Dualized Gravity beyond Linear Approximation

Abstract

We will construct a loop space formalism for general relativity, and construct the Polyakov variables as connections for such a loop space. We will use these Polyakov variables to construct a dual theory of gravity beyond linear approximation. It will be demonstrated that this loop space duality reduces to the Hodge duality for linearized gravity. Furthermore, a loop space curvature will be constructed from this Polyakov variable. It will be shown that this loop space curvature vanishes in the absence of topological defects, and so it can be used to investigate gravitational monopoles. We will also construct the suitable monopole charge for such gravitational monopoles.

arXiv comment16 pages

References in corpus (39)

• Unity of Superstring Dualities
• E_11 and M Theory
• Gravito-electromagnetism
• Duality in Gravity and Higher Spin Gauge Fields
• Global Aspects of Electric-Magnetic Duality
• Duality in linearized gravity
• Strongly Coupled Gravity and Duality
• Consistent deformations of dual formulations of linearized gravity: A no-go result
• Gauge Theories under Incorporation of a Generalized Uncertainty Principle
• A note on spin-s duality
• Gravitational Casimir effect
• Symmetries and Compactifications of (4,0) Conformal Gravity
• Generalised geometry, eleven dimensions and E11
• Anomaly of the Electromagnetic Duality of Maxwell Theory
• Singular Monopoles and Gravitational Instantons
• Generalised geometry from the ground up
• A Generalized Duality Symmetry for Nonabelian Yang-Mills Fields
• A Nonabelian Yang-Mills Analogue of Classical Electromagnetic Duality
• Static Gravitational Global Monopoles
• CKM Matrix and Fermion Masses in the Dualized Standard Model
• 't Hooft's Order-Disorder Parameters and the Dual Potential
• Dual actions for massless, partially-massless and massive gravitons in (A)dS
• Gravitational Wu-Yang Monopoles
• Neutrino Oscillations in the Dualized Standard Model
• Some Remarks on Gravitational Global Monopoles
• A note about a pure spin-connection formulation of General Relativity and spin-2 duality in (A)dS
• Flavour-Changing Neutral Currents in the Dualized Standard Model
• The Dualized Standard Model and its Applications
• 3+1 decomposition in modified gravities within the Palatini formalism and some applications
• Palatini gravity with nonmetricity, torsion, and boundaries in metric and connection variables
• Massive Dual Spinless Fields Revisited
• Superloop Space
• Topological Defects in a Deformed Gauge Theory
• Dimensional reduction via a novel Higgs mechanism
• Monopoles in Superloop Space
• Renormalizing gravity: a new insight into an old problem
• Polyakov Loops for the ABJ Theory
• Supersymmetric Duality in Deformed Superloop Space
• Gravitational monopoles, anomalies and M$E_8$ bundles