Models of geometric flows pertaining to R 2 scale invariant (super) gravity theories coupled to conformally invariant matter fields are investigated. Related to this work are supersymmetric scalar manifolds that are isomorphic to the Kählerian spaces M n = SU (1, 1 + k)/U (1) × SU (1 + k) as generalizations of the non-supersymmetric analogs with SO(1, 1 + k)/SO(1 + k) manifolds. For curved superspaces with geometric evolution of physical objects, a complete supersymmetric theory has to be elaborated on nonholonomic (super) manifolds and bundles determined by non-integrable superdistributions with additional constraints on (super) field dynamics and geometric evolution equations. We also consider generalizations of Perelman's functionals using such nonholonomic variables which result in the decoupling of geometric flow equations and Ricci soliton equations with supergravity modifications of the R 2 gravity theory. As such, it is possible to construct exact non-homogeneous and locally anisotropic cosmological solutions for various types of (super) gravity theories modelled as modified Ricci soliton configurations. Such solutions are defined by employing the general ansatz encompassing coefficients of generic off-diagonal metrics and generalized connections that depend generically on all spacetime coordinates. We consider nonholonomic constraints resulting in diagonal homogeneous configurations encoding contributions from possible nonlinear parametric geometric evolution scenarios, off-diagonal interactions and anisotropic polarization/ modification of physical constants. In particular, we analyze small parametric deformations when the underlying scale symmetry is preserved and the nontrivial anisotropic vacuum corresponds to generalized de Sitter spaces. Such configurations may mimic quantum effects whenever transitions to flat space are possible. Our approach allows us to generate solutions with scale violating terms induced by geometric flows, off-diagonal interactions and supersymmetric modifications of effective potentials. We study reconstructing the formalism for (super) geometric flows and modified gravity cosmological scenarios. We also analyze the conditions under which such modified mimetic type theories and solutions reproduce the Starobinsky inflationary models in the double scalar approach.
An attempt is made to fill in the particle-mass gap between the ordinary masses of a few hundred GeV and the grand unification mass of lOI5 GeV by incorporating two and three stages of spontaneous symmetry breaking In the various descents of SO(10) to the low-energy symmetry SU(2), X U(l) X SU (3),. It is shown that intermediate masses of order 10" GeV can exist in the particle-mass gap. Values lower than 101° GeV can only be achieved at the expense of pushing the grand unifying mass to the Planck mass. Also similarities in the gauge structure and differences in the Higgs-scalar and fermion representations of the SU(2), X SU(2), X SU(4),-based Pati-Salam model and its synthesis into SO(10) are pointed out.
We introduce Weyl's scale symmetry into the standard model (SM) as a local symmetry. This necessarily introduces gravitational interactions in addition to the local scale invariance group U (1) and the SM groups SU(3) × SU(2) × U(1). The only other new ingredients are a new scalar field σ and the gauge field for U (1) we call the Weylon. A noteworthy feature is that the system admits the Stückelberg-type compensator. The σ couples to the scalar curvature as (−ζ/2) σ 2 R, and is in turn related to a Stückelberg-type compensator ϕ by σ ≡ M P e −ϕ/M P with the Planck mass M P . The particular gauge ϕ = 0 in the Stückelberg formalism corresponds to σ = M P , and the Hilbert action is induced automatically. In this sense, our model presents yet another mechanism for breaking scale invariance at the classical level. We show that our model naturally accommodates the chaotic inflation scenario with no extra field.
We present an N = 1 supersymmetric non-Abelian compensator formulation for a vector multiplet in three-dimensions. Our total field content is the off-shell vector multiplet (A µ I , λ I ) with the off-shell scalar multiplet (ϕ I , χ I ; F I ) both in the adjoint representation of an arbitrary non-Abelian gauge group. This system is reduced to a supersymmetric σ -model on a group manifold, in the zero-coupling limit. Based on this result, we formulate a 'self-dual' non-Abelian vector multiplet in three-dimensions. By an appropriate identification of parameters, the mass of the self-dual vector multiplet is quantized. Additionally, we also show that the self-dual non-Abelian vector multiplet can be coupled to supersymmetric Dirac-Born-Infeld action. These results are further reformulated in superspace to get a clear overall picture.
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