5 research outputs found
Towards Loop Quantum Supergravity (LQSG) II. p-Form Sector
In our companion paper, we focussed on the quantisation of the
Rarita-Schwinger sector of Supergravity theories in various dimensions by using
an extension of Loop Quantum Gravity to all spacetime dimensions. In this
paper, we extend this analysis by considering the quantisation of additional
bosonic fields necessary to obtain a complete SUSY multiplet next to graviton
and gravitino in various dimensions. As a generic example, we study concretely
the quantisation of the 3-index photon of 11d SUGRA, but our methods easily
extend to more general p-form fields. Due to the presence of a Chern-Simons
term for the 3-index photon, which is due to local SUSY, the theory is
self-interacting and its quantisation far from straightforward. Nevertheless,
we show that a reduced phase space quantisation with respect to the 3-index
photon Gauss constraint is possible. Specifically, the Weyl algebra of
observables, which deviates from the usual CCR Weyl algebras by an interesting
twist contribution proportional to the level of the Chern-Simons theory, admits
a background independent state of the Narnhofer-Thirring type.Comment: 12 pages. v2: Journal version. Minor clarifications and correction
Hidden Quantum Gravity in 4d Feynman diagrams: Emergence of spin foams
We show how Feynman amplitudes of standard QFT on flat and homogeneous space
can naturally be recast as the evaluation of observables for a specific spin
foam model, which provides dynamics for the background geometry. We identify
the symmetries of this Feynman graph spin foam model and give the gauge-fixing
prescriptions. We also show that the gauge-fixed partition function is
invariant under Pachner moves of the triangulation, and thus defines an
invariant of four-dimensional manifolds. Finally, we investigate the algebraic
structure of the model, and discuss its relation with a quantization of 4d
gravity in the limit where the Newton constant goes to zero.Comment: 28 pages (RevTeX4), 7 figures, references adde
Poincare 2-group and quantum gravity
We show that General Relativity can be formulated as a constrained
topological theory for flat 2-connections associated to the Poincar\'e 2-group.
Matter can be consistently coupled to gravity in this formulation. We also show
that the edge lengths of the spacetime manifold triangulation arise as the
basic variables in the path-integral quantization, while the state-sum
amplitude is an evaluation of a colored 3-complex, in agreement with the
category theory results. A 3-complex amplitude for Euclidean quantum gravity is
proposed.Comment: v3: published versio