Jean-François Fortin

Metastable supersymmetry breaking and multitrace deformations of SQCD

Metastable vacua in supersymmetric QCD in the presence of single and multitrace deformations of the superpotential are explored, with the aim of obtaining an acceptable phenomenology. The metastable vacua appear at one loop, have a broken R-symmetry, and a magnetic gauge group that is completely Higgsed. With only a single trace deformation, the adjoint fermions from the meson superfield are approximately massless at one loop, even though they are massive at tree level and R-symmetry is broken. Consequently, if charged under the standard model, they are unacceptably light. A multitrace quadratic deformation generates fermion masses proportional to the deformation parameter. Phenomenologically viable models of direct gauge mediation can then be obtained, and some of their features are discussed.

Scale without conformal invariance: An example

Abstract We give an explicit example of a model in D = 4 − ϵ space–time dimensions that is scale but not conformally invariant, is unitary, and has finite correlators. The invariance is associated with a limit cycle renormalization group (RG) trajectory. We also prove, to second order in the loop expansion, in D = 4 − ϵ , that scale implies conformal invariance for models of any number of real scalars. For models with one real scalar and any number of Weyl spinors we show that scale implies conformal invariance to all orders in perturbation theory.

Current OPEs in superconformal theories

It’s well known that in conformal theories the two- and three-point functions of a subset of the local operators — the conformal primaries — suffice, via the operator product expansion (OPE), to determine all local correlation functions of operators. It’s less well known that, in superconformal theories, the OPE of superdescendants is generally undetermined from those of the superprimaries, and there is no universal notion of superconformal blocks. We recall these and related aspects of 4d (S)CFTs, and then we focus on the super operator product expansion (sOPE) of conserved currents in 4d

Scale without Conformal Invariance at Three Loops

\mathcal{N} = 1

Tunneling constraints on effective theories of stable de Sitter space

SCFTs. The current-current OPE J(x)J(0) has applications to general gauge mediation. We show how the superconformal symmetry, when combined with current conservation, determines the OPE coefficients of superconformal descendants in terms of those of the superconformal primaries. We show that only integer-spin real superconformal-primary operators of vanishing R-charge, and their descendants, appear in the sOPE. We also discuss superconformal blocks for four-point functions of the conserved currents.

Cyclic unparticle physics

A bstractWe present the theoretical underpinnings of scale without conformal invariance in quantum field theory. In light of our results the gradient-flow interpretation of renormalization-group (RG) flow is challenged, due to deep connections between scaleinvariant theories and recurrent behaviors in the RG. We show that, on scale-invariant trajectories, there is a redefinition of the dilatation current that leads to generators of dilatations that generate dilatations. Finally, we develop a systematic algorithm for the search of scale-invariant trajectories in perturbation theory.

Landau pole in the pyramid scheme

A bstractWe carry out a three-loop computation that establishes the existence of scale without conformal invariance in dimensional regularization with the MS scheme in unitary theories in d = 4 − ϵ spacetime dimensions. We also comment on the effects of scheme changes in theories with many couplings, as well as in theories that live on non-conformal scale-invariant renormalization group trajectories. Stability properties of such trajectories are analyzed, revealing both attractive and repulsive directions in a specific example. We explain how our results are in accord with those of Jack & Osborn on a c-theorem in d = 4 (and d = 4 − ϵ) dimensions. Finally, we point out that limit cycles with turning points are unlike limit cycles with continuous scale invariance.

Undetected Higgs decays and neutrino masses in gauge mediated, lepton number violating models

The regions in the Minimal Supersymmetric Standard Model with the minimal amount of fine-tuning of electroweak symmetry breaking are presented for general messenger scale. No a priori relations among the soft supersymmetry breaking parameters are assumed and fine-tuning is minimized with respect to all the important parameters which affect electroweak symmetry breaking. The superpartner spectra in the minimally tuned region of parameter space are quite distinctive with large stop mixing at the low scale and negative squark soft masses at the high scale. The minimal amount of tuning increases enormously for a Higgs mass beyond roughly 120 GeV.