Abstract
The (heterotic) double field theories and the exceptional field theories are manifestly duality covariant formulations, describing low-energy limit of various super-string and M-theory compactifications. These field theories are known to be reduced to the standard descriptions by introducing appropriately parameterized generalized metric and by applying suitably chosen section conditions. In this paper, we apply these formulations to non-geometric backgrounds. We introduce different parameterizations for the generalized metric in terms of the dual fields which are pertinent to non-geometric fluxes. Under certain simplifying assumptions, we construct new effective action for non-geometric backgrounds. We then study the non-geometric backgrounds sourced by exotic branes and find their U -duality monodromy matrices. The charge of exotic branes obtained from these monodromy matrices agrees with the charge obtained from the non-geometric flux integral.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
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].
W. Siegel, Manifest duality in low-energy superstrings, hep-th/9308133 [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].
D.S. Berman and M.J. Perry, Generalized geometry and M-theory, JHEP 06 (2011) 074 [arXiv:1008.1763] [INSPIRE].
D.S. Berman, H. Godazgar and M.J. Perry, SO(5, 5) duality in M-theory and generalized geometry, Phys. Lett. B 700 (2011) 65 [arXiv:1103.5733] [INSPIRE].
D.S. Berman, H. Godazgar, M. Godazgar and M.J. Perry, The local symmetries of M-theory and their formulation in generalised geometry, JHEP 01 (2012) 012 [arXiv:1110.3930] [INSPIRE].
D.S. Berman, H. Godazgar, M.J. Perry and P. West, Duality invariant actions and generalised geometry, JHEP 02 (2012) 108 [arXiv:1111.0459] [INSPIRE].
D.S. Berman, M. Cederwall, A. Kleinschmidt and D.C. Thompson, The gauge structure of generalised diffeomorphisms, JHEP 01 (2013) 064 [arXiv:1208.5884] [INSPIRE].
O. Hohm and H. Samtleben, Exceptional form of D = 11 supergravity, Phys. Rev. Lett. 111 (2013) 231601 [arXiv:1308.1673] [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].
G. Aldazabal, M. Graña, D. Marqués and J.A. Rosabal, The gauge structure of exceptional field theories and the tensor hierarchy, JHEP 04 (2014) 049 [arXiv:1312.4549] [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].
O. Hohm and H. Samtleben, Exceptional field theory. III. E 8(8), Phys. Rev. D 90 (2014) 066002 [arXiv:1406.3348] [INSPIRE].
J.A. Rosabal, On the exceptional generalised Lie derivative for d ≥ 7, JHEP 09 (2015) 153 [arXiv:1410.8148] [INSPIRE].
E. Musaev and H. Samtleben, Fermions and supersymmetry in E 6(6) exceptional field theory, JHEP 03 (2015) 027 [arXiv:1412.7286] [INSPIRE].
O. Hohm and Y.-N. Wang, Tensor hierarchy and generalized Cartan calculus in SL(3) × SL(2) exceptional field theory, JHEP 04 (2015) 050 [arXiv:1501.01600] [INSPIRE].
A. Abzalov, I. Bakhmatov and E.T. Musaev, Exceptional field theory: SO(5, 5), JHEP 06 (2015) 088 [arXiv:1504.01523] [INSPIRE].
E.T. Musaev, Exceptional field theory: SL(5), JHEP 02 (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].
F. Ciceri, A. Guarino and G. Inverso, The exceptional story of massive IIA supergravity, JHEP 08 (2016) 154 [arXiv:1604.08602] [INSPIRE].
A. Baguet and H. Samtleben, E 8(8) exceptional field theory: geometry, fermions and supersymmetry, JHEP 09 (2016) 168 [arXiv:1607.03119] [INSPIRE].
P.C. West, E 11 and 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].
P.C. West, The IIA, IIB and eleven-dimensional theories and their common E 11 origin, Nucl. Phys. B 693 (2004) 76 [hep-th/0402140] [INSPIRE].
C.M. Hull, Generalised geometry for M-theory, JHEP 07 (2007) 079 [hep-th/0701203] [INSPIRE].
