George Zoupanos

Finite SU(3){sup 3} model

We consider N = 1 supersymmetric gauge theories based on the group SU(N)1×SU(N)2×…×SU(N)k with matter content (N,N*,1,…,1)+(1,N,N*,…,1)+…+(N*,1,1,…,N) as candidates for the unification symmetry of all particles. In particular we examine to which extent such theories can become finite, and find that a necessary condition is that there should be exactly three families. From phenomenological considerations an SU(3)3 model is singled out. We consider an all‐loop and a two‐loop finite model based on this gauge group and we study their predictions concerning the third generation quark masses.

Reduction of Couplings in Quantum Field Theories with Applications in Finite Theories and the MSSM

We apply the method of reduction of couplings in a Finite Unified Theory and in the MSSM. The method consists on searching for renormalization group invariant relations among couplings of a renormalizable theory holding to all orders in perturbation theory. It has a remarkable predictive power, since it leads to relations between gauge and Yukawa couplings in the dimensionless sectors and relations involving the trilinear terms and the Yukawa couplings, as well as a sum rule among scalar masses in the soft breaking sector, at the GUT scale. In both the MSSM and the FUT model we predict the masses of the top and bottom quarks and the light Higgs in remarkable agreement with the experiment. Furthermore we also predict the masses of the other Higgses, as well as the supersymmetric spectrum, the latter being in very comfortable agreement with the LHC bounds on supersymmetric particles.

Reduction of N=1, E8 SYM over SU(3)/U(1)×U(1)×Z3 and its four-dimensional effective action

Abstract We propose an extension of the Standard Model inspired by the E 8 × E 8 Heterotic String. In order that a reasonable effective Lagrangian is presented we neglect everything else other than the ten-dimensional N = 1 supersymmetric Yang–Mills sector associated with one of the gauge factors and certain couplings necessary for anomaly cancellation. We consider a compactified space–time M 4 × B 0 / Z 3 , where B 0 is the nearly Kahler manifold SU ( 3 ) / U ( 1 ) × U ( 1 ) and Z 3 is a freely acting discrete group on B 0 . Then we reduce dimensionally the E 8 on this manifold and we employ the Wilson flux mechanism leading in four dimensions to an SU ( 3 ) 3 gauge theory with the spectrum of a N = 1 supersymmetric theory. We compute the effective four-dimensional Lagrangian and demonstrate that an extension of the Standard Model is obtained with interesting features including a conserved baryon number and fixed tree level Yukawa couplings and scalar potential. The spectrum contains new states such as right-handed neutrinos and heavy vector-like quarks.

Reduction of N=1, E_8 SYM over SU(3)/U(1) x U(1) x Z_3 and its four-dimensional effective action

Abstract We propose an extension of the Standard Model inspired by the E 8 × E 8 Heterotic String. In order that a reasonable effective Lagrangian is presented we neglect everything else other than the ten-dimensional N = 1 supersymmetric Yang–Mills sector associated with one of the gauge factors and certain couplings necessary for anomaly cancellation. We consider a compactified space–time M 4 × B 0 / Z 3 , where B 0 is the nearly Kahler manifold SU ( 3 ) / U ( 1 ) × U ( 1 ) and Z 3 is a freely acting discrete group on B 0 . Then we reduce dimensionally the E 8 on this manifold and we employ the Wilson flux mechanism leading in four dimensions to an SU ( 3 ) 3 gauge theory with the spectrum of a N = 1 supersymmetric theory. We compute the effective four-dimensional Lagrangian and demonstrate that an extension of the Standard Model is obtained with interesting features including a conserved baryon number and fixed tree level Yukawa couplings and scalar potential. The spectrum contains new states such as right-handed neutrinos and heavy vector-like quarks.

Reduction of Couplings: Applications in Finite Theories and the MSSM

The method of reduction of couplings is applied to a Finite Unified Theory and in the MSSM. We search for renormalization group invariant relations among couplings of a renormalizable theory which holds to all orders in perturbation theory. The method leads to relations, at the unification scale, between gauge and Yukawa couplings (in the dimensionless sectors of the theory) and relations among the couplings of the trilinear terms and the Yukawa couplings, as well as a sum rule among the scalar masses and the gaugino mass (in the soft breaking sector). In the Finite Unified Theory model we predict, with remarkable agreement with the experiment, the masses of the top and bottom quarks while our predictions for the light Higgs mass and the rest supersymmetric spectrum masses are in comfortable agreement with the LHC bounds on Higgs and supersymmetric particles. In the case of the reduced MSSM the predictions are less successful but recent improvements in the code used to calculate the Higgs masses give promises for better results.

Reduction of couplings in a finite GUT and the MSSM

We apply the method of reduction of couplings in a Finite Unified Theory and in the MSSM. The method consists on searching for renormalization group invariant relations among couplings of a renormalizable theory holding to all orders in perturbation theory. In both cases we predict the masses of the top and bottom quarks and the light Higgs in remarkable agreement with the experiment. Moreover, we predict the masses of the other Higgses too, as well as the supersymmetric spectrum, the latter being in very confortable agreement with the LHC bounds on supersymmetric particles.

The trinification model SU(3)3 from orbifolds for fuzzy spheres

In this review, we consider an N = 4 supersymmetric SU(3N) gauge theory defined on the Minkowski spacetime. Then we apply an orbifold projection leading to an N = 1 supersymmetric SU(N)3 model, with a truncated particle spectrum. Then, we present the dynamical generation of (twisted) fuzzy spheres as vacuum solutions of the projected field theory, breaking the SU(N)3 spontaneously to a chiral effective theory with unbroken gauge group the trinification group, SU(3)3.

Reduction of N=1N=1, E8E8 SYM over SU(3)/U(1)×U(1)×Z3SU(3)/U(1)×U(1)×Z3 and its four-dimensional effective action

Abstract We propose an extension of the Standard Model inspired by the E 8 × E 8 Heterotic String. In order that a reasonable effective Lagrangian is presented we neglect everything else other than the ten-dimensional N = 1 supersymmetric Yang–Mills sector associated with one of the gauge factors and certain couplings necessary for anomaly cancellation. We consider a compactified space–time M 4 × B 0 / Z 3 , where B 0 is the nearly Kahler manifold SU ( 3 ) / U ( 1 ) × U ( 1 ) and Z 3 is a freely acting discrete group on B 0 . Then we reduce dimensionally the E 8 on this manifold and we employ the Wilson flux mechanism leading in four dimensions to an SU ( 3 ) 3 gauge theory with the spectrum of a N = 1 supersymmetric theory. We compute the effective four-dimensional Lagrangian and demonstrate that an extension of the Standard Model is obtained with interesting features including a conserved baryon number and fixed tree level Yukawa couplings and scalar potential. The spectrum contains new states such as right-handed neutrinos and heavy vector-like quarks.