Built on

G. Aldazabal, D. Marques and C. Nunez, “Double Field Theory: A Pedagogical Review,” Class. Quant. Grav. 30
Original
1907
Earlier work this paper cites.
H. P. Künzle, “Galilei and Lorentz structures on space-time - comparison of the corresponding geometry and physics,” Ann. Inst. H. Poincare Phys. Theor. 17
1972
Earlier work this paper cites.
C. Duval, G. Burdet, H. P. Kunzle and M. Perrin, “Bargmann Structures and Newton-Cartan Theory,” Phys. Rev. D 31
1985
Earlier work this paper cites.
M. J. Duff, “Hidden String Symmetries?,” Phys. Lett. B 173
1986
Earlier work this paper cites.
T. H. Buscher, “A Symmetry of the String Background Field Equations,” Phys. Lett. B 194
1987
Earlier work this paper cites.
T. H. Buscher, “Path Integral Derivation of Quantum Duality in Nonlinear Sigma Models,” Phys. Lett. B 201
1988
Earlier work this paper cites.
M. J. Duff, “Duality Rotations in String Theory,” Nucl. Phys. B 335
1990
Earlier work this paper cites.
A. A. Tseytlin, “Duality Symmetric Formulation of String World Sheet Dynamics,” Phys. Lett. B 242
1990
Earlier work this paper cites.
A. Dabholkar, G. W. Gibbons, J. A. Harvey and F. Ruiz Ruiz, “Superstrings and Solitons,” Nucl. Phys. B 340
1990
Earlier work this paper cites.
A. A. Tseytlin, “Duality symmetric closed string theory and interacting chiral scalars,” Nucl. Phys. B 350
1991
Earlier work this paper cites.
C. Duval, G. W. Gibbons and P. Horvathy, “Celestial mechanics, conformal structures and gravitational waves,” Phys. Rev. D 43
1991
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.
W. Siegel, “Superspace duality in low-energy superstrings,” Phys. Rev. D 48
1993
Earlier work this paper cites.
C. Duval, “On Galilean isometries,” Class. Quant. Grav. 10
Original
1993
Earlier work this paper cites.
B. Julia and H. Nicolai, “Null Killing vector dimensional reduction and Galilean geometrodynamics,” Nucl. Phys. B 439
1995
Earlier work this paper cites.
J. Gomis and H. Ooguri, “Nonrelativistic closed string theory,” J. Math. Phys. 42
2001
Earlier work this paper cites.
N. Hitchin, “Generalized Calabi-Yau manifolds,” Quart. J. Math. 54
2003
Earlier work this paper cites.
A. N. Bernal and M. Sanchez, “Leibnizian, Galilean and Newtonian structures of space-time,” J. Math. Phys. 44
2003
Earlier work this paper cites.
C. M. Hull, “A Geometry for non-geometric string backgrounds,” JHEP 0510
2005
Earlier work this paper cites.
M. Grana, “Flux compactifications in string theory: A Comprehensive review,” Phys. Rept. 423
2005
Earlier work this paper cites.
E. Minguzzi, “Classical aspects of lightlike dimensional reduction,” Class. Quant. Grav. 23
2006
Earlier work this paper cites.
C. M. Hull, “Global aspects of T-duality, gauged sigma models and T-folds,” JHEP 0710
2007
Earlier work this paper cites.
C. M. Hull, “Doubled Geometry and T-Folds,” JHEP 0707
2007
Earlier work this paper cites.
C. Hull and B. Zwiebach, “Double Field Theory,” JHEP 0909
Original
2009
Earlier work this paper cites.
C. Hull and B. Zwiebach, “The Gauge algebra of double field theory and Courant brackets,” JHEP 0909
Original
2009
Earlier work this paper cites.
O. Hohm, C. Hull and B. Zwiebach, “Generalized metric formulation of double field theory,” JHEP 1008
Original
2010
Earlier work this paper cites.

