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.
V. G. Drinfel’d, “Hopf algebras and the quantum Yang-Baxter equation,” Sov. Math. Dokl. 32
1985
Earlier work this paper cites.
C. G. Callan, Jr., E. J. Martinec, M. J. Perry and D. Friedan, “Strings in Background Fields,” Nucl. Phys. B 262
1985
Earlier work this paper cites.
M. T. Grisaru, P. Howe, L. Mezincescu, B. E. W. Nilsson and P. K. Townsend, “ N = 2 N=2 superstrings in a supergravity background,” Phys. Lett. B 162
1986
Earlier work this paper cites.
C. M. Hull and P. K. Townsend, “Finiteness and Conformal Invariance in Nonlinear σ \sigma Models,” Nucl. Phys. B 274
1986
Earlier work this paper cites.
A. A. Tseytlin, “Conformal Anomaly in Two-Dimensional Sigma Model on Curved Background and Strings,” Phys. Lett. B 178
1986
Earlier work this paper cites.
G. M. Shore, “A Local Renormalization Group Equation, Diffeomorphisms, and Conformal Invariance in σ \sigma Models,” Nucl. Phys. B 286
1987
Earlier work this paper cites.
A. A. Tseytlin, “ σ \sigma Model Weyl Invariance Conditions and String Equations of Motion,” Nucl. Phys. B 294
1987
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. A. Tseytlin, “Duality symmetric closed string theory and interacting chiral scalars,” Nucl. Phys. B 350
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.
R. M. Wald, “Black hole entropy is the Noether charge,” Phys. Rev. D 48
1993
Earlier work this paper cites.
V. Iyer and R. M. Wald, “Some properties of Noether charge and a proposal for dynamical black hole entropy,” Phys. Rev. D 50
1994
Earlier work this paper cites.
V. Iyer and R. M. Wald, “A Comparison of Noether charge and Euclidean methods for computing the entropy of stationary black holes,” Phys. Rev. D 52
1995
Earlier work this paper cites.
P. C. West, “E(11) and M theory,” Class. Quant. Grav. 18
2001
Earlier work this paper cites.
P. C. West, “E(11), SL(32) and central charges,” Phys. Lett. B 575
2003
Earlier work this paper cites.
P. C. West, “The IIA, IIB and eleven-dimensional theories and their common E(11) origin,” Nucl. Phys. B 693
2004
Earlier work this paper cites.
C. M. Hull, “Generalised Geometry for M-Theory,” JHEP 0707
2007
Earlier work this paper cites.
D. S. Berman, N. B. Copland and D. C. Thompson, “Background Field Equations for the Duality Symmetric String,” Nucl. Phys. B 791
Original
2008
Earlier work this paper cites.
D. S. Berman and D. C. Thompson, “Duality Symmetric Strings, Dilatons and O(d,d) Effective Actions,” Phys. Lett. B 662
Original
2008
Earlier work this paper cites.
P. Pires Pacheco and D. Waldram, “M-theory, exceptional generalised geometry and superpotentials,” JHEP 0809
Original
2008
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.
C. Hillmann, “Generalized E(7(7)) coset dynamics and D=11 supergravity,” JHEP 0903
Original
2009
Earlier work this paper cites.
O. Hohm, C. Hull and B. Zwiebach, “Background independent action for double field theory,” JHEP 1007
Original
2010
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.
S. K. Kwak, “Invariances and Equations of Motion in Double Field Theory,” JHEP 1010
Original
2010
Earlier work this paper cites.
I. Jeon, K. Lee and J. H. Park, “Differential geometry with a projection: Application to double field theory,” JHEP 1104
Original
2011
Earlier work this paper cites.
O. Hohm and S. K. Kwak, “Frame-like Geometry of Double Field Theory,” J. Phys. A 44
Original
2011
Earlier work this paper cites.
I. Jeon, K. Lee and J. H. Park, “Stringy differential geometry, beyond Riemann,” Phys. Rev. D 84
Original
2011
Earlier work this paper cites.
O. Hohm, S. K. Kwak and B. Zwiebach, “Unification of Type II Strings and T-duality,” Phys. Rev. Lett. 107
Original
2011
Earlier work this paper cites.

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2016

Generalized gravity from modified DFT

Sakatani, Yuho, Uehara, Shozo, Yoshida, Kentaroh

Understand

Recently, generalized equations of type IIB supergravity have been derived from the requirement of classical kappa-symmetry of type IIB superstring theory in the Green-Schwarz formulation.

