Abstract
We find the conserved current associated to invariance under generalised diffeomorphisms in double field theory. This can be used to define a generalised Komar integral. We comment on its applications to solutions, in particular to the fundamental string/pp-wave. We also discuss the current in the context of Scherk-Schwarz compactifications. We calculate the current for both the original double field theory action, corresponding to the NSNS sector alone, and for the RR sector.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
N. Hitchin, Generalized Calabi-Yau manifolds, Quart. J. Math. 54 (2003) 281 [math/0209099] [INSPIRE].
M. Gualtieri, Generalized complex geometry, math/0401221 [INSPIRE].
A. Coimbra, C. Strickland-Constable and D. Waldram, Supergravity as Generalised Geometry I: Type II Theories, JHEP 11 (2011) 091 [arXiv:1107.1733] [INSPIRE].
A. Coimbra, C. Strickland-Constable and D. Waldram, Generalised Geometry and type-II Supergravity, Fortsch. Phys. 60 (2012) 982 [arXiv:1202.3170] [INSPIRE].
M.J. Duff, Duality Rotations in String Theory, Nucl. Phys. B 335 (1990) 610 [INSPIRE].
A.A. Tseytlin, Duality Symmetric Formulation of String World Sheet Dynamics, Phys. Lett. B 242 (1990) 163 [INSPIRE].
A.A. Tseytlin, Duality symmetric closed string theory and interacting chiral scalars, Nucl. Phys. B 350 (1991) 395 [INSPIRE].
W. Siegel, Two vierbein formalism for string inspired axionic gravity, Phys. Rev. D 47 (1993) 5453 [hep-th/9302036] [INSPIRE].
W. Siegel, Superspace duality in low-energy superstrings, Phys. Rev. D 48 (1993) 2826 [hep-th/9305073] [INSPIRE].
C. Hull and B. Zwiebach, Double Field Theory, JHEP 09 (2009) 099 [arXiv:0904.4664] [INSPIRE].
C. Hull and B. Zwiebach, The Gauge algebra of double field theory and Courant brackets, JHEP 09 (2009) 090 [arXiv:0908.1792] [INSPIRE].
O. Hohm, C. Hull and B. Zwiebach, Background independent action for double field theory, JHEP 07 (2010) 016 [arXiv:1003.5027] [INSPIRE].
O. Hohm, C. Hull and B. Zwiebach, Generalized metric formulation of double field theory, JHEP 08 (2010) 008 [arXiv:1006.4823] [INSPIRE].
O. Hohm and S.K. Kwak, Frame-like Geometry of Double Field Theory, J. Phys. A 44 (2011) 085404 [arXiv:1011.4101] [INSPIRE].
O. Hohm, S.K. Kwak and B. Zwiebach, Unification of Type II Strings and T-duality, Phys. Rev. Lett. 107 (2011) 171603 [arXiv:1106.5452] [INSPIRE].
O. Hohm, S.K. Kwak and B. Zwiebach, Double Field Theory of Type II Strings, JHEP 09 (2011) 013 [arXiv:1107.0008] [INSPIRE].
O. Hohm and S.K. Kwak, Double Field Theory Formulation of Heterotic Strings, JHEP 06 (2011) 096 [arXiv:1103.2136] [INSPIRE].
O. Hohm and S.K. Kwak, Massive Type II in Double Field Theory, JHEP 11 (2011) 086 [arXiv:1108.4937] [INSPIRE].
O. Hohm and S.K. Kwak, N=1 Supersymmetric Double Field Theory, JHEP 03 (2012) 080 [arXiv:1111.7293] [INSPIRE].
O. Hohm and H. Samtleben, Gauge theory of Kaluza-Klein and winding modes, Phys. Rev. D 88 (2013) 085005 [arXiv:1307.0039] [INSPIRE].
I. Jeon, K. Lee and J.-H. Park, Incorporation of fermions into double field theory, JHEP 11 (2011) 025 [arXiv:1109.2035] [INSPIRE].
