Perturbative and nonperturbative studies of CFTs with MN global symmetry

Fixed points in three dimensions described by conformal field theories with \ensuremath{M N}_{m,n} = O(m)^n\rtimes S_nMNm,n=O(m)n⋊Sn global symmetry have extensive applications in critical phenomena. Associated experimental data for m=n=2m=n=2 suggest the existence of two non-trivial fixed points, while the \varepsilonε expansion predicts only one, resulting in a puzzling state of affairs. A recent numerical conformal bootstrap study has found two kinks for small values of the parameters mm and nn, with critical exponents in good agreement with experimental determinations in the m=n=2m=n=2 case. In this paper we investigate the fate of the corresponding fixed points as we vary the parameters mm and nn. We find that one family of kinks approaches a perturbative limit as mm increases, and using large spin perturbation theory we construct a large mm expansion that fits well with the numerical data. This new expansion, akin to the large NN expansion of critical O(N)O(N) models, is compatible with the fixed point found in the \varepsilonε expansion. For the other family of kinks, we find that it persists only for n=2n=2, where for large mm it approaches a non-perturbative limit with \Delta_\phi\approx 0.75Δϕ≈0.75. We investigate the spectrum in the case \ensuremath{M N}_{100,2}MN100,2 and find consistency with expectations from the lightcone bootstrap.

THE EFFECT OF A LIGHT RADION ON THE TRIVIALITY BOUND ON HIGGS MASS

In this paper we study how the triviality bound on Higgs mass in the context of the Standard Model is modified by a light stabilized radion of the Goldberger–Wise variety. Our approach is inherently perturbative. Including the radion contribution to β(λ) and β(gt) to one-loop we evolve the Higgs self coupling λ from the cutoff Λ(=<ϕ>) down to the electroweak scale μ0=v. The triviality bound is obtained by requiring that [Formula: see text] which is the perturbative limit. We also study the effect of small changes in the UVBC on the triviality bound both in the presence and absence of a light radion.

Reorganizing Finite Temperature Field Theory: Part I.: Scalar Field Theory

I present a method for self-consistently including the effects of screening in finite-temperature field theory calculations. The method reproduces the perturbative limit in the weak-coupling limit and for intermediate couplings this method has much better convergence than standard perturbation theory. The method relies on a reorganization of perturbation theory accomplished by shifting the expansion point used to calculate quantum loop corrections. I will present results from a three-loop calculation within this formalism for scalar λϕ4.