Non-supersymmetric Dualities Research Articles

Non-supersymmetric duality cascade of QCD(BF) via semiclassics on ℝ2× T2 with the baryon-’t Hooft flux

We study the phase diagrams of the bifundamental QCD (QCD(BF)) of different ranks, which is the 4d SU(N1) × SU(N2) gauge theory coupled with a bifundamental Dirac fermion. After discussing the anomaly constraints on possible vacuum structures, we apply a novel semiclassical approach on ℝ2× T2 with the baryon-’t Hooft flux to obtain the concrete dynamics. The 2d effective theory is derived by the dilute gas approximation of center vortices, and it serves as the basis for determining the phase diagram of the model under the assumption of adiabatic continuity. As an application, we justify the non-supersymmetric duality cascade between different QCD(BF), which has been conjectured in the large-N argument. Combined with the semiclassics and the large-N1,2 limit, we construct the explicit duality map from the parent theory, SU(N1) × SU(N2) QCD(BF), to the daughter theory, SU(N1) × SU(N2− N1) QCD(BF), including the correspondence of the coupling constants. We numerically examine the validity of the duality also for finite N1,2 within our semiclassics, finding a remarkable agreement of the phase diagrams between the parent and daughter sides.

Chiral gauge dynamics: candidates for non-supersymmetric dualities

We study the dynamics of chiral SU(N) gauge theories. These contain Weyl fermions in the symmetric or anti-symmetric representation of the gauge group, together with further fermions in the fundamental and anti-fundamental. We revisit an old proposal of Bars and Yankielowicz who match the ‘t Hooft anomalies of this theory to free fermions. We show that there are novel and, in some cases, quite powerful constraints on the dynamics in the large N limit.In addition, we study these SU(N) theories with an extra Weyl fermion transforming in the adjoint representation. Here we show that all 21 ‘t Hooft anomalies for global symmetries are matched with those of a Spin(8) gauge theory. This suggests a non-supersymmetric extension of the duality of Pouliot and Strassler. Finally, we also discuss some non-supersymmetric dualities with vector-like matter content for SO(N) and Sp(N) gauge theories and the constraints imposed by Weingarten inequalities.

Novel 3d bosonic dualities from bosonization and holography

We use 3d bosonization dualities to derive new non-supersymmetric dualities between bosonic quiver theories in 2 + 1 dimensions. It is shown that such dualities are a natural non-Abelian generalization of the bosonic particle-vortex duality. A special case of such dualities is applicable to Chern-Simons theories living on interfaces in 3 + 1 dimensional SU(N) Yang-Mills theory across which the theta angle jumps. We also analyze such interfaces in a holographic construction which provides further evidence for novel dualities between quiver gauge theories and gauge theories with adjoint scalars. These conjectured dualities pass some stringent consistency tests.

Nonsupersymmetric Dualities from Mirror Symmetry.

We study supersymmetry breaking perturbations of the simplest dual pair of (2+1)-dimensional N=2 supersymmetric field theories-the free chiral multiplet and N=2 super QED with a single flavor. We find dual descriptions of a phase diagram containing four distinct massive phases. The equivalence of the intervening critical theories gives rise to several nonsupersymmetric avatars of mirror symmetry: we find dualities relating scalar QED to a free fermion and Wilson-Fisher theories to both scalar and fermionic QED. Thus, mirror symmetry can be viewed as the multicritical parent duality from which these nonsupersymmetric dualities directly descend.

Seiberg duality versus hidden local symmetry

It is widely believed that the emergent magnetic gauge symmetry of SQCD is analogous to a hidden local symmetry (HLS). We explore this idea in detail, deriving the entire (spontaneously broken) magnetic theory by applying the HLS formalism to spontaneously broken SU(N) SQCD. We deduce the K\"ahler potential in the HLS description, and show that gauge and flavour symmetry are smoothly restored along certain scaling directions in moduli space. We propose that it is these symmetry restoring directions, associated with the R-symmetry of the theory, that allow full Seiberg duality. Reconsidering the origin of the magnetic gauge bosons as the rho-mesons of the electric theory, colour-flavour locking allows a simple determination of the parameter "a". Its value continuously interpolates between a=2 on the baryonic branch of moduli space - corresponding to "vector meson dominance" - and a=1 on the mesonic branch. Both limiting values are consistent with previous results in the literature. The HLS formalism is further applied to SO and Sp groups, where the usual Seiberg duals are recovered, as well as adjoint SQCD. Finally we discuss some possible future applications, including (naturally) the unitarisation of composite W scattering, blended Higgs/technicolour models, real world QCD and non-supersymmetric dualities.

Seiberg duality ande+e−experiments

Seiberg duality in supersymmetric gauge theories is the claim that two different theories describe the same physics in the infrared limit. However, one cannot easily work out physical quantities in strongly coupled theories and hence it has been difficult to compare the physics of the electric and magnetic theories. In order to gain more insight into the equivalence of two theories, we study the ``${e}^{+}{e}^{\ensuremath{-}}$'' cross sections into ``hadrons'' for both theories in the superconformal window. We describe a technique which allows us to compute the cross sections exactly in the infrared limit. They are indeed equal in the low-energy limit and the equality is guaranteed because of the anomaly matching condition. The ultraviolet behavior of the total ``${e}^{+}{e}^{\ensuremath{-}}$'' cross section is different for the two theories. We comment on proposed non-supersymmetric dualities. We also analyze the agreement of the ``$\ensuremath{\gamma}\ensuremath{\gamma}$'' and ``$\mathrm{WW}$'' scattering amplitudes in both theories, and in particular try to understand if their equivalence can be explained by the anomaly matching condition.

A comment on nonsupersymmetric fixed points and duality at large $N$

We review some of the problems associated with deriving field theoretic results from nonsupersymmetric AdS, focusing on how to control the behavior of the field theory along the flat directions. We discuss an example in which the origin of the moduli space remains a stable vacuum at finite N, and argue that it corresponds to an interacting CFT in three dimensions. Associated to this fixed point is a statement of nonsupersymmetric duality. Because 1/N corrections may change the global picture of the RG flow, the statement of duality is much weaker than in the supersymmetric case.