P. Pires Pacheco and D. Waldram, M-theory, exceptional generalised geometry and superpotentials, JHEP 09 (2008) 123 [arXiv:0804.1362] [INSPIRE].
C. Hillmann, Generalized E 7(7) coset dynamics and D = 11 supergravity, JHEP 03 (2009) 135 [arXiv:0901.1581] [INSPIRE].
J.-H. Park and Y. Suh, U-geometry: SL(5), JHEP 04 (2013) 147 [Erratum ibid. 11 (2013) 210] [arXiv:1302.1652] [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].
N. Hitchin, Generalized Calabi-Yau manifolds, Quart. J. Math. 54 (2003) 281 [math/0209099] [INSPIRE].
M. Gualtieri, Generalized complex geometry, math/0401221 [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].
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, E d(d) × ℝ + generalised geometry, connections and M-theory, JHEP 02 (2014) 054 [arXiv:1112.3989] [INSPIRE].
A. Coimbra, C. Strickland-Constable and D. Waldram, Supergravity as Generalised Geometry II: E d(d) × ℝ + and M-theory, JHEP 03 (2014) 019 [arXiv:1212.1586] [INSPIRE].
A. Dabholkar and C. Hull, Duality twists, orbifolds and fluxes, JHEP 09 (2003) 054 [hep-th/0210209] [INSPIRE].
C.M. Hull, A geometry for non-geometric string backgrounds, JHEP 10 (2005) 065 [hep-th/0406102] [INSPIRE].
J. Shelton, W. Taylor and B. Wecht, Nongeometric flux compactifications, JHEP 10 (2005) 085 [hep-th/0508133] [INSPIRE].
A. Dabholkar and C. Hull, Generalised T-duality and non-geometric backgrounds, JHEP 05 (2006) 009 [hep-th/0512005] [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].
S. Elitzur, A. Giveon, D. Kutasov and E. Rabinovici, Algebraic aspects of matrix theory on T d, Nucl. Phys. B 509 (1998) 122 [hep-th/9707217] [INSPIRE].
M. Blau and M. O’Loughlin, Aspects of U duality in matrix theory, Nucl. Phys. B 525 (1998) 182 [hep-th/9712047] [INSPIRE].
C.M. Hull, U duality and BPS spectrum of super Yang-Mills theory and M-theory, JHEP 07 (1998) 018 [hep-th/9712075] [INSPIRE].
N.A. Obers, B. Pioline and E. Rabinovici, M theory and U duality on T d with gauge backgrounds, Nucl. Phys. B 525 (1998) 163 [hep-th/9712084] [INSPIRE].
N.A. Obers and B. Pioline, U duality and M-theory, Phys. Rept. 318 (1999) 113 [hep-th/9809039] [INSPIRE].
E. Eyras and Y. Lozano, Exotic branes and nonperturbative seven-branes, Nucl. Phys. B 573 (2000) 735 [hep-th/9908094] [INSPIRE].
E. Lozano-Tellechea and T. Ortín, 7-branes and higher Kaluza-Klein branes, Nucl. Phys. B 607 (2001) 213 [hep-th/0012051] [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, 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].
R. Blumenhagen, A. Deser, E. Plauschinn and F. Rennecke, A bi-invariant Einstein-Hilbert action for the non-geometric string, Phys. Lett. B 720 (2013) 215 [arXiv:1210.1591] [INSPIRE].
R. Blumenhagen, A. Deser, E. Plauschinn and F. Rennecke, Non-geometric strings, symplectic gravity and differential geometry of Lie algebroids, JHEP 02 (2013) 122 [arXiv:1211.0030] [INSPIRE].
R. Blumenhagen, A. Deser, E. Plauschinn, F. Rennecke and C. Schmid, The intriguing structure of non-geometric frames in string theory, Fortsch. Phys. 61 (2013) 893 [arXiv:1304.2784] [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].
