# Poincaré-Einstein Holography for Forms via Conformal Geometry in the Bulk

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*A. Rod Gover; Emanuele Latini; Andrew Waldron*

The authors study higher form Proca equations on Einstein manifolds with boundary data along conformal infinity. They solve these Laplace-type boundary problems formally, and to all orders, by constructing an operator which projects arbitrary forms to solutions. They also develop a product formula for solving these asymptotic problems in general. The central tools of their approach are (i) the conformal geometry of differential forms and the associated exterior tractor calculus, and (ii) a generalised notion of scale which encodes the connection between the underlying geometry and its boundary. The latter also controls the breaking of conformal invariance in a very strict way by coupling conformally invariant equations to the scale tractor associated with the generalised scale.

#### Table of Contents

# Table of Contents

## Poincare-Einstein Holography for Forms via Conformal Geometry in the Bulk

- Cover Cover11 free
- Title page i2 free
- Chapter 1. Introduction 18 free
- Chapter 2. Bulk conformal geometry and extension problems 714 free
- 2.1. Riemannian conventions 714
- 2.2. Conformal and almost Riemannian geometry 714
- 2.3. Extension problems 916
- 2.4. The generalised divergence extension problem 916
- 2.5. Conformal tractor calculus 1219
- 2.6. The calculus of scale 1421
- 2.7. The Laplace–Robin solution generating algebra 1522
- 2.8. Product solutions 1623

- Chapter 3. Tractor exterior calculus 2330
- Chapter 4. The exterior calculus of scale 4350
- Chapter 5. Higher form Proca equations 5966
- Chapter 6. Obstructions, detours, gauge operators and 𝑄-curvature 7784
- Appendix A. The ambient manifold 8794
- Appendix B. List of common symbols 9198
- Bibliography 93100
- Back Cover Back Cover1108