http://arxiv.org/abs/0902.3903
**Group field theory and simplicial quantum gravity**
Daniele Oriti

11 pages

(Submitted on 23 Feb 2009)

"We present a new Group Field Theory for 4d quantum gravity. It incorporates the constraints that give gravity from BF theory, and has quantum amplitudes with the explicit form of simplicial path integrals for 1st order gravity. The geometric interpretation of the variables and of the contributions to the quantum amplitudes is manifest. This allows a direct link with other simplicial gravity approaches, like quantum Regge calculus, in the form of the amplitudes of the model, and dynamical triangulations, which we show to correspond to a simple restriction of the same."

http://arxiv.org/abs/0902.3657
**Spectral Dimension of Spacetime in Quantum Gravity at a Lifgarbagez Point**
Petr Horava

11 pages, 1 figure

(Submitted on 23 Feb 2009)

"We extend the definition of "spectral dimension" (usually defined for fractal and lattice geometries) to theories on smooth spacetimes with anisotropic scaling. We show that in quantum gravity dominated by a Lifgarbagez point with dynamical critical exponent z in D+1 spacetime dimensions, the spectral dimension of spacetime is equal to d_s=1+D/z. In the case of gravity in 3+1 dimensions presented in arXiv:0901.3775, which is dominated by z=3 in the UV and flows to z=1 in the IR, the spectral dimension of spacetime flows from d_s=4 at large scales, to d_s=2 at short distances.

**Remarkably, this is the qualitative behavior of d_s found numerically by Ambjorn, Jurkiewicz and Loll in their causal dynamical triangulations approach to quantum gravity**."

Brief mention:

http://arxiv.org/abs/0902.3817
**Noncommutative D=4 gravity coupled to fermions**
Paolo Aschieri, Leonardo Castellani

19 pages

(Submitted on 23 Feb 2009)

http://arxiv.org/abs/0902.3823
**Noncommutative supergravity in D=3 and D=4**
Paolo Aschieri, Leonardo Castellani

22 pages

(Submitted on 23 Feb 2009)