I. Jeon, K. Lee and J.-H. Park, Supersymmetric Double Field Theory: Stringy Reformulation of Supergravity, Phys. Rev. D 85 (2012) 081501 [Erratum ibid. D 86 (2012) 089903] [arXiv:1112.0069] [INSPIRE].
I. Jeon, K. Lee and J.-H. Park, Ramond-Ramond Cohomology and O(D,D) T-duality, JHEP 09 (2012) 079 [arXiv:1206.3478] [INSPIRE].
I. Jeon, K. Lee, J.-H. Park and Y. Suh, Stringy Unification of Type IIA and IIB Supergravities under N = 2 D = 10 Supersymmetric Double Field Theory, Phys. Lett. B 723 (2013)245 [arXiv:1210.5078] [INSPIRE].
I. Jeon, K. Lee and J.-H. Park, Differential geometry with a projection: Application to double field theory, JHEP 04 (2011) 014 [arXiv:1011.1324] [INSPIRE].
I. Jeon, K. Lee and J.-H. Park, Stringy differential geometry, beyond Riemann, Phys. Rev. D 84 (2011) 044022 [arXiv:1105.6294] [INSPIRE].
O. Hohm and B. Zwiebach, On the Riemann Tensor in Double Field Theory, JHEP 05 (2012) 126 [arXiv:1112.5296] [INSPIRE].
O. Hohm and B. Zwiebach, Towards an invariant geometry of double field theory, J. Math. Phys. 54 (2013) 032303 [arXiv:1212.1736] [INSPIRE].
D.S. Berman, C.D.A. Blair, E. Malek and M.J. Perry, The O D,D geometry of string theory, Int. J. Mod. Phys. A 29 (2014) 1450080 [arXiv:1303.6727] [INSPIRE].
M. Graña and D. Marqués, Gauged Double Field Theory, JHEP 04 (2012) 020 [arXiv:1201.2924] [INSPIRE].
G. Aldazabal, W. Baron, D. Marqués and C. Núñez, The effective action of Double Field Theory, JHEP 11 (2011) 052 [Erratum ibid. 11 (2011) 109] [arXiv:1109.0290] [INSPIRE].
D.S. Berman and K. Lee, Supersymmetry for Gauged Double Field Theory and Generalised Scherk-Schwarz Reductions, Nucl. Phys. B 881 (2014) 369 [arXiv:1305.2747] [INSPIRE].
D.S. Berman, E.T. Musaev and M.J. Perry, Boundary Terms in Generalized Geometry and doubled field theory, Phys. Lett. B 706 (2011) 228 [arXiv:1110.3097] [INSPIRE].
D. Geissbühler, Double Field Theory and N = 4 Gauged Supergravity, JHEP 11 (2011) 116 [arXiv:1109.4280] [INSPIRE].
D. Geissbühler, D. Marqués, C. Núñez and V. Penas, Exploring Double Field Theory, JHEP 06 (2013) 101 [arXiv:1304.1472] [INSPIRE].
O. Hohm and B. Zwiebach, Large Gauge Transformations in Double Field Theory, JHEP 02 (2013) 075 [arXiv:1207.4198] [INSPIRE].
J.-H. Park, Comments on double field theory and diffeomorphisms, JHEP 06 (2013) 098 [arXiv:1304.5946] [INSPIRE].
D.S. Berman, M. Cederwall and M.J. Perry, Global aspects of double geometry, JHEP 09 (2014) 066 [arXiv:1401.1311] [INSPIRE].
G. Papadopoulos, Seeking the balance: Patching double and exceptional field theories, JHEP 10 (2014) 089 [arXiv:1402.2586] [INSPIRE].
M. Cederwall, The geometry behind double geometry, JHEP 09 (2014) 070 [arXiv:1402.2513] [INSPIRE].
M. Cederwall, T-duality and non-geometric solutions from double geometry, Fortsch. Phys. 62 (2014) 942 [arXiv:1409.4463] [INSPIRE].