D. Andriot and A. Betz, Supersymmetry with non-geometric fluxes, or a β-twist in generalized geometry and Dirac operator, JHEP 04 (2015) 006 [arXiv:1411.6640] [INSPIRE].
E.A. Bergshoeff, T. Ortín and F. Riccioni, Defect branes, Nucl. Phys. B 856 (2012) 210 [arXiv:1109.4484] [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].
F. Hassler and D. Lüst, Non-commutative/non-associative IIA (IIB) Q- and R-branes and their intersections, JHEP 07 (2013) 048 [arXiv:1303.1413] [INSPIRE].
D. Geissbuhler, D. Marques, C. Núñez and V. Penas, Exploring double field theory, JHEP 06 (2013) 101 [arXiv:1304.1472] [INSPIRE].
T. Kimura and S. Sasaki, Gauged linear σ-model for exotic five-brane, Nucl. Phys. B 876 (2013) 493 [arXiv:1304.4061] [INSPIRE].
T. Kimura and S. Sasaki, Worldsheet instanton corrections to 5 22 -brane geometry, JHEP 08 (2013) 126 [arXiv:1305.4439] [INSPIRE].
A. Chatzistavrakidis, F.F. Gautason, G. Moutsopoulos and M. Zagermann, Effective actions of nongeometric five-branes, Phys. Rev. D 89 (2014) 066004 [arXiv:1309.2653] [INSPIRE].
T. Kimura and S. Sasaki, Worldsheet description of exotic five-brane with two gauged isometries, JHEP 03 (2014) 128 [arXiv:1310.6163] [INSPIRE].
D. Andriot and A. Betz, NS-branes, source corrected Bianchi identities and more on backgrounds with non-geometric fluxes, JHEP 07 (2014) 059 [arXiv:1402.5972] [INSPIRE].
T. Kimura, S. Sasaki and M. Yata, World-volume effective actions of exotic five-branes, JHEP 07 (2014) 127 [arXiv:1404.5442] [INSPIRE].
T. Okada and Y. Sakatani, Defect branes as Alice strings, JHEP 03 (2015) 131 [arXiv:1411.1043] [INSPIRE].
C.M. Hull and P.K. Townsend, Unity of superstring dualities, Nucl. Phys. B 438 (1995) 109 [hep-th/9410167] [INSPIRE].
Y. Sakatani, Exotic branes and non-geometric fluxes, JHEP 03 (2015) 135 [arXiv:1412.8769] [INSPIRE].
G. Aldazabal, P.G. Camara, A. Font and L.E. Ibáñez, More dual fluxes and moduli fixing, JHEP 05 (2006) 070 [hep-th/0602089] [INSPIRE].
G. Aldazabal, P.G. Camara and J.A. Rosabal, Flux algebra, Bianchi identities and Freed-Witten anomalies in F-theory compactifications, Nucl. Phys. B 814 (2009) 21 [arXiv:0811.2900] [INSPIRE].
G. Aldazabal, E. Andres, P.G. Camara and M. Graña, U-dual fluxes and generalized geometry, JHEP 11 (2010) 083 [arXiv:1007.5509] [INSPIRE].
E. Malek, U-duality in three and four dimensions, arXiv:1205.6403 [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].
G. Dibitetto, J.J. Fernandez-Melgarejo, D. Marques and D. Roest, Duality orbits of non-geometric fluxes, Fortsch. Phys. 60 (2012) 1123 [arXiv:1203.6562] [INSPIRE].
O. Hohm and S.K. Kwak, Double field theory formulation of heterotic strings, JHEP 06 (2011) 096 [arXiv:1103.2136] [INSPIRE].
M. Graña and D. Marques, Gauged double field theory, JHEP 04 (2012) 020 [arXiv:1201.2924] [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].
W. Cho, J.J. Fernández-Melgarejo, I. Jeon and J.-H. Park, Supersymmetric gauged double field theory: systematic derivation by virtue of twist, JHEP 08 (2015) 084 [arXiv:1505.01301] [INSPIRE].
