New variables for classical and quantum gravity in all dimensions: I. Hamiltonian analysis
Abstract
Loop quantum gravity (LQG) relies heavily on a connection formulation of general relativity such that (1) the connection Poisson commutes with itself and (2) the corresponding gauge group is compact. This can be achieved starting from the Palatini or Holst action when imposing the time gauge. Unfortunately, this method is restricted to D + 1 = 4 spacetime dimensions. However, interesting string theories and supergravity theories require higher dimensions and it would therefore be desirable to have higher dimensional supergravity loop quantizations at one’s disposal in order to compare these approaches. In this series of papers we take first steps toward this goal. The present first paper develops a classical canonical platform for a higher dimensional connection formulation of the purely gravitational sector. The new ingredient is a different extension of the ADM phase space than the one used in LQG which does not require the time gauge and which generalizes to any dimension D > 1. The result is a YangMills theory phase space subject to Gauß, spatial diffeomorphism and Hamiltonian constraint as well as one additional constraint, called the simplicity constraint. The structure group can be chosen to be SO(1, D) or SO(D + 1) and the latter choice is preferred for purposes of quantization.
 Publication:

Classical and Quantum Gravity
 Pub Date:
 February 2013
 DOI:
 10.1088/02649381/30/4/045001
 arXiv:
 arXiv:1105.3703
 Bibcode:
 2013CQGra..30d5001B
 Keywords:

 General Relativity and Quantum Cosmology;
 High Energy Physics  Theory;
 Mathematical Physics
 EPrint:
 28 pages. v2: Journal version. Minor clarifications