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Some aspects of holographic W-gravity

Wei Li, Stefan Theisen

Abstract

We use the Chern-Simons formulation of higher spin theories in three dimensions to study aspects of holographic W-gravity. Concepts which were useful in studies of pure bulk gravity theories, such as the Fefferman-Graham gauge and the residual gauge transformations, which induce Weyl transformations in the boundary theory and their higher spin generalizations, are reformulated in the Chern-Simons language. Flat connections that correspond to conformal and lightcone gauges in the boundary theory are considered.

Some aspects of holographic W-gravity

Abstract

We use the Chern-Simons formulation of higher spin theories in three dimensions to study aspects of holographic W-gravity. Concepts which were useful in studies of pure bulk gravity theories, such as the Fefferman-Graham gauge and the residual gauge transformations, which induce Weyl transformations in the boundary theory and their higher spin generalizations, are reformulated in the Chern-Simons language. Flat connections that correspond to conformal and lightcone gauges in the boundary theory are considered.

Paper Structure

This paper contains 15 sections, 216 equations.

Table of Contents

  1. Introduction
  2. Spin two
  3. Generalities
  4. Conformal gauge
  5. $\mu$ - gauge
  6. Spin three and higher
  7. Generalities
  8. Conformal gauge
  9. $\mu$ - gauge
  10. Conclusions
  11. Conventions
  12. $\mathfrak{sl}(N)$
  13. $\mathfrak{sl}(2)$
  14. $\mathfrak{sl}(3)$
  15. Some explicit results for $\textrm{SL}(N)$