Effective Weinberg-Salam Model from Higher Dimensions

International Journal of Modern Physics D

We consider an eight-dimensional gravitational theory, which possesses a principle fiber bundle structure, with Lorentz-scalar fields coupled to the metric. One of them plays the role of a Higgs field and the other one of a dilaton field. The effective cosmological constant is interpreted as a Higgs potential. As usual we introduce by hand the Yukawa couplings. The extra dimensions are a SU(2)L×U(1)Y×SU(2)R group manifold. A Dirac field is coupled to the metric. As a result, we obtain an effective four-dimensional theory which contains all couplings of a Weinberg-Salam-Glashow theory in a curved space-time. The true masses of the gauge bosons and of the first two fermions families are given by the theory.

International Journal of Modern Physics A, 2001

We extend the previously proposed generalized gauge theory formulation of the Chern–Simons type and topological Yang–Mills type actions into Yang–Mills type actions. We formulate gauge fields and Dirac–Kähler matter fermions by all degrees of differential forms. The simplest version of the model which includes only zero and one-form gauge fields accommodated with the graded Lie algebra of SU (2|1) supergroup leads the Weinberg–Salam model. Thus the Weinberg–Salam model formulated by noncommutative geometry is a particular example of the present formulation.

International Journal of Modern Physics A, 2007

Non-Abelian higher gauge theory has recently emerged as a generalization of standard gauge theory to higher-dimensional (two-dimensional in the present context) connection forms, and as such, it has been successfully applied to the non-Abelian generalizations of the Yang–Mills theory and 2-form electrodynamics. (2+1)-dimensional gravity, on the other hand, has been a fertile testing ground for many concepts related to classical and quantum gravity, and it is therefore only natural to investigate whether we can find an application of higher gauge theory in this latter context. In the present paper we investigate the possibility of applying the formalism of higher gauge theory to gravity in 2+1 dimensions, and we show that a nontrivial model of (2+1)-dimensional gravity coupled to scalar and tensorial matter fields — the ΣΦEA model — can be formulated as a higher gauge theory (as well as a standard gauge theory). Since the model has a very rich structure — it admits as solutions black...

arXiv: High Energy Physics - Theory, 2019

The one-loop effective action for the scalar field part of a non-Abelian gauge theory based on a general gauge group of the form $G\times U(1)$, where the gauge group $G$ is arbitrary, is calculated. A complex scalar field, both Abelian and non-Abelian gauge fields and Dirac fermions coupled to gauge and scalar fields are included. A general mass term for the Dirac fields that includes a pseudoscalar term as well as both scalar and pseudoscalar Yukawa couplings is considered. The background field method is used in its manifestly gauge condition independent and gauge invariant form to isolate the divergent part of the one-loop effective action and to calculate the associated renormalisation group functions. Terms in the renormalised effective action up to and including those quadratic in the curvature are calculated using renormalisation group methods. The background scalar field is not assumed to be constant, so the second order derivative terms in the effective action can be calcul...

Journal of High Energy Physics, 2006

1999

It is well known that, in the first-order formalism, pure three-dimensional gravity is just the BF theory. Similarly, four-dimensional general relativity can be formulated as BF theory with an additional constraint term added to the Lagrangian. In this paper we show that the same is true also for higherdimensional Einstein gravity: in any dimension gravity can be described as a constrained BF theory. Moreover, in any dimension these constraints are quadratic in the B field. After describing in details the structure of these constraints, we scketch the “spin foam” quantization of these theories, which proves to be quite similar to the spin foam quantization of general relativity in three and four dimensions. In particular, in any dimension, we solve the quantum constraints and find the so-called simple representations and intertwiners. These exhibit a simple and beautiful structure that is common to all dimensions. ∗E-mail addresses: freidel,krasnov,puzio@phys.psu.edu

Proceedings of 7th International Conference on Mathematical Methods in Physics — PoS(ICMP 2012), 2013

Physical Review D, 2007

2021

We give a brief overview how to couple general relativity to the Standard Model of elementary particles, within the higher gauge theory framework, suitable for the spinfoam quantization procedure. We begin by providing a short review of all relevant mathematical concepts, most notably the idea of a categorical ladder, 3-groups and generalized parallel transport. Then, we give an explicit construction of the algebraic structure which describes the full Standard Model coupled to Einstein-Cartan gravity, along with the classical action, written in the form suitable for the spinfoam quantization procedure. We emphasize the usefulness of the 3-group concept as a superior tool to describe gauge symmetry, compared to an ordinary Lie group, as well as the possibility to employ this new structure to classify matter fields and study their spectrum, including the origin of fermion families.

Physical Review D, 2006