Abstract
We construct a background for M-theory that is moduli free. This background is then shown to be related to a topological phase of the E8(8) exceptional field theory (ExFT). The key ingredient in the construction is the embedding of non-Riemannian geometry in ExFT. This allows one to describe non-relativistic geometries, such as Newton-Cartan or Gomis-Ooguri-type limits, using the ExFT framework originally developed to describe maximal supergravity. This generalises previous work by Morand and Park in the context of double field theory.
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References
C. Hull and B. Zwiebach, Double Field Theory, JHEP09 (2009) 099 [arXiv:0904.4664] [INSPIRE].
C. Hillmann, Generalized E(7(7)) coset dynamics and D = 11 supergravity, JHEP03 (2009) 135 [arXiv:0901.1581] [INSPIRE].
D.S. Berman and M.J. Perry, Generalized Geometry and M-theory, JHEP06 (2011) 074 [arXiv:1008.1763] [INSPIRE].
D.S. Berman, H. Godazgar, M. Godazgar and M.J. Perry, The Local symmetries of M-theory and their formulation in generalised geometry, JHEP01 (2012) 012 [arXiv:1110.3930] [INSPIRE].
D.S. Berman, H. Godazgar, M.J. Perry and P. West, Duality Invariant Actions and Generalised Geometry, JHEP02 (2012) 108 [arXiv:1111.0459] [INSPIRE].
D.S. Berman, M. Cederwall, A. Kleinschmidt and D.C. Thompson, The gauge structure of generalised diffeomorphisms, JHEP01 (2013) 064 [arXiv:1208.5884] [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].
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].
W. Siegel, Superspace duality in low-energy superstrings, Phys. Rev.D 48 (1993) 2826 [hep-th/9305073] [INSPIRE].
W. Siegel, Two vierbein formalism for string inspired axionic gravity, Phys. Rev.D 47 (1993) 5453 [hep-th/9302036] [INSPIRE].
P.C. West, E 11and M-theory, Class. Quant. Grav.18 (2001) 4443 [hep-th/0104081] [INSPIRE].
P.C. West, E 11, SL(32) and central charges, Phys. Lett.B 575 (2003) 333 [hep-th/0307098] [INSPIRE].
M. Gualtieri, Generalized complex geometry, math/0401221.
N. Hitchin, Generalized Calabi-Yau manifolds, Quart. J. Math. Oxford Ser.54 (2003) 281 [math/0209099].
O. Hohm and H. Samtleben, Gauge theory of Kaluza-Klein and winding modes, Phys. Rev.D 88 (2013) 085005 [arXiv:1307.0039] [INSPIRE].
O. Hohm, C. Hull and B. Zwiebach, Generalized metric formulation of double field theory, JHEP08 (2010) 008 [arXiv:1006.4823] [INSPIRE].
O. Hohm and Y.-N. Wang, Tensor hierarchy and generalized Cartan calculus in SL(3) × SL(2) exceptional field theory, JHEP04 (2015) 050 [arXiv:1501.01600] [INSPIRE].
A. Abzalov, I. Bakhmatov and E.T. Musaev, Exceptional field theory: SO(5, 5), JHEP06 (2015) 088 [arXiv:1504.01523] [INSPIRE].
E.T. Musaev, Exceptional field theory: SL(5), JHEP02 (2016) 012 [arXiv:1512.02163] [INSPIRE].
D.S. Berman, C.D.A. Blair, E. Malek and F.J. Rudolph, An action for F-theory: SL(2)ℝ+exceptional field theory, Class. Quant. Grav.33 (2016) 195009 [arXiv:1512.06115] [INSPIRE].
G. Bossard, F. Ciceri, G. Inverso, A. Kleinschmidt and H. Samtleben, E 9exceptional field theory. Part I. The potential, JHEP03 (2019) 089 [arXiv:1811.04088] [INSPIRE].
C.D.A. Blair, E. Malek and J.-H. Park, M-theory and Type IIB from a Duality Manifest Action, JHEP01 (2014) 172 [arXiv:1311.5109] [INSPIRE].
