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Register a new userMore Exact Results on Chiral Gauge Theories: the Case of the Symmetric Tensor
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We study dynanics of $SU(N-4)$ gauge theories with fermions in rank-2 symmetric tensor and $N$ anti-fundamental representations, by perturbing supersymmetric theories with anomaly-mediated supersymmetry breaking. We find the $SU(N)times U(1)$ global symmetry is dynamically broken to $SO(N)$ for $Ngeq 17$, a different result from conjectures in the literature. For $N<17$, theories flow to infrared fixed points.
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We derive exact formulae for the partition function and the expectation values of Wilson/t Hooft loops, thus directly checking their S-duality transformations. We focus on a special class of N=2 gauge theories on S^4 with fundamental matter. In particular we show that, for a specific choice of the masses, the matrix model integral defining the gauge theory partition function localizes around a finite set of critical points where it can be explicitly evaluated and written in terms of generalized hypergeometric functions. From the AGT perspective the gauge theory partition function, evaluated with this choice of masses, is viewed as a four point correlator involving the insertion of a degenerated field. The well known simplicity of the degenerated correlator reflects the fact that for these choices of masses only a very restrictive type of instanton configurations contributes to the gauge theory partition function.
We study $N=1$ SUSY gauge theories in four dimensions with gauge group $Spin(7)$ and $N_f$ flavors of quarks in the spinorial representation. We find that in the range $6< N_f < 15$, this theory has a long distance description in terms of an $SU(N_f-4)$ gauge theory with a symmetric tensor and $N_f$ antifundamentals. As a spin-off, we obtain by deforming along a flat direction a dual description of the theories based on the exceptional gauge group $G_2$ with $N_f$ fundamental flavors of quarks.
At large N, a field theory and its orbifolds (given by projecting out some of its fields) share the same planar graphs. If the parent-orbifold relation continues even nonperturbatively, then properties such as confinement and chiral symmetry breaking will appear in both parent and orbifold. N=1 supersymmetric Yang-Mills has many nonsupersymmetric orbifolds which resemble QCD. A nonperturbative parent-orbifold relation predicts many surprising effects, exactly valid at large N, and expected to suffer only mild 1/N corrections. These include degeneracies among bosonic hadrons and exact predictions for domain wall tensions. Other predictions are valid even when supersymmetry in the parent is broken. Since these theories are QCD-like, simulation is possible, so these predictions may be numerically tested. The method also relates wide classes of nonsupersymmetric theories.
We investigate the IR phases of non-supersymmetric (non-SUSY) $SO(N_c)$ gauge theories with $N_F$ fermions in the vector representation obtained by perturbing the SUSY theory with anomaly mediated SUSY breaking (AMSB). We find that of the wide variety of phases appearing in the SUSY theory only two survive: for $N_F<frac{3}{2} (N_c-2)$ the theory confines, breaking the $SU(N_F)$ global symmetry to $SO(N_F)$, while for $frac{3}{2} (N_c-2)<N_F<3(N_c-2)$ the theory flows to a (super)-conformal fixed point. The abelian Coulomb and free magnetic phases do not survive and collapse to the confining phase. We also investigate the behavior of loop operators in order to provide a clear distinction between the confining and screened phases. With the choice of $Spin(N_c)$ for the global structure of the gauge group, we find that the electric Wilson loop indeed obeys an area law, providing one of the first demonstrations of true confinement with chiral symmetry breaking in a non-SUSY theory. We identify monopole condensation as the dynamics underlying confinement. These monopoles arise naturally for $N_F=N_c-2$. The case with smaller number of flavors can be obtained by integrating out flavors, and we confirm numerically that the monopole condensate persists in the presence of AMSB and mass perturbations.
I propose a controlled approximation to QCD-like theories with massless quarks by employing supersymmetric QCD perturbed by anomaly-mediated supersymmetry breaking. They have identical massless particle contents. Thanks to the ultraviolet-insensitivity of anomaly mediation, dynamics can be worked out exactly when $m ll Lambda$, where $m$ is the size of supersymmetry breaking and $Lambda$ the dynamical scale of the gauge theory. I demonstrate that chiral symmetry is dynamically broken for $N_{f} leq frac{3}{2} N_{c}$ while the theories lead to non-trivial infrared fixed points for larger number of flavors. While there may be a phase transition as $m$ is increased beyond $Lambda$, qualitative agreements with expectations in QCD are encouraging and suggest that two limits $m ll Lambda$ and $m gg Lambda$ may be in the same universality class.
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