Built on

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V. C. de Andrade and J. G. Pereira, “Gravitational Lorentz force and the description of the gravitational interaction,” Phys. Rev. D 56
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M. Grana, R. Minasian, M. Petrini and D. Waldram, “T-duality, Generalized Geometry and Non-Geometric Backgrounds,” JHEP 0904
Original
2009
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2018

Deformed Weitzenb\"ock Connections and Double Field Theory

Penas, Victor A.

Understand

We revisit the generalized connection of Double Field Theory.

We implement a procedure that allow us to re-write the Double Field Theory equations of motion in terms of geometric quantities (like generalized torsion and non-metricity tensors) based on other connections rather than the usual generalized Levi-Civita connection and the generalized Riemann curvature.
We define a generalized contorsion tensor and obtain, as a particular case, the Teleparallel equivalent of Double Field Theory.
To do this, we first need to revisit generic connections in standard geometry written in terms of first-order derivatives of the vielbein in order to obtain equivalent theories to Einstein Gravity (like for instance the Teleparallel Gravity case).

Built on

A. Einstein, Sitzungsber. Preuss. Akad. Wiss. (1928) 217. A. Einstein, Math. Annal. 102
1963
Earlier work this paper cites.
K. Hayashi and T. Shirafuji, “New General Relativity,” Phys. Rev. D 19
1982
Earlier work this paper cites.
Y. N. Obukhov, “Conformal Invariance And Space-time Torsion,” Phys. Lett. A 90
1982
Earlier work this paper cites.
W. Siegel, “Two vierbein formalism for string inspired axionic gravity,” Phys. Rev. D 47
1993
Earlier work this paper cites.
F. W. Hehl, J. D. McCrea, E. W. Mielke and Y. Ne’eman, “Metric affine gauge theory of gravity: Field equations, Noether identities, world spinors, and breaking of dilation invariance,” Phys. Rept. 258
1995
Earlier work this paper cites.
J. M. Nester and H. J. Yo, “Symmetric teleparallel general relativity,” Chin. J. Phys. 37
1999
Earlier work this paper cites.
N. Hitchin, “Generalized Calabi-Yau manifolds,” Quart. J. Math. 54
2003
Earlier work this paper cites.
Y. N. Obukhov and J. G. Pereira, “Metric affine approach to teleparallel gravity,” Phys. Rev. D 67
2003
Earlier work this paper cites.
H. I. Arcos and J. G. Pereira, “Torsion gravity: A Reappraisal,” Int. J. Mod. Phys. D 13
2004
Earlier work this paper cites.
V. C. de Andrade and J. G. Pereira, “Gravitational Lorentz force and the description of the gravitational interaction,” Phys. Rev. D 56
2004
Earlier work this paper cites.
R. Ferraro and F. Fiorini, “Modified teleparallel gravity: Inflation without inflaton,” Phys. Rev. D 75
2007
Earlier work this paper cites.
K. Peeters, “A Field-theory motivated approach to symbolic computer algebra,” Comput. Phys. Commun. 176
2007
Earlier work this paper cites.
Y. Itin, “Coframe geometry as a new unification scheme,” gr-qc/0409071. Y. Itin, “Coframe geometry and gravity”, in "Classical and Quantum Gravity Research Progress", edited by M. N. Christiansen and T. K. Rasmussen, Nova Science Publishers, Hauppauge, NY, 2008 [arXiv:0711.4209 [gr-qc]]. Y.Itin,“Maxwell-type behavior from a geometrical structure,” Class. \ \backslash Quant. \ \backslash Grav. \ \backslash { \ \backslash bf 23}, 3361 (2006)
Original
2008
Earlier work this paper cites.
M. Grana, R. Minasian, M. Petrini and D. Waldram, “T-duality, Generalized Geometry and Non-Geometric Backgrounds,” JHEP 0904
Original
2009
Earlier work this paper cites.