Quantum Gravity and Renormalization: The Tensor Track

We propose a new program to quantize and renormalize gravity based on recent progress on the analysis of large random tensors. We compare it briefly with other existing approaches.

[1]  Simple spin networks as Feynman graphs , 1999, hep-th/9903192.

[2]  P. Di Francesco,et al.  2D gravity and random matrices , 1993 .

[3]  R. Gurau.  The 1/N Expansion of Colored Tensor Models , 2010, 1011.2726.

[4]  Razvan Gurau,et al.  The Complete 1/N Expansion of Colored Tensor Models in Arbitrary Dimension , 2011, 1102.5759.

[5]  Carlo Rovelli.  Quantum gravity , 2008, Scholarpedia.

[6]  H. Grosse,et al.  Renormalisation of ϕ4-Theory on Noncommutative ℝ4 in the Matrix Base , 2004, hep-th/0401128.

[7]  Non-commutative Renormalization , 2004, 0705.0705.

[8]  C. Rovelli,et al.  Loop-quantum-gravity vertex amplitude. , 2007, Physical review letters.

[9]  Razvan Gurau,et al.  Colored Group Field Theory , 2009, 0907.2582.

[10]  Bergfinnur Durhuus,et al.  Quantum Geometry: A Statistical Field Theory Approach , 1997 .

[11]  S. Alexandrov,et al.  Critical Overview of Loops and Foams , 2010, 1009.4475.

[12]  Vincent Rivasseau,et al.  The 1/N expansion of colored tensor models in arbitrary dimension , 2011, 1101.4182.

[13]  L. Sindoni.  Gravity as an emergent phenomenon: a GFT perspective , 2011, 1105.5687.

[14]  M. Smerlak,et al.  Bubble Divergences: Sorting out Topology from Cell Structure , 2011, 1103.3961.

[15]  H. Nicolai,et al.  Loop quantum gravity: an outside view , 2005, hep-th/0501114.

[16]  D. Oriti.  Foundations of Space and Time: The microscopic dynamics of quantum space as a group field theory , 2011, 1110.5606.

[17]  R. Gurau.  A generalization of the Virasoro algebra to arbitrary dimensions , 2011, 1105.6072.

[18]  D. Oriti,et al.  Group field theory renormalization - the 3d case: power counting of divergences , 2009, 0905.3772.

[19]  Simone Severini,et al.  Quantum graphity: A model of emergent locality , 2008, 0801.0861.

[20]  J. Ryan,et al.  Colored Tensor Models - a Review , 2011, 1109.4812.

[21]  V. Rivasseau,et al.  A Translation-Invariant Renormalizable Non-Commutative Scalar Model , 2008, 0802.0791.

[22]  V. Rivasseau.  Towards Renormalizing Group Field Theory , 2011, 1103.1900.

[23]  A. Baratin,et al.  Group field theory and simplicial gravity path integrals: A model for Holst-Plebanski gravity , 2011, 1111.5842.

[24]  J. Magnen,et al.  Linearized group field theory and power-counting theorems , 2010, 1002.3592.

[25]  Group Field Theory: An Overview , 2005, hep-th/0505016.

[26]  F. Saueressig,et al.  Renormalization group flow of quantum gravity in the Einstein-Hilbert truncation , 2002 .

[27]  F. David,et al.  A model of random surfaces with non-trivial critical behaviour , 1985 .

[28]  A. Baratin,et al.  Ten questions on Group Field Theory (and their tentative answers) , 2011, 1112.3270.

[29]  Elisa Ercolessi,et al.  The Renormalization Group and Critical Phenomena , 2001 .

[30]  L. Sindoni.  Emergent Models for Gravity: an Overview of Microscopic Models , 2011, 1110.0686.

[31]  L. Sindoni,et al.  Emergent models for gravity: an overview , 2011 .

[32]  C. Rovelli,et al.  Spin foams as Feynman diagrams , 2000, gr-qc/0002083.

[33]  Bergfinnur Durhuus,et al.  THREE-DIMENSIONAL SIMPLICIAL QUANTUM GRAVITY AND GENERALIZED MATRIX MODELS , 1991 .

[34]  D. Oriti.  A quantum field theory of simplicial geometry and the emergence of spacetime , 2006, hep-th/0612301.

[35]  M. Gross.  Tensor models and simplicial quantum gravity in >2-D , 1992 .

[36]  Muxin Han,et al.  Asymptotics of the spin foam amplitude on simplicial manifold: Euclidean theory , 2011, 1109.0500.

[37]  Naoki Sasakura,et al.  TENSOR MODEL FOR GRAVITY AND ORIENTABILITY OF MANIFOLD , 1991 .

[38]  K. Krasnov,et al.  A new spin foam model for 4D gravity , 2007, 0708.1595.

[39]  Loop Quantum Gravity: An Inside View , 2006, hep-th/0608210.

[40]  Joseph Ben Geloun,et al.  A Renormalizable 4-Dimensional Tensor Field Theory , 2011, 1111.4997.

[41]  M. Stephanov,et al.  Random Matrices , 2005, hep-ph/0509286.

[42]  R. Gurau.  Universality for Random Tensors , 2011, 1111.0519.

[43]  J. Jurkiewicz,et al.  The universe from scratch , 2005, hep-th/0509010.

[44]  Valentin Bonzom,et al.  Critical behavior of colored tensor models in the large N limit , 2011, 1105.3122.

[45]  E. Trubowitz,et al.  An intrinsic 1/N expansion for many-Fermion systems , 1993 .

[46]  C. Rovelli.  A Critical Look at Strings , 2011, 1108.0868.

[47]  V. Kazakov.  Bilocal Regularization of Models of Random Surfaces , 1985 .

[48]  A. Baratin,et al.  Diffeomorphisms in group field theories , 2011, 1101.0590.

[49]  D. Oriti.  Group field theory as the microscopic description of the quantum spacetime fluid: a new perspective on the continuum in quantum gravity , 2007, 0710.3276.

[50]  G. Hooft.  A Planar Diagram Theory for Strong Interactions , 1974 .