D. Andriot, O. Hohm, M. Larfors, D. Lüst and P. Patalong, Non-Geometric Fluxes in Supergravity and Double Field Theory, Fortsch. Phys. 60 (2012) 1150 [arXiv:1204.1979] [INSPIRE].
J. Berkeley, D.S. Berman and F.J. Rudolph, Strings and Branes are Waves, JHEP 06 (2014) 006 [arXiv:1403.7198] [INSPIRE].
D.S. Berman and F.J. Rudolph, Branes are Waves and Monopoles, JHEP 05 (2015) 015 [arXiv:1409.6314] [INSPIRE].
R. Blumenhagen, F. Hassler and D. Lüst, Double Field Theory on Group Manifolds, JHEP 02 (2015) 001 [arXiv:1410.6374] [INSPIRE].
R. Blumenhagen, P.d. Bosque, F. Hassler and D. Lüst, Generalized Metric Formulation of Double Field Theory on Group Manifolds, JHEP 08 (2015) 056 [arXiv:1502.02428] [INSPIRE].
G. Aldazabal, D. Marqués and C. Núñez, Double Field Theory: A Pedagogical Review, Class. Quant. Grav. 30 (2013) 163001 [arXiv:1305.1907] [INSPIRE].
D.S. Berman and D.C. Thompson, Duality Symmetric String and M-theory, Phys. Rept. 566 (2014) 1 [arXiv:1306.2643] [INSPIRE].
O. Hohm, D. Lüst and B. Zwiebach, The Spacetime of Double Field Theory: Review, Remarks and Outlook, Fortsch. Phys. 61 (2013) 926 [arXiv:1309.2977] [INSPIRE].
J.-H. Park, S.-J. Rey, W. Rim and Y. Sakatani, O(D, D) covariant Noether currents and global charges in double field theory, JHEP 11 (2015) 131 [arXiv:1507.07545] [INSPIRE].
T. Ortin, Gravity and strings, Cambridge University Press (2004).
S.K. Kwak, Invariances and Equations of Motion in Double Field Theory, JHEP 10 (2010) 047 [arXiv:1008.2746] [INSPIRE].
U. Naseer, Canonical formulation and conserved charges of double field theory, JHEP 10 (2015) 158 [arXiv:1508.00844] [INSPIRE].
D. Andriot, M. Larfors, D. Lüst and P. Patalong, A ten-dimensional action for non-geometric fluxes, JHEP 09 (2011) 134 [arXiv:1106.4015] [INSPIRE].
D. Andriot, O. Hohm, M. Larfors, D. Lüst and P. Patalong, A geometric action for non-geometric fluxes, Phys. Rev. Lett. 108 (2012) 261602 [arXiv:1202.3060] [INSPIRE].
D. Andriot and A. Betz, β-supergravity: a ten-dimensional theory with non-geometric fluxes and its geometric framework, JHEP 12 (2013) 083 [arXiv:1306.4381] [INSPIRE].
J. de Boer and M. Shigemori, Exotic branes and non-geometric backgrounds, Phys. Rev. Lett. 104 (2010) 251603 [arXiv:1004.2521] [INSPIRE].
J. de Boer and M. Shigemori, Exotic Branes in String Theory, Phys. Rept. 532 (2013) 65 [arXiv:1209.6056] [INSPIRE].
E.A. Bergshoeff, T. Ortín and F. Riccioni, Defect Branes, Nucl. Phys. B 856 (2012) 210 [arXiv:1109.4484] [INSPIRE].
Y. Sakatani, Exotic branes and non-geometric fluxes, JHEP 03 (2015) 135 [arXiv:1412.8769] [INSPIRE].
D.S. Berman and F.J. Rudolph, Strings, Branes and the Self-dual Solutions of Exceptional Field Theory, JHEP 05 (2015) 130 [arXiv:1412.2768] [INSPIRE].
