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We construct asymptotically safe extensions of the standard model by adding gauged vectorlike fermions. Using large number-of-flavor techniques we argue that all gauge couplings, including the hypercharge and, under certain conditions, the Higgs coupling, can achieve an interacting ultraviolet fixed point.

We propose a direct test of the existence of gauge duals for nonsupersymmetric asymptotically free gauge theories developing an infrared fixed point by computing the S parameter in the electric and dual magnetic description. In particular we show that at the lower bound of the conformal window the magnetic S parameter, i.e., the one determined via the dual magnetic gauge theory, assumes a simple expression in terms of the elementary magnetic degrees of freedom. The results further support our recent conjecture of the existence of a universal lower bound on the S parameter and indicates that it is an ideal operator for counting the active physical degrees of freedom within the conformal window. Our results can be directly used to unveil possible four-dimensional gauge duals and constitute the first explicit computation of a nonperturbative quantity, in the electric variables, via nonsupersymmetric gauge duality.

We construct an effective Lagrangian which illustrates why color deconfines when chiral symmetry is restored in hot gauge theories with quarks in the fundamental representation. For quarks in the adjoint representation we show that, while deconfinement and the chiral transition do not need to coincide, entanglement between them is still present. Extension to the chemical potential driven transition is discussed.

We show that all of the relevant features of a phase transition can be determined using a non-order-parameter field which is a physical state of the theory. This fact allows us to describe the deconfining transition of the pure Yang-Mills theory via the physical excitations rather than using the Polyakov loop.