Gravity in $${\varvec{d=2+\epsilon }}$$ dimensions and realizations of the diffeomorphisms group

We discuss two separate realizations of the diffeomorphism group for metric gravity, which give rise to theories that are classically equivalent, but quantum mechanically distinct. We renormalize them in $$d=2+\epsilon $$ d = 2 + ϵ dimensions, developing a new procedure for dimensional continuation of metric theories and highlighting connections with the constructions that previously appeared in the literature. Our hope is to frame candidates for ultraviolet completions of quantum gravity in $$d>2$$ d > 2 and give some perturbative mean to assess their existence in $$d=4$$ d = 4 , but also to speculate on some potential obstructions in the continuation of such candidates to finite values of $$\epsilon $$ ϵ . Our results suggest the presence of a conformal window in d which seems to extend to values higher than four.

Gliding Down the QCD Transition Line, from Nf = 2 till the Onset of Conformality

We review the hot QCD transition with varying number of flavours, from two till the onset of the conformal window. We discuss the universality class for Nf=2, along the critical line for two massless light flavours, and a third flavour whose mass serves as an interpolator between Nf=2 and Nf=3. We identify a possible scaling window for the 3D O(4) universality class transition, and its crossover to a mean field behaviour. We follow the transition from Nf=3 to larger Nf, when it remains of first order, with an increasing coupling strength; we summarise its known properties, including possible cosmological applications as a model for a strong electroweak transition. The first order transition, and its accompanying second order endpoint, finally morphs into the essential singularity at the onset of the conformal window, following the singular behaviour predicted by the functional renormalisation group.

SQCD and pairs of pants

We show that the 4d$$ \mathcal{N} $$ N = 1 SU(3) Nf = 6 SQCD is the model obtained when compactifying the rank one E-string theory on a three punctured sphere (a trinion) with a particular value of flux. The SU(6) × SU(6) × U(1) global symmetry of the theory, when decomposed into the SU(2)3× U(1)3× SU(6) subgroup, corresponds to the three SU(2) symmetries associated to the three punctures and the U(1)3× SU(6) subgroup of the E8 symmetry of the E-string theory. All the puncture symmetries are manifest in the UV and thus we can construct ordinary Lagrangians flowing in the IR to any compactification of the E-string theory. We generalize this claim and argue that the $$ \mathcal{N} $$ N = 1 SU(N + 2) SQCD in the middle of the conformal window, Nf = 2N + 4, is the theory obtained by compactifying the 6d minimal (DN +3, DN +3) conformal matter SCFT on a sphere with two maximal SU(N + 1) punctures, one minimal SU(2) puncture, and with a particular value of flux. The SU(2N + 4) × SU(2N + 4) × U(1) symmetry of the UV Lagrangian decomposes into SU(N + 1)2× SU(2) puncture symmetries and the U(1)3× SU(2N + 4) subgroup of the SO(12 + 4N ) symmetry group of the 6d SCFT. The models constructed from the trinions exhibit a variety of interesting strong coupling effects. For example, one of the dualities arising geometrically from different pair-of-pants decompositions of a four punctured sphere is an SU(N + 2) generalization of the Intriligator-Pouliot duality of SU(2) SQCD with Nf = 4, which is a degenerate, N = 0, instance of our discussion.

Constraints on electroweak gauged unparticle model from the oblique parameters S and T

We calculate the one loop contribution from an unparticle gauged model, based on the group SU(2)[Formula: see text]U(1), to the electroweak oblique parameters [Formula: see text] and [Formula: see text]. Using the current bounds on [Formula: see text] and [Formula: see text] from electroweak measurements, we find the constraints on the scale dimension [Formula: see text] of the unparticle fermionic fields to be [Formula: see text] and the constraints on the conformal breaking scale [Formula: see text] to be [Formula: see text] Gev. The bounds on [Formula: see text] impose a lower limit on the conformal window of the unparticle fields which means that unparticle are not detectable below [Formula: see text] Gev.