E. Plauschinn, Non-geometric backgrounds in string theory, Phys. Rept.798 (2019) 1 [arXiv:1811.11203] [INSPIRE].
G. Dibitetto, J.J. Fernandez-Melgarejo, D. Marqués and D. Roest, Duality orbits of non-geometric fluxes, Fortsch. Phys.60 (2012) 1123 [arXiv:1203.6562] [INSPIRE].
O. Hohm and S.K. Kwak, Massive Type II in Double Field Theory, JHEP11 (2011) 086 [arXiv:1108.4937] [INSPIRE].
F. Ciceri, A. Guarino and G. Inverso, The exceptional story of massive IIA supergravity, JHEP08 (2016) 154 [arXiv:1604.08602] [INSPIRE].
L. Wulff and A.A. Tseytlin, κ-symmetry of superstring σ-model and generalized 10d supergravity equations, JHEP06 (2016) 174 [arXiv:1605.04884] [INSPIRE].
Y. Sakatani, S. Uehara and K. Yoshida, Generalized gravity from modified DFT, JHEP04 (2017) 123 [arXiv:1611.05856] [INSPIRE].
A. Baguet, M. Magro and H. Samtleben, Generalized IIB supergravity from exceptional field theory, JHEP03 (2017) 100 [arXiv:1612.07210] [INSPIRE].
N.A. Obers and B. Pioline, U duality and M-theory, Phys. Rept.318 (1999) 113 [hep-th/9809039] [INSPIRE].
J. de Boer and M. Shigemori, Exotic Branes in String Theory, Phys. Rept.532 (2013) 65 [arXiv:1209.6056] [INSPIRE].
C.D.A. Blair and E. Malek, Geometry and fluxes of SL(5) exceptional field theory, JHEP03 (2015) 144 [arXiv:1412.0635] [INSPIRE].
I. Bakhmatov, D. Berman, A. Kleinschmidt, E. Musaev and R. Otsuki, Exotic branes in Exceptional Field Theory: the SL(5) duality group, JHEP08 (2018) 021 [arXiv:1710.09740] [INSPIRE].
J.J. Fernández-Melgarejo, T. Kimura and Y. Sakatani, Weaving the Exotic Web, JHEP09 (2018) 072 [arXiv:1805.12117] [INSPIRE].
D.S. Berman, E.T. Musaev and R. Otsuki, Exotic Branes in Exceptional Field Theory: E 7(7)and Beyond, JHEP12 (2018) 053 [arXiv:1806.00430] [INSPIRE].
M. Graña, R. Minasian, M. Petrini and D. Waldram, T-duality, Generalized Geometry and Non-Geometric Backgrounds, JHEP04 (2009) 075 [arXiv:0807.4527] [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].
E. Cartan, Sur les variétés à connexion affine et la théorie de la relativité généralisée. (Première partie), Annales Sci. Ecole Norm. Sup.40 (1923) 325.
E. Cartan, Sur les variétés à connexion affine et la théorie de la relativité généralisée. (Première partie) (Suite), Annales Sci. Ecole Norm. Sup.41 (1924) 1.
J. Gomis and H. Ooguri, Nonrelativistic closed string theory, J. Math. Phys.42 (2001) 3127 [hep-th/0009181] [INSPIRE].
U.H. Danielsson, A. Guijosa and M. Kruczenski, IIA/B, wound and wrapped, JHEP 10 (2000) 020 [hep-th/0009182] [INSPIRE].
U.H. Danielsson, A. Guijosa and M. Kruczenski, Newtonian gravitons and D-brane collective coordinates in wound string theory, JHEP03 (2001) 041 [hep-th/0012183] [INSPIRE].
K. Lee and J.-H. Park, Covariant action for a string in “doubled yet gauged” spacetime, Nucl. Phys.B 880 (2014) 134 [arXiv:1307.8377] [INSPIRE].
S.M. Ko, C. Melby-Thompson, R. Meyer and J.-H. Park, Dynamics of Perturbations in Double Field Theory & Non-Relativistic String Theory, JHEP12 (2015) 144 [arXiv:1508.01121] [INSPIRE].
