# Diffeomorphisms and Weyl transformations in AdS_3 gravity

@article{Bautier1999DiffeomorphismsAW, title={Diffeomorphisms and Weyl transformations in AdS\_3 gravity}, author={Karin Bautier}, journal={arXiv: High Energy Physics - Theory}, year={1999} }

It is shown that the AdS_3 gravity action with boundary terms is non invariant under diffeomorphisms and that its Lie derivative has the form of the Weyl anomaly in two dimensions. This variation is compensated by a Weyl transformation of the boundary metric when the radial derivative of the metric on the boundary is expressed in terms of the stress tensor of a Liouville field. The obtained invariance of the action under the combined transformation of a diffeomorphism and a Weyl transformation…

## 13 Citations

### Diffeomorphisms and holographic anomalies

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Using the relation between diffeomorphisms in the bulk and Weyl transformations on the boundary, we study the Weyl transformation properties of the bulk metric on-shell and of the boundary action. We…

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Abstract
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- 2001

In this thesis we study two different approaches to holography, and comment on the possible relation between
them. The first approach is an analysis of the high-energy regime of quantum gravity in…

## References

SHOWING 1-8 OF 8 REFERENCES

### The holographic Weyl anomaly

- PhysicsJournal of High Energy Physics
- 1998

We calculate the Weyl anomaly for conformal field theories that can be described via the adS/CFT correspondence. This entails regularizing the gravitational part of the corresponding supergravity…

### SUPER WEYL ANOMALIES IN THE AdS/CFT CORRESPONDENCE

- Physics
- 1999

Anomalies of N=(4,4) superconformal field theories coupled to a conformal supergravity background in two dimensions are computed by using the AdS/CFT correspondence. We find that Weyl, axial gauge…

### Central charges in the canonical realization of asymptotic symmetries: An example from three dimensional gravity

- Mathematics
- 1986

It is shown that the global charges of a gauge theory may yield a nontrivial central extension of the asymptotic symmetry algebra already at the classical level. This is done by studying three…

### The asymptotic dynamics of three-dimensional Einstein gravity with a negative cosmological constant

- Physics
- 1995

Liouville theory is shown to describe the asymptotic dynamics of three-dimensional Einstein gravity with a negative cosmological constant. This is because (i) Chern - Simons theory with a gauge group…

### Conformal Invariants.

- Physics, MedicineProceedings of the National Academy of Sciences of the United States of America
- 1926

### Field theory anomalies from the AdS/CFT correspondence, Talk given at Strings 99, Postdam, Germany

- 1999