Gauge from Holography and Holographic Gravitational Observables

Abstract EN

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 ∂Σ⊂∂U.

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.