Phys.Lett.B, 838, 137673 (2023)
On the Lagrangian holographic relation at D → 2 and 4 limits of gravity
H. Khodabakhshi1, Hong Lü1 and R. B. Mann2,3
1 Center for Joint Quantum Studies, Department of Physics, School of Science, Tianjin University, Tianjin 300350, China.
2 Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario, Canada, N2L 3G1.
3 Perimeter Institute, 31 Caroline St. N., Waterloo, Ontario, N2L 2Y5, Canada.
* h khodabakhshi@tju.edu.cn, mrhonglu@gmail.com, rbmann@uwaterloo.ca
Abstract
The gravitational Lagrangian can be written as a summation of a bulk and a total derivative term. For some theories of gravity such as Einstein gravity, or more general Lovelock gravities, there are Lagrangian holographic relations between the bulk and the total derivative term such that the latter is fully determined by the former. However at the D → 2&4 limit, the bulks of Einstein or Gauss-Bonnet theories become themselves total derivatives. Performing the Kaluza-Klein reduction on Einstein and Gauss-Bonnet gravities gives rise to some two dimensional or four-dimensional scalar-tensor theories respectively. We obtain the holographic relations for the D = 2 and D = 4 cases, which have the same form as the holographic relations in pure gravity in the foliation independent formalism.
