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Construction of Bulk Fields with Gauge Redundancy

Idse Heemskerk

TL;DR

The paper develops a perturbative framework for constructing bulk gauge fields and gravity in AdS/CFT by fixing gauges and representing bulk operators as smeared boundary operators. It demonstrates that Gauss'-law constraints generate intrinsic non-locality in the bulk-boundary correspondence and derives leading-order smearing functions in generalized Coulomb and radial gauges for Maxwell fields and linearized gravity. The results illuminate how holography and locality coexist in gauge/gravity theories and provide explicit kernels linking bulk operators to boundary currents and stress tensors. These findings lay groundwork for covariant formulations and non-perturbative extensions of bulk reconstruction in AdS/CFT.

Abstract

We extend the construction of field operators in AdS as smeared single trace operators in the boundary CFT to gauge fields and gravity. Bulk field operators in a fixed gauge can be thought of as non-local gauge invariant observables. Non-local commutators result from the Gauss law constraint, which for gravity implies a perturbative notion of holography. We work out these commutators in a generalized Coulomb gauge and obtain leading order smearing functions in radial gauge.

Construction of Bulk Fields with Gauge Redundancy

TL;DR

The paper develops a perturbative framework for constructing bulk gauge fields and gravity in AdS/CFT by fixing gauges and representing bulk operators as smeared boundary operators. It demonstrates that Gauss'-law constraints generate intrinsic non-locality in the bulk-boundary correspondence and derives leading-order smearing functions in generalized Coulomb and radial gauges for Maxwell fields and linearized gravity. The results illuminate how holography and locality coexist in gauge/gravity theories and provide explicit kernels linking bulk operators to boundary currents and stress tensors. These findings lay groundwork for covariant formulations and non-perturbative extensions of bulk reconstruction in AdS/CFT.

Abstract

We extend the construction of field operators in AdS as smeared single trace operators in the boundary CFT to gauge fields and gravity. Bulk field operators in a fixed gauge can be thought of as non-local gauge invariant observables. Non-local commutators result from the Gauss law constraint, which for gravity implies a perturbative notion of holography. We work out these commutators in a generalized Coulomb gauge and obtain leading order smearing functions in radial gauge.

Paper Structure

This paper contains 9 sections, 64 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Local observables and gauge invariance
  3. Maxwell field in AdS
  4. AdS$_2$
  5. AdS$_{d+1>2}$
  6. Linearized Einstein gravity
  7. Gauss' law and holography
  8. Smearing function in radial gauge
  9. Discussion

Figures (1)

  • Figure 1: A Wilson line along $C_1$ connects a charged scalar to the boundary. The gauge invariant integral of $A$ along $C_2$ reduces to the scalar potential $A_0$ in radial gauge.