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Register a new userProduct Group S-Confinement in SUSY Gauge Theories
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Benjamin Lillard
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We propose a new set of s-confining theories with product gauge groups and no tree-level superpotential, based on a model with one antisymmetric matter field and four flavors of quarks. For each product group we find a set of gauge-invariant operators which satisfy the t Hooft anomaly matching conditions, and we identify the dynamically generated superpotential which reproduces the classical constraints between operators. Several of these product gauge theories confine without breaking chiral symmetry, even in cases where the classical moduli space is quantum-modified. These results may be useful for composite model building, particularly in cases where small meson operators are absent, or for theories with multiple natural energy scales, and may provide new ways to break supersymmetry dynamically.
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As an extension of the weak perturbation theory obtained in recent analysis on infinite-derivative non-local non-Abelian gauge theories motivated from p-adic string field theory, and postulated as direction of UV-completion in 4-D Quantum Field Theory (QFT), here we investigate the confinement conditions and $beta-$function in the strong coupling regime. We extend the confinement criterion, previously obtained by Kugo and Ojima for the local theory based on the Becchi-Rouet-Stora-Tyutin (BRST) invariance, to the non-local theory, by using a set of exact solutions of the corresponding local theory. We show that the infinite-derivatives which are active in the UV provides finite contributions also in the infrared (IR) limit and provide a proof of confinement, granted by the absence of the Landau pole. The main difference with the local case is that the IR fixed point is moved to infinity. We also show that in the limit of the energy scale of non-locality $M rightarrow infty$ we reproduce the local theory results and see how asymptotic freedom is properly recovered.
Quantum field theories of strongly interacting matter sometimes have a useful holographic description in terms of the variables of a gravitational theory in higher dimensions. This duality maps time dependent physics in the gauge theory to time dependent solutions of the Einstein equations in the gravity theory. In order to better understand the process by which real world theories such as QCD behave out of thermodynamic equilibrium, we study time dependent perturbations to states in a model of a confining, strongly coupled gauge theory via holography. Operationally, this involves solving a set of non-linear Einstein equations supplemented with specific time dependent boundary conditions. The resulting solutions allow one to comment on the timescale by which the perturbed states thermalize, as well as to quantify the properties of the final state as a function of the perturbation parameters. We comment on the influence of the dual gauge theorys confinement scale on these results, as well as the appearance of a previously anticipated universal scaling regime in the abrupt quench limit.
Recently a non-perturbative formula for the RG flow between UV and IR fixed points of the coefficient in the trace of the energy momentum tensor of the Euler density has been obtained for N=1 SUSY gauge theories by relating the trace and R-current anomalies. This result is compared here with an earlier perturbation theory analysis based on a naturally defined metric on the space of couplings for general renormalisable quantum field theories. This approach is specialised to N=1 supersymmetric theories and extended, using consistency arguments, to obtain the Euler coefficient at fixed points to 4-loops. The result agrees completely, to this order, with the exact formula.
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.
A solution to the infinite coupling problem for N=2 conformal supersymmetric gauge theories in four dimensions is presented. The infinitely-coupled theories are argued to be interacting superconformal field theories (SCFTs) with weakly gauged flavor groups. Consistency checks of this proposal are found by examining some low-rank examples. As part of these checks, we show how to compute new exact quantities in these SCFTs: the central charges of their flavor current algebras. Also, the isolated rank 1 E_6 and E_7 SCFTs are found as limits of Lagrangian field theories.
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