K. Morand and J.-H. Park, Classification of non-Riemannian doubled-yet-gauged spacetime, Eur. Phys. J.C 77 (2017) 685 [Erratum ibid.C 78 (2018) 901] [arXiv:1707.03713] [INSPIRE].
K. Cho, K. Morand and J.-H. Park, Kaluza-Klein reduction on a maximally non-Riemannian space is moduli-free, Phys. Lett.B 793 (2019) 65 [arXiv:1808.10605] [INSPIRE].
C.M. Hull, A Geometry for non-geometric string backgrounds, JHEP10 (2005) 065 [hep-th/0406102] [INSPIRE].
J.-H. Park and Y. Suh, U-gravity: SL(N), JHEP06 (2014) 102 [arXiv:1402.5027] [INSPIRE].
W. Siegel, Amplitudes for left-handed strings, arXiv:1512.02569 [INSPIRE].
E. Casali and P. Tourkine, On the null origin of the ambitwistor string, JHEP11 (2016) 036 [arXiv:1606.05636] [INSPIRE].
E. Casali and P. Tourkine, Windings of twisted strings, Phys. Rev.D 97 (2018) 061902 [arXiv:1710.01241] [INSPIRE].
K. Lee, S.-J. Rey and J.A. Rosabal, A string theory which isn’t about strings, JHEP11 (2017) 172 [arXiv:1708.05707] [INSPIRE].
K. Lee and J.A. Rosabal, A Note on Circle Compactification of Tensile Ambitwistor String, Nucl. Phys.B 933 (2018) 482 [arXiv:1712.05874] [INSPIRE].
N.A. Nekrasov, Lectures on curved beta-gamma systems, pure spinors and anomalies, hep-th/0511008 [INSPIRE].
M.J. Duff, J.X. Lu, R. Percacci, C.N. Pope, H. Samtleben and E. Sezgin, Membrane Duality Revisited, Nucl. Phys.B 901 (2015) 1 [arXiv:1509.02915] [INSPIRE].
A.S. Arvanitakis and C.D.A. Blair, Unifying Type-II Strings by Exceptional Groups, Phys. Rev. Lett.120 (2018) 211601 [arXiv:1712.07115] [INSPIRE].
A.S. Arvanitakis and C.D.A. Blair, The Exceptional σ-model, JHEP04 (2018) 064 [arXiv:1802.00442] [INSPIRE].
Y. Sakatani and S. Uehara, Exceptional M-brane σ-models and η-symbols, PTEP2018 (2018) 033B05 [arXiv:1712.10316] [INSPIRE].
M.J. Duff and J.X. Lu, Duality Rotations in Membrane Theory, Nucl. Phys.B 347 (1990) 394 [INSPIRE].
O. Hohm and H. Samtleben, Leibniz-Chern-Simons Theory and Phases of Exceptional Field Theory, Commun. Math. Phys. (2019) 1 [arXiv:1805.03220] [INSPIRE].
O. Hohm and H. Samtleben, Reviving 3D \( \mathcal{N} \)= 8 superconformal field theories, JHEP04 (2019) 047 [arXiv:1810.12311] [INSPIRE].
A.A. Tseytlin, On the First Order Formalism in Quantum Gravity, J. Phys. A 15 (1982) L105 [INSPIRE].
E. Witten, Topological σ-models, Commun. Math. Phys.118 (1988) 411 [INSPIRE].
G.T. Horowitz, Exactly Soluble Diffeomorphism Invariant Theories, Commun. Math. Phys.125 (1989) 417 [INSPIRE].
C.M. Hull and B. Julia, Duality and moduli spaces for timelike reductions, Nucl. Phys.B 534 (1998) 250 [hep-th/9803239] [INSPIRE].
J. Berkeley, D.S. Berman and F.J. Rudolph, Strings and Branes are Waves, JHEP06 (2014) 006 [arXiv:1403.7198] [INSPIRE].
O. Hohm and H. Samtleben, The dual graviton in duality covariant theories, Fortsch. Phys.67 (2019) 1900021 [arXiv:1807.07150] [INSPIRE].
