Branes and Quantization for an a-Model Complexification of Einstein Gravity in Almost Kähler Variables

Vacaru, Sergiu I.

doi:10.1142/s0219887809003849

Cited by 29 publications

(115 citation statements)

References 55 publications

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“…This can be important for research in classical and quantum gravity, string theory, deformation quantization, geometric flows with algebroid structure etc. [38,39,40,41]. The present work can be considered as a supersymmetric / superflow partner of our recent works [24,23,32,33] where the direction is developed for supergeometric flow models and exact solutions in superstring MGTs, in particular, related to R 2 theories and cosmology.…”

Section: Introductionmentioning

confidence: 81%

On supersymmetric geometric flows andR2inflation from scale invariant supergravity

2017

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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.

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Section: Introductionmentioning

confidence: 81%

On supersymmetric geometric flows andR2inflation from scale invariant supergravity

2017

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“…Such constructions were elaborated, for instance, in Refs. [4,5,6] following geometric ideas originally considered for vector and tangent bundles [7,8].…”

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confidence: 99%

On General Solutions of Einstein Equations

Vacaru

2011

Int. J. Geom. Methods Mod. Phys.

220

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We show how the Einstein equations with cosmological constant (and/or various types of matter field sources) can be integrated in a very general form following the anholonomic deformation method for constructing exact solutions in four and five dimensional gravity (S. Vacaru, IJGMMP 4 (2007) 1285. In this letter, we prove that such a geometric method can be used for constructing general non-Killing solutions. The key idea is to introduce an auxiliary linear connection which is also metric compatible and completely defined by the metric structure but contains some torsion terms induced nonholonomically by generic off-diagonal coefficients of metric. There are some classes of nonholonomic frames with respect to which the Einstein equations (for such an auxiliary connection) split into an integrable system of partial differential equations. We have to impose additional constraints on generating and integration functions in order to transform the auxiliary connection into the Levi-Civita one. This way, we extract general exact solutions (parametrized by generic off-diagonal metrics and depending on all coordinates) in Einstein gravity and five dimensional extensions.

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“…By nonholonomic frame transforms and distortions of the canonical d-connection, the above metric can be rewritten in canonical almost-Kähler variables on 6-d internal space, as we prove in [48]. We omit such constructions (being very important in various models of deformation and brane quantization of MGTs and geometric evolution theories [10,11,63,70]) in this work.…”

Section: -D Deformations With Ns 3-form and 6-d Almost Kähler Intermentioning

confidence: 99%

“…This involves phenomenological applications in high energy physics, various approaches to quantum gravity and attempts to explain observational data in modern accelerating cosmology. For review of such subjects, we cite respectively [1,2,3,4,5,6,7], on superstrings, flux compactifications, D-branes, instantons etc; [8,9,10,11], on geometric methods in quantum gravity; and [12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30], on MGTs and applications, see also references therein.The supergravity/superstring and MGT gravitational field equations are formulated as sophisticated systems of nonlinear partial differential equations, PDEs. Various types of advanced analytic and numeric methods for constructing exact and approximate solutions of such equations have been explored.…”

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confidence: 99%

Off-diagonal deformations of Kerr metrics and black ellipsoids in heterotic supergravity

Vacaru

Irwin

2017

Eur. Phys. J. C

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Geometric methods for constructing exact solutions of equations of motion with first order α corrections to the heterotic supergravity action implying a nontrivial Yang-Mills sector and six-dimensional, 6-d, almostKähler internal spaces are studied. In 10-d spacetimes, general parametrizations for generic off-diagonal metrics, nonlinear and linear connections, and matter sources, when the equations of motion decouple in very general forms are considered. This allows us to construct a variety of exact solutions when the coefficients of fundamental geometric/physical objects depend on all higher-dimensional spacetime coordinates via corresponding classes of generating and integration functions, generalized effective sources and integration constants. Such generalized solutions are determined by generic off-diagonal metrics and nonlinear and/or linear connections; in particular, as configurations which are warped/compactified to lower dimensions and for Levi-Civita connections. The corresponding metrics can have (non-) Killing and/or Lie algebra symmetries and/or describe (1 + 2)-d and/or (1 + 3)-d domain wall configurations, with possible warping nearly almost-Kähler manifolds, with gravitational and gauge instantons for nonlinear vacuum configurations and effective polarizations of cosmological and interaction constants encoding string gravity effects. A series of examples of exact solutions describing generic off-diagonal supergravity modifications to black hole/ellipsoid and solitonic configurations are provided and analyzed. We prove that it is possible to reproduce the Kerr and other type black solutions in general relativity (with certain types of string corrections) in the 4-d case and to generalize the solutions to non-vacuum configurations in (super-) gravity/string theories.a

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Branes and Quantization for an a-Model Complexification of Einstein Gravity in Almost Kähler Variables

Cited by 29 publications

References 55 publications

On supersymmetric geometric flows andR2inflation from scale invariant supergravity

On supersymmetric geometric flows andR2inflation from scale invariant supergravity

On General Solutions of Einstein Equations

Off-diagonal deformations of Kerr metrics and black ellipsoids in heterotic supergravity

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