Canonical Charges and Asymptotic Symmetries in Four Dimensional Conformal Gravity Holography

Lovrekovic, Iva

doi:10.22323/1.231.0155

Cited by 1 publication

(6 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The size of ASA or coordinates on which corresponding γ (1) ij depends, do not impose restriction on the construction of these global solutions. We have constructed geon solutions also from four (studied as well in in [15] and in [18]), three and two dimensional ASA where in the latest case γ (1) ij depend on all the coordinates on the manifold. Geons can be described as smooth horizonless geometries, and it was shown in [8] that they can be connected to an onset of the super radiance instability, which translates into connecting the nonlinear, weakly turbulent instability of AdS to super radiant instability of Kerr-AdS.…”

Section: Resultsmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

“…ij and obtain the set of asymptotic Killing vectors (KVs) ξ (0) i . And the subleading order equation (18) for the given subset of Killing vectors defines γ (1) ij or we can define γ (1) ij to obtain these Killing vectors.…”

Section: Asymptotic Symmetries In Conformal Gravitymentioning

confidence: 99%

“…we can insert (86) in (18) and find the further KVs. (To avoid clutter we have written γ (1) ij (86) that is not of the most general form, the most general form of the γ (1) ij is given in [17].)…”

Section: Appendix B: Classification According To the Generators Of Thmentioning

confidence: 99%

“…The vanishing of the linear term in the FG expansion (6) leads to the vanishing of the subleading Killing equation (18) which means the asymptotic symmetry algebra is pure conformal algebra. If the linear term in (6) does not vanish, one needs to analyse ASA using (18), which can be performed in one of the two ways 1. First can be called "top-down" approach in which we bring full solution of CG to FG form for flat γ (0) ij .…”

Section: Analysis Of the Leading Order Conformal Killing Equationmentioning

confidence: 99%

See 4 more Smart Citations

Asymptotic symmetry algebra of conformal gravity

Irakleidou

Lovrekovic

2017

Phys. Rev. D

Self Cite

View full text Add to dashboard Cite

We compute asymptotic symmetry algebras of conformal gravity. Due to more general boundary conditions allowed in conformal gravity in comparison to those in Einstein gravity, we can classify the corresponding algebras. The highest algebra for non-trivial boundary conditions is five dimensional and it leads to global geon solution with non-vanishing charges.PACS numbers: 04.20. Ha, 04.50.Kd, 95.35.+d, ContentsIntroduction 2 Conformal gravity 2Asymptotic symmetries in conformal gravity 3 Analysis of the leading order conformal Killing equation 4Asymptotic symmetry algebras of the known global solutions 5Highest asymptotic symmetry algebras 6 Five dimensional algebra 6 Four dimensional algebras 7Global solutions for asymptotic symmetry algebras 8 Global solution from five dimensional algebra 8 Global solution from four dimensional algebras 8 Constant γ(1) ij 8 γ (1) ij dependent on two coordinates 9 Global solution from three dimensional subalgebra 10 Global solution dependent on three coordinates on the manifold 11 Conclusion 11Acknowledgements 12Appendix 12Appendix A: Dependency on coordinates 12Appendix B: Classification according to the generators of the conformal group 13 Conformal gravity (CG) is higher derivative theory of gravity that has recently obtained many interests since it can reproduce the solutions obtained by Einstein gravity (EG) [19], which is one of the main requirements for the effective gravity theory.Its advantage is that it is two loop renormalizable while EG is not, however it contains ghosts while EG is ghost free. From theoretical aspects CG has been studied by 't Hooft in series of articles [11,26,27]. In [12], he considers conformal symmetry to play a fundamental role for understanding the physics at the Planck energy scale. It arises from the twistor string theory [4] and as a counterterm from five dimensional EG. On the phenomenological grounds it has been studied by Mannheim to explain the galactic rotation curves without the addition of the dark matter [21,22]. Furthermore, it was proven in [9] that the analogous, linear, term which in two dimensional toy model provides additional matter, is allowed to appear in CG. In four dimensional CG, that term leads to the response function that appears in CG beside the standard EG response function, which is Brown-York stress energy tensor. This linear term was included taking into account the most general boundary condition, as explained in [9]. Asymptotic symmetry algebra (ASA) of CG for vanishing of the linear term is conformal algebra, which is known to be ASA of Einstein gravity. The equations of motion of CG allow for linear term in the expansion of the metric, while equations of motion of EG do not. Linear term can be further restricted with the choice of its components. Taking the conformal algebra as ASA for trivial boundary conditions (linear term = 0) we show that the boundary conditions can be classified according to the subalgebras when linear term = 0.The response functions define boundary charges in the AdS/CF T framework whi...

show abstract