Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2009-06-14
Nucl.Phys.B825:268-302,2010
Physics
High Energy Physics
High Energy Physics - Theory
38 pages; v2. reference added + minor changes; v3. published version; v4. minor changes
Scientific paper
10.1016/j.nuclphysb.2009.09.027
We define a theory of gravity by constructing a gravitational holonomy operator in twistor space. The theory is a gauge theory whose Chan-Paton factor is given by a trace over elements of Poincar\'{e} algebra and Iwahori-Hecke algebra. This corresponds to a fact that, in a spinor-momenta formalism, gravitational theories are invariant under spacetime translations and diffeomorphism. The former symmetry is embedded in tangent spaces of frame fields while the latter is realized by a braid trace. We make a detailed analysis on the gravitational Chan-Paton factor and show that an S-matrix functional for graviton amplitudes can be expressed in terms of a supersymmetric version of the holonomy operator. This formulation will shed a new light on studies of quantum gravity and cosmology in four dimensions.
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