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#### Group field theory and simplicial gravity path integrals: A model for Holst-Plebanski gravity

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##### Fulltext (public)

1111.5842

(Preprint), 333KB

PRD85_044003.pdf

(Any fulltext), 277KB

##### Supplementary Material (public)

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##### Citation

Baratin, A., & Oriti, D. (2012). Group field theory and simplicial gravity path
integrals: A model for Holst-Plebanski gravity.* Physical Review D,* *85*:
044003. doi:10.1103/PhysRevD.85.044003.

Cite as: http://hdl.handle.net/11858/00-001M-0000-000F-86F5-C

##### Abstract

In a recent work, a dual formulation of group field theories as
non-commutative quantum field theories has been proposed, providing an exact
duality between spin foam models and non-commutative simplicial path integrals
for constrained BF theories. In light of this new framework, we define a model
for 4d gravity which includes the Immirzi parameter gamma. It reproduces the
Barrett-Crane amplitudes when gamma goes to infinity, but differs from existing
models otherwise; in particular it does not require any rationality condition
for gamma. We formulate the amplitudes both as BF simplicial path integrals
with explicit non-commutative B variables, and in spin foam form in terms of
Wigner 15j-symbols. Finally, we briefly discuss the correlation between
neighboring simplices, often argued to be a problematic feature, for example,
in the Barrett-Crane model.