These equations are covariant under generalized T-duality transformations and hence one may expect a formulation similar to double field theory (DFT).
In this paper, we consider a modification of the DFT equations of motion by relaxing a condition for the generalized covariant derivative with an extra generalized vector.
In this modified double field theory (mDFT), we show that the flatness condition of the modified generalized Ricci tensor leads to the NS-NS part of the generalized equations of type IIB supergravity.

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.
V. G. Drinfel’d, “Hopf algebras and the quantum Yang-Baxter equation,” Sov. Math. Dokl. 32
1985
Earlier work this paper cites.
C. G. Callan, Jr., E. J. Martinec, M. J. Perry and D. Friedan, “Strings in Background Fields,” Nucl. Phys. B 262
1985
Earlier work this paper cites.
M. T. Grisaru, P. Howe, L. Mezincescu, B. E. W. Nilsson and P. K. Townsend, “ N = 2 N=2 superstrings in a supergravity background,” Phys. Lett. B 162
1986
Earlier work this paper cites.
C. M. Hull and P. K. Townsend, “Finiteness and Conformal Invariance in Nonlinear σ \sigma Models,” Nucl. Phys. B 274
1986
Earlier work this paper cites.
A. A. Tseytlin, “Conformal Anomaly in Two-Dimensional Sigma Model on Curved Background and Strings,” Phys. Lett. B 178
1986
Earlier work this paper cites.
G. M. Shore, “A Local Renormalization Group Equation, Diffeomorphisms, and Conformal Invariance in σ \sigma Models,” Nucl. Phys. B 286
1987
Earlier work this paper cites.
A. A. Tseytlin, “ σ \sigma Model Weyl Invariance Conditions and String Equations of Motion,” Nucl. Phys. B 294
1987
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. A. Tseytlin, “Duality symmetric closed string theory and interacting chiral scalars,” Nucl. Phys. B 350
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.
R. M. Wald, “Black hole entropy is the Noether charge,” Phys. Rev. D 48
1993
Earlier work this paper cites.
V. Iyer and R. M. Wald, “Some properties of Noether charge and a proposal for dynamical black hole entropy,” Phys. Rev. D 50
1994
Earlier work this paper cites.
V. Iyer and R. M. Wald, “A Comparison of Noether charge and Euclidean methods for computing the entropy of stationary black holes,” Phys. Rev. D 52
1995
Earlier work this paper cites.
P. C. West, “E(11) and M theory,” Class. Quant. Grav. 18
2001
Earlier work this paper cites.
P. C. West, “E(11), SL(32) and central charges,” Phys. Lett. B 575
2003
Earlier work this paper cites.
P. C. West, “The IIA, IIB and eleven-dimensional theories and their common E(11) origin,” Nucl. Phys. B 693
2004
Earlier work this paper cites.
C. M. Hull, “Generalised Geometry for M-Theory,” JHEP 0707
2007
Earlier work this paper cites.
D. S. Berman, N. B. Copland and D. C. Thompson, “Background Field Equations for the Duality Symmetric String,” Nucl. Phys. B 791
Original
2008
Earlier work this paper cites.
D. S. Berman and D. C. Thompson, “Duality Symmetric Strings, Dilatons and O(d,d) Effective Actions,” Phys. Lett. B 662
Original
2008
Earlier work this paper cites.
P. Pires Pacheco and D. Waldram, “M-theory, exceptional generalised geometry and superpotentials,” JHEP 0809
Original
2008
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.
C. Hillmann, “Generalized E(7(7)) coset dynamics and D=11 supergravity,” JHEP 0903
Original
2009
Earlier work this paper cites.
O. Hohm, C. Hull and B. Zwiebach, “Background independent action for double field theory,” JHEP 1007
Original
2010
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.
S. K. Kwak, “Invariances and Equations of Motion in Double Field Theory,” JHEP 1010
Original
2010
Earlier work this paper cites.
I. Jeon, K. Lee and J. H. Park, “Differential geometry with a projection: Application to double field theory,” JHEP 1104
Original
2011
Earlier work this paper cites.
O. Hohm and S. K. Kwak, “Frame-like Geometry of Double Field Theory,” J. Phys. A 44
Original
2011
Earlier work this paper cites.
I. Jeon, K. Lee and J. H. Park, “Stringy differential geometry, beyond Riemann,” Phys. Rev. D 84
Original
2011
Earlier work this paper cites.
O. Hohm, S. K. Kwak and B. Zwiebach, “Unification of Type II Strings and T-duality,” Phys. Rev. Lett. 107
Original
2011
Earlier work this paper cites.