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I. Jeon, K. Lee and J. H. Park, “Stringy differential geometry, beyond Riemann,” Phys. Rev. D 84
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Then

M. Cederwall, “T-duality and non-geometric solutions from double geometry,” Fortsch. Phys. 62
Original
2014
Later among the works it cites.
J. Berkeley, D. S. Berman and F. J. Rudolph, “Strings and Branes are Waves,” JHEP 1406
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Later among the works it cites.
D. S. Berman and K. Lee, “Supersymmetry for Gauged Double Field Theory and Generalised Scherk-Schwarz Reductions,” Nucl. Phys. B 881
Original
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Later among the works it cites.
M. Garcia-Fernandez, “Torsion-free generalized connections and Heterotic Supergravity,” Commun. Math. Phys. 332
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2017

Classification of non-Riemannian doubled-yet-gauged spacetime

Morand, Kevin, Park, Jeong-Hyuck

Understand

Assuming $\mathbf{O}(D,D)$ covariant fields as the `fundamental' variables, Double Field Theory can accommodate novel geometries where a Riemannian metric cannot be defined, even locally.

Here we present a complete classification of such non-Riemannian spacetimes in terms of two non-negative integers, $(n,\bar{n})$, $0\leq n+\bar{n}\leq D$.
Upon these backgrounds, strings become chiral and anti-chiral over $n$ and $\bar{n}$ directions respectively, while particles and strings are frozen over the $n+\bar{n}$ directions.
In particular, we identify $(0,0)$ as Riemannian manifolds, $(1,0)$ as non-relativistic spacetime, $(1,1)$ as Gomis-Ooguri non-relativistic string, $(D{-1},0)$ as ultra-relativistic Carroll geometry, and $(D,0)$ as Siegel's chiral string.

Built on

G. Aldazabal, D. Marques and C. Nunez, “Double Field Theory: A Pedagogical Review,” Class. Quant. Grav. 30
Original
1907
Earlier work this paper cites.
H. P. Künzle, “Galilei and Lorentz structures on space-time - comparison of the corresponding geometry and physics,” Ann. Inst. H. Poincare Phys. Theor. 17
1972
Earlier work this paper cites.
C. Duval, G. Burdet, H. P. Kunzle and M. Perrin, “Bargmann Structures and Newton-Cartan Theory,” Phys. Rev. D 31
1985
Earlier work this paper cites.
M. J. Duff, “Hidden String Symmetries?,” Phys. Lett. B 173
1986
Earlier work this paper cites.
T. H. Buscher, “A Symmetry of the String Background Field Equations,” Phys. Lett. B 194
1987
Earlier work this paper cites.
T. H. Buscher, “Path Integral Derivation of Quantum Duality in Nonlinear Sigma Models,” Phys. Lett. B 201
1988
Earlier work this paper cites.
M. J. Duff, “Duality Rotations in String Theory,” Nucl. Phys. B 335
1990
Earlier work this paper cites.
A. A. Tseytlin, “Duality Symmetric Formulation of String World Sheet Dynamics,” Phys. Lett. B 242
1990
Earlier work this paper cites.
A. Dabholkar, G. W. Gibbons, J. A. Harvey and F. Ruiz Ruiz, “Superstrings and Solitons,” Nucl. Phys. B 340
1990
Earlier work this paper cites.
A. A. Tseytlin, “Duality symmetric closed string theory and interacting chiral scalars,” Nucl. Phys. B 350
1991
Earlier work this paper cites.
C. Duval, G. W. Gibbons and P. Horvathy, “Celestial mechanics, conformal structures and gravitational waves,” Phys. Rev. D 43
1991
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.
W. Siegel, “Superspace duality in low-energy superstrings,” Phys. Rev. D 48
1993
Earlier work this paper cites.
C. Duval, “On Galilean isometries,” Class. Quant. Grav. 10
Original
1993
Earlier work this paper cites.
B. Julia and H. Nicolai, “Null Killing vector dimensional reduction and Galilean geometrodynamics,” Nucl. Phys. B 439
1995
Earlier work this paper cites.
J. Gomis and H. Ooguri, “Nonrelativistic closed string theory,” J. Math. Phys. 42
2001
Earlier work this paper cites.
N. Hitchin, “Generalized Calabi-Yau manifolds,” Quart. J. Math. 54
2003
Earlier work this paper cites.
A. N. Bernal and M. Sanchez, “Leibnizian, Galilean and Newtonian structures of space-time,” J. Math. Phys. 44
2003
Earlier work this paper cites.
C. M. Hull, “A Geometry for non-geometric string backgrounds,” JHEP 0510
2005
Earlier work this paper cites.
M. Grana, “Flux compactifications in string theory: A Comprehensive review,” Phys. Rept. 423
2005
Earlier work this paper cites.
E. Minguzzi, “Classical aspects of lightlike dimensional reduction,” Class. Quant. Grav. 23
2006
Earlier work this paper cites.
C. M. Hull, “Global aspects of T-duality, gauged sigma models and T-folds,” JHEP 0710
2007
Earlier work this paper cites.
C. M. Hull, “Doubled Geometry and T-Folds,” JHEP 0707
2007
Earlier work this paper cites.
C. Hull and B. Zwiebach, “Double Field Theory,” JHEP 0909
Original
2009
Earlier work this paper cites.
C. Hull and B. Zwiebach, “The Gauge algebra of double field theory and Courant brackets,” JHEP 0909
Original
2009
Earlier work this paper cites.
O. Hohm, C. Hull and B. Zwiebach, “Generalized metric formulation of double field theory,” JHEP 1008
Original
2010
Earlier work this paper cites.

