Towards the graviton from spinfoams: Higher order corrections in the 3D toy model
Abstract
We consider the recent calculation by Rovelli of the graviton propagator in the spinfoam formalism. Within the 3D toy model introduced by Speziale, we test how the spinfoam formalism can be used to construct the perturbative expansion of graviton amplitudes. Although the 3D graviton is a pure gauge, one can choose to work in a gauge where it is not zero and thus reproduce the structure of the 4D perturbative calculations. We compute explicitly the nexttoleading and nexttonexttoleading orders, corresponding to oneloop and twoloop corrections. We show that while the first arises entirely from the expansion of the Regge action around the flat background, the latter receives contributions from the microscopic, nonReggelike, quantum geometry. Surprisingly, this new contribution reduces the magnitude of the nexttonexttoleading order. It thus appears that the spinfoam formalism is likely to substantially modify the conventional perturbative expansion at higher orders. This result supports the interest in this approach. We then address a number of open issues in the rest of the paper. First, we discuss the boundary state ansatz, which is a key ingredient in the whole construction. We propose a way to enhance the ansatz in order to make the edge lengths and dihedral anglesmore »
 Authors:
 Laboratoire de Physique, ENS Lyon, CNRS UMR 5672, 46 Allee d'Italie, 69364 Lyon (France) and Perimeter Institute, 31 Caroline Street North, Waterloo, Ontario N2L 2Y5 (Canada)
 (Canada)
 Publication Date:
 OSTI Identifier:
 21010908
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Physical Review. D, Particles Fields; Journal Volume: 75; Journal Issue: 2; Other Information: DOI: 10.1103/PhysRevD.75.024038; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ACTION INTEGRAL; AMPLITUDES; CORRECTIONS; COSMOLOGY; FOURDIMENSIONAL CALCULATIONS; GAUGE INVARIANCE; GEOMETRY; GRAVITONS; PROPAGATOR; QUANTUM FIELD THEORY; QUANTUM GRAVITY; REGGE POLES; THREEDIMENSIONAL CALCULATIONS; TOPOLOGY
Citation Formats
Livine, Etera R., Speziale, Simone, Willis, Joshua L., Perimeter Institute, 31 Caroline Street North, Waterloo, Ontario N2L 2Y5, and Department of Mathematics, University of Western Ontario, London, Ontario N6A 5B7. Towards the graviton from spinfoams: Higher order corrections in the 3D toy model. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVD.75.024038.
Livine, Etera R., Speziale, Simone, Willis, Joshua L., Perimeter Institute, 31 Caroline Street North, Waterloo, Ontario N2L 2Y5, & Department of Mathematics, University of Western Ontario, London, Ontario N6A 5B7. Towards the graviton from spinfoams: Higher order corrections in the 3D toy model. United States. doi:10.1103/PHYSREVD.75.024038.
Livine, Etera R., Speziale, Simone, Willis, Joshua L., Perimeter Institute, 31 Caroline Street North, Waterloo, Ontario N2L 2Y5, and Department of Mathematics, University of Western Ontario, London, Ontario N6A 5B7. Mon .
"Towards the graviton from spinfoams: Higher order corrections in the 3D toy model". United States.
doi:10.1103/PHYSREVD.75.024038.
@article{osti_21010908,
title = {Towards the graviton from spinfoams: Higher order corrections in the 3D toy model},
author = {Livine, Etera R. and Speziale, Simone and Willis, Joshua L. and Perimeter Institute, 31 Caroline Street North, Waterloo, Ontario N2L 2Y5 and Department of Mathematics, University of Western Ontario, London, Ontario N6A 5B7},
abstractNote = {We consider the recent calculation by Rovelli of the graviton propagator in the spinfoam formalism. Within the 3D toy model introduced by Speziale, we test how the spinfoam formalism can be used to construct the perturbative expansion of graviton amplitudes. Although the 3D graviton is a pure gauge, one can choose to work in a gauge where it is not zero and thus reproduce the structure of the 4D perturbative calculations. We compute explicitly the nexttoleading and nexttonexttoleading orders, corresponding to oneloop and twoloop corrections. We show that while the first arises entirely from the expansion of the Regge action around the flat background, the latter receives contributions from the microscopic, nonReggelike, quantum geometry. Surprisingly, this new contribution reduces the magnitude of the nexttonexttoleading order. It thus appears that the spinfoam formalism is likely to substantially modify the conventional perturbative expansion at higher orders. This result supports the interest in this approach. We then address a number of open issues in the rest of the paper. First, we discuss the boundary state ansatz, which is a key ingredient in the whole construction. We propose a way to enhance the ansatz in order to make the edge lengths and dihedral angles conjugate variables in a mathematically welldefined way. Second, we show that the leading order is stable against different choices of the face weights of the spinfoam model; the nexttoleading order, on the other hand, is changed in a simple way, and we show that the topological face weight minimizes it. Finally, we extend the leadingorder result to the case of a regular, but not equilateral, tetrahedron.},
doi = {10.1103/PHYSREVD.75.024038},
journal = {Physical Review. D, Particles Fields},
number = 2,
volume = 75,
place = {United States},
year = {Mon Jan 15 00:00:00 EST 2007},
month = {Mon Jan 15 00:00:00 EST 2007}
}

Standard model higher order corrections to the {ital WW}{sub {gamma}}/{ital WWZ} vertex
Using the Smatrix pinch technique we obtain to one loop order gauge independent {gamma} {ital W}{sup }{ital W}{sup +} and {ital Z}{ital W}{sup }{ital W}{sup +} vertices in the context of the standard model, with all incoming momenta offshell. We show that the vertices so constructed satisfy simple QEDlike Ward identities. These gauge invariant vertices give rise to expressions for the magnetic dipole and electric quadrupole form factors of the {ital W} gauge boson, which unlike previous treatments, satisfy the crucial properties of infrared finiteness and perturbative unitarity. {copyright} 1995 {ital American Institute of Physics.}