E. Malek, Timelike U-dualities in Generalised Geometry, JHEP 11 (2013) 185 [arXiv:1301.0543] [INSPIRE].
I.T. Ellwood, NS-NS fluxes in Hitchin’s generalized geometry, JHEP 12 (2007) 084 [hep-th/0612100] [INSPIRE].
M. Graña, R. Minasian, M. Petrini and D. Waldram, T-duality, Generalized Geometry and Non-Geometric Backgrounds, JHEP 04 (2009) 075 [arXiv:0807.4527] [INSPIRE].
E.A. Bergshoeff and F. Riccioni, D-Brane Wess-Zumino Terms and U-duality, JHEP 11 (2010) 139 [arXiv:1009.4657] [INSPIRE].
E.A. Bergshoeff and F. Riccioni, String Solitons and T-duality, JHEP 05 (2011) 131 [arXiv:1102.0934] [INSPIRE].
E.A. Bergshoeff and F. Riccioni, Branes and wrapping rules, Phys. Lett. B 704 (2011) 367 [arXiv:1108.5067] [INSPIRE].
E.A. Bergshoeff, A. Marrani and F. Riccioni, Brane orbits, Nucl. Phys. B 861 (2012) 104 [arXiv:1201.5819] [INSPIRE].
D.S. Berman and M.J. Perry, Generalized Geometry and M-theory, JHEP 06 (2011) 074 [arXiv:1008.1763] [INSPIRE].
G. Aldazabal, M. Graña, D. Marqués and J.A. Rosabal, Extended geometry and gauged maximal supergravity, JHEP 06 (2013) 046 [arXiv:1302.5419] [INSPIRE].
O. Hohm and H. Samtleben, Exceptional Field Theory I: E 6(6) covariant Form of M-theory and Type IIB, Phys. Rev. D 89 (2014) 066016 [arXiv:1312.0614] [INSPIRE].
O. Hohm and H. Samtleben, Exceptional field theory. II. E 7(7), Phys. Rev. D 89 (2014) 066017 [arXiv:1312.4542] [INSPIRE].
O. Hohm and H. Samtleben, Exceptional field theory. III. E 8(8), Phys. Rev. D 90 (2014) 066002 [arXiv:1406.3348] [INSPIRE].
H. Godazgar, M. Godazgar, O. Hohm, H. Nicolai and H. Samtleben, Supersymmetric E 7(7) Exceptional Field Theory, JHEP 09 (2014) 044 [arXiv:1406.3235] [INSPIRE].
C.D.A. Blair and E. Malek, Geometry and fluxes of SL(5) exceptional field theory, JHEP 03 (2015) 144 [arXiv:1412.0635] [INSPIRE].
D.N. Page, Classical Stability of Round and Squashed Seven Spheres in Eleven-dimensional Supergravity, Phys. Rev. D 28 (1983) 2976 [INSPIRE].
D. Marolf, Chern-Simons terms and the three notions of charge, in Quantization, gauge theory, and strings, Proceedings of the International Conference dedicated to the memory of Professor Efim Fradkin, Moscow, Russia, 5-10 June 2000, Volume 1+2, pg. 312-320 [hep-th/0006117] [INSPIRE].
T. Kikuchi, T. Okada and Y. Sakatani, Rotating string in doubled geometry with generalized isometries, Phys. Rev. D 86 (2012) 046001 [arXiv:1205.5549] [INSPIRE].
T. Okada and Y. Sakatani, Defect branes as Alice strings, JHEP 03 (2015) 131 [arXiv:1411.1043] [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1507.07541
Present email: cblair@vub.ac.be (Chris D.A. Blair).
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Blair, C.D. Conserved currents of double field theory. J. High Energ. Phys. 2016, 180 (2016). https://doi.org/10.1007/JHEP04(2016)180
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP04(2016)180