Exact results for $$ {Z}_m^{\mathrm{OS}} $$ and $$ {Z}_2^{\mathrm{OS}} $$ with two mass scales and up to three loops

We consider the on-shell mass and wave function renormalization constants $$ {Z}_m^{\mathrm{OS}} $$ Z m OS and $$ {Z}_2^{\mathrm{OS}} $$ Z 2 OS up to three-loop order allowing for a second non-zero quark mass. We obtain analytic results in terms of harmonic polylogarithms and iterated integrals with the additional letters $$ \sqrt{1-{\tau}^2} $$ 1 − τ 2 and $$ \sqrt{1-{\tau}^2}/\tau $$ 1 − τ 2 / τ which extends the findings from ref. [1] where only numerical expressions are presented. Furthermore, we provide terms of order $$ \mathcal{O} $$ O (ϵ2) and $$ \mathcal{O} $$ O (ϵ) at two- and three-loop order which are crucial ingredients for a future four-loop calculation. Compact results for the expansions around the zero-mass, equal-mass and large-mass cases allow for a fast high-precision numerical evaluation.

Renormalization of the bilocal sine-Gordon model

The functional renormalization group treatment is presented for the two-dimensional sine-Gordon model including a bilocal term in the potential, which contributes to the flow at the tree level. It is shown that the flow of the bilocal term can substitute the evolution of the wave function renormalization constant, since it can recover the Kosterlitz–Thouless type phase transition. The flows can also reveal the connection between the sine-Gordon and the noninteracting Thirring models at a special value of the wave number parameter.

Phase structure of the Euclidean three-dimensional O(1) ghost model

We have treated the Euclidean three-dimensional O(1) ghost model with a modified version of the effective average action (EAA) renormalization group (RG) method, developed by us. We call it Fourier–Wetterich RG approach and it is used to investigate the occurrence of a periodic condensate in terms of the functional RG. The modification involves additional terms in the ansatz of the EAA, corresponding to the Fourier-modes of the periodic condensate. The RG flow equations are derived keeping the terms up to the fourth order of the gradient expansion (GE), however the numerical calculations are conducted in the second order (or next-to-leading order, NLO) of the GE. The expansion of the flow equations around the nontrivial minimum of the local potential takes into account properly the vertices induced by the periodic condensate even if the wave function renormalization is set to be field-independent. The numerical analysis reveals several different phases with three multicritical points.

Photon splitting in strongly magnetized medium with taking into account positronium influence

The process of the photon splitting, γ → γγ, is investigated in strongly magnetized vacuum with taking into account positronium influence. The dispersion properties of photons and the new polarization selection rules are obtained. The absorption rate of the leading photon splitting channels are calculated with taking account of the photon dispersion and wave function renormalization.

Higgs bosons in extra dimensions

In this paper, motivated by the recent discovery of a Higgs-like boson at the Large Hadron Collider (LHC) with a mass mH≃125 GeV , we review different models where the hierarchy problem is solved by means of a warped extra dimension. In the Randall–Sundrum (RS) model electroweak observables provide very strong bounds on the mass of KK modes which motivates extensions to overcome this problem. Two extensions are briefly discussed. One particular extension is based on the deformation of the metric such that it strongly departs from the AdS5 structure in the IR region while it goes asymptotically to AdS5 in the UV brane. This model has the IR brane close to a naked metric singularity (which is outside the physical interval) characteristic of soft-walls constructions. The proximity of the singularity provides a strong wave function renormalization for the Higgs field which suppresses the T and S parameters. The second class of considered extensions are based on the introduction of an extra gauge group in the bulk such that the custodial SU (2)R symmetry is gauged and protects the T parameter. By further enlarging the bulk gauge symmetry one can find models where the Higgs is identified with the fifth component of gauge fields and for which the Higgs potential along with the Higgs mass can be dynamically determined by the Coleman–Weinberg mechanism.

Inflation via gravitino condensation in dynamically broken supergravity

Gravitino-condensate-induced inflation via the super-Higgs effect is a UV-motivated scenario for both inflating the early universe and breaking local supersymmetry dynamically, entirely independent of any coupling to external matter. As an added benefit, this also removes the (as of yet unobserved) massless Goldstino associated to global supersymmetry breaking from the particle spectrum. In this review, we detail the pertinent properties and outline previously hidden details of the various steps required in this context in order to make contact with current inflationary phenomenology. The class of models of SUGRA we use to exemplify our approach are minimal four-dimensional N = 1 supergravity and extensions thereof with broken conformal symmetry. Therein, the gravitino condensate itself can play the role of the inflation, however the requirement of slow-roll necessitates unnaturally large values of the wave function renormalization. Nevertheless, there is an alternative scenario that may provide Starobinsky-type inflation, occurring in the broken-SUGRA phase around the nontrivial minima of the gravitino-condensate effective potential. In this scenario higher curvature corrections to the effective action, crucial for the onset of an inflationary phase, arise as a result of integrating out massive quantum gravitino fields in the path integral. The latter scenario is compatible with Planck satellite phenomenology but not with BICEP2 data.