalies. Finally, we comment on the moduli space of these gauge theories and discuss other potential non-supersymmetric examples that could exhibit similar dualities.

Figures (1)

• Figure 1: The conjectured phase structure of OQCD as a function of the number of flavors $N_f$. At infinite $N$ we recover the phase structure of ${\cal N}=1$ SQCD with gauge group $U(N_c)$. This picture makes sense for $N_c>5$.