Similar

I. Jeon, K. Lee and J. H. Park, “Stringy differential geometry, beyond Riemann,” Phys. Rev. D 84
Original
2011
Cited alongside, same era.
R. Blumenhagen, A. Deser, D. Lust, E. Plauschinn and F. Rennecke, “Non-geometric Fluxes, Asymmetric Strings and Nonassociative Geometry,” J. Phys. A 44
Original
2011
Cited alongside, same era.
I. Jeon, K. Lee and J. H. Park, “Differential geometry with a projection: Application to double field theory,” JHEP 1104
Original
2011
Cited alongside, same era.
I. Jeon, K. Lee and J. H. Park, “Double field formulation of Yang-Mills theory,” Phys. Lett. B 701
Original
2011
Cited alongside, same era.
D. Geissbuhler, “Double Field Theory and N=4 Gauged Supergravity,” JHEP 1111

Then

M. Cederwall, “T-duality and non-geometric solutions from double geometry,” Fortsch. Phys. 62
Original
2014
Later among the works it cites.
J. Berkeley, D. S. Berman and F. J. Rudolph, “Strings and Branes are Waves,” JHEP 1406
Original
2014
Later among the works it cites.
D. S. Berman and K. Lee, “Supersymmetry for Gauged Double Field Theory and Generalised Scherk-Schwarz Reductions,” Nucl. Phys. B 881
Original
2014
Later among the works it cites.
M. Garcia-Fernandez, “Torsion-free generalized connections and Heterotic Supergravity,” Commun. Math. Phys. 332
Original
2014
Later among the works it cites.
O. Hohm, W. Siegel and B. Zwiebach, “Doubled α ′ \alpha^{\prime} -geometry,” JHEP 1402

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

Original

2011

Cited alongside, same era.

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2011

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Original

2012

Cited alongside, same era.

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Cited alongside, same era.

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Original

2012

Cited alongside, same era.

I. Jeon, K. Lee and J. H. Park, “Ramond-Ramond Cohomology and 𝐎 ⁡ ( D , D ) \mathbf{O}(D,D) T-duality,” JHEP 1209

Original

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Cited alongside, same era.

I. Jeon, K. Lee and J. H. Park, “Supersymmetric Double Field Theory: Stringy Reformulation of Supergravity,” Phys. Rev. D 85

Original

2012

Cited alongside, same era.

Original

2014