Gauge from Holography and Holographic Gravitational Observables

Zapata, José A.  (Centro de Ciencias Matemáticas, Universidad Nacional Autónoma de México, Morelia, MICH, Mexico)

08 February 2019

Abstract: In a spacetime divided into two regions U1 and U2 by a hypersurface Σ , a perturbation of the field in U1 is coupled to perturbations in U2 by means of the holographic imprint that it leaves on Σ . The linearized gluing field equation constrains perturbations on the two sides of a dividing hypersurface, and this linear operator may have a nontrivial null space. A nontrivial perturbation of the field leaving a holographic imprint on a dividing hypersurface which does not affect perturbations on the other side should be considered physically irrelevant. This consideration, together with a locality requirement, leads to the notion of gauge equivalence in Lagrangian field theory over confined spacetime domains. Physical observables in a spacetime domain U can be calculated integrating (possibly nonlocal) gauge invariant conserved currents on hypersurfaces such that ΣU . The set of observables of this type is sufficient to distinguish gauge inequivalent solutions. The integral of a conserved current on a hypersurface is sensitive only to its homology class [Σ] , and if U is homeomorphic to a four ball the homology class is determined by its boundary S=Σ . We will see that a result of Anderson and Torre implies that for a class of theories including vacuum general relativity all local observables are holographic in the sense that they can be written as integrals of over the two-dimensional surface S . However, nonholographic observables are needed to distinguish between gauge inequivalent solutions.


Published in: Advances in High Energy Physics 2019 (2019) 9781620
Published by: Hindawi
DOI: 10.1155/2019/9781620
arXiv: 1704.07959
License: CC-BY-3.0



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