A. Baguet and H. Samtleben, E 8(8)Exceptional Field Theory: Geometry, Fermions and Supersymmetry, JHEP09 (2016) 168 [arXiv:1607.03119] [INSPIRE].
D.L. Welch, Timelike duality, Phys. Rev.D 50 (1994) 6404 [hep-th/9405070] [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, JHEP11 (2015) 131 [arXiv:1507.07545] [INSPIRE].
R. Dijkgraaf, B. Heidenreich, P. Jefferson and C. Vafa, Negative Branes, Supergroups and the Signature of Spacetime, JHEP02 (2018) 050 [arXiv:1603.05665] [INSPIRE].
C.M. Hull, Timelike T duality, de Sitter space, large N gauge theories and topological field theory, JHEP07 (1998) 021 [hep-th/9806146] [INSPIRE].
C.M. Hull, Duality and the signature of space-time, JHEP11 (1998) 017 [hep-th/9807127] [INSPIRE].
O. Hohm, S.K. Kwak and B. Zwiebach, Double Field Theory of Type II Strings, JHEP09 (2011) 013 [arXiv:1107.0008] [INSPIRE].
C.D.A. Blair, Doubled strings, negative strings and null waves, JHEP11 (2016) 042 [arXiv:1608.06818] [INSPIRE].
T. Harmark, J. Hartong and N.A. Obers, Nonrelativistic strings and limits of the AdS/CFT correspondence, Phys. Rev.D 96 (2017) 086019 [arXiv:1705.03535] [INSPIRE].
T. Harmark, J. Hartong, L. Menculini, N.A. Obers and Z. Yan, Strings with Non-Relativistic Conformal Symmetry and Limits of the AdS/CFT Correspondence, JHEP11 (2018) 190 [arXiv:1810.05560] [INSPIRE].
E. Bergshoeff, J. Gomis and Z. Yan, Nonrelativistic String Theory and T-duality, JHEP11 (2018) 133 [arXiv:1806.06071] [INSPIRE].
C.D.A. Blair, E. Malek and D.C. Thompson, O-folds: Orientifolds and Orbifolds in Exceptional Field Theory, JHEP09 (2018) 157 [arXiv:1805.04524] [INSPIRE].
C.D.A. Blair, Particle actions and brane tensions from double and exceptional geometry, JHEP10 (2017) 004 [arXiv:1707.07572] [INSPIRE].
E. Malek, Timelike U-dualities in Generalised Geometry, JHEP11 (2013) 185 [arXiv:1301.0543] [INSPIRE].
D.C. Thompson, Duality Invariance: From M-theory to Double Field Theory, JHEP08 (2011) 125 [arXiv:1106.4036] [INSPIRE].
D.S. Berman and F.J. Rudolph, Branes are Waves and Monopoles, JHEP05 (2015) 015 [arXiv:1409.6314] [INSPIRE].
D.S. Berman and F.J. Rudolph, Strings, Branes and the Self-dual Solutions of Exceptional Field Theory, JHEP05 (2015) 130 [arXiv:1412.2768] [INSPIRE].
J. Kluson, (m, n)-String and D1-Brane in Stringy Newton-Cartan Background, JHEP04 (2019) 163 [arXiv:1901.11292] [INSPIRE].
E. Musaev and H. Samtleben, Fermions and supersymmetry in E 6(6)exceptional field theory, JHEP03 (2015) 027 [arXiv:1412.7286] [INSPIRE].
H. Godazgar, M. Godazgar, O. Hohm, H. Nicolai and H. Samtleben, Supersymmetric E 7(7)Exceptional Field Theory, JHEP09 (2014) 044 [arXiv:1406.3235] [INSPIRE].
A. Le Diffon, H. Samtleben and M. Trigiante, N = 8 Supergravity with Local Scaling Symmetry, JHEP04 (2011) 079 [arXiv:1103.2785] [INSPIRE].
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Berman, D.S., Blair, C.D.A. & Otsuki, R. Non-Riemannian geometry of M-theory. J. High Energ. Phys. 2019, 175 (2019). https://doi.org/10.1007/JHEP07(2019)175
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DOI: https://doi.org/10.1007/JHEP07(2019)175