R. Blumenhagen and R. Sun, T-duality, non-geometry and Lie algebroids in heterotic double field theory, JHEP 02 (2015) 097 [arXiv:1411.3167] [INSPIRE].
A.G. Tumanov and P. West, Generalised vielbeins and non-linear realisations, JHEP 10 (2014) 009 [arXiv:1405.7894] [INSPIRE].
T. Kimura, Supersymmetry projection rules on exotic branes, PTEP 2016 (2016) 053B05 [arXiv:1601.02175] [INSPIRE].
A.D. Shapere and F. Wilczek, Selfdual models with theta terms, Nucl. Phys. B 320 (1989) 669 [INSPIRE].
A. Giveon, E. Rabinovici and G. Veneziano, Duality in string background space, Nucl. Phys. B 322 (1989) 167 [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. Giveon, M. Porrati and E. Rabinovici, Target space duality in string theory, Phys. Rept. 244 (1994) 77 [hep-th/9401139] [INSPIRE].
R.L. Arnowitt, S. Deser and C.W. Misner, The dynamics of general relativity, Gen. Rel. Grav. 40 (2008) 1997 [gr-qc/0405109] [INSPIRE].
L.D. Landau and E.M. Lifschits, The classical theory of fields, Butterworth-Heinemann, U.K. (1980).
G. Aldazabal, W. Baron, D. Marques and C. Núñez, The effective action of Double Field Theory, JHEP 11 (2011) 052 [Erratum ibid. 11 (2011) 109] [arXiv:1109.0290] [INSPIRE].
D. Geissbuhler, Double field theory and N = 4 gauged supergravity, JHEP 11 (2011) 116 [arXiv:1109.4280] [INSPIRE].
K. Lee, Towards weakly constrained double field theory, Nucl. Phys. B 909 (2016) 429 [arXiv:1509.06973] [INSPIRE].
C.D.A. Blair, E. Malek and J.-H. Park, M-theory and type IIB from a duality manifest action, JHEP 01 (2014) 172 [arXiv:1311.5109] [INSPIRE].
M.J. Duff and J.X. Lu, Duality rotations in membrane theory, Nucl. Phys. B 347 (1990) 394 [INSPIRE].
M. Hatsuda and K. Kamimura, SL(5) duality from canonical M 2-brane, JHEP 11 (2012) 001 [arXiv:1208.1232] [INSPIRE].
M. Hatsuda and K. Kamimura, M 5 algebra and SO(5, 5) duality, JHEP 06 (2013) 095 [arXiv:1305.2258] [INSPIRE].
I. Schnakenburg and P.C. West, Kac-Moody symmetries of 2B supergravity, Phys. Lett. B 517 (2001) 421 [hep-th/0107181] [INSPIRE].
P.C. West, E 11 , ten forms and supergravity, JHEP 03 (2006) 072 [hep-th/0511153] [INSPIRE].
O.A. Bedoya, D. Marques and C. Núñez, Heterotic α’-corrections in double field theory, JHEP 12 (2014) 074 [arXiv:1407.0365] [INSPIRE].
D. Andriot, Heterotic string from a higher dimensional perspective, Nucl. Phys. B 855 (2012) 222 [arXiv:1102.1434] [INSPIRE].
M. Garcia-Fernandez, Torsion-free generalized connections and heterotic supergravity, Commun. Math. Phys. 332 (2014) 89 [arXiv:1304.4294] [INSPIRE].
D. Baraglia and P. Hekmati, Transitive courant algebroids, string structures and T-duality, Adv. Theor. Math. Phys. 19 (2015) 613 [arXiv:1308.5159] [INSPIRE].
L.B. Anderson, J. Gray and E. Sharpe, Algebroids, heterotic moduli spaces and the Strominger system, JHEP 07 (2014) 037 [arXiv:1402.1532] [INSPIRE].
X. de la Ossa and E.E. Svanes, Holomorphic bundles and the moduli space of N = 1 supersymmetric heterotic compactifications, JHEP 10 (2014) 123 [arXiv:1402.1725] [INSPIRE].
X. de la Ossa and E.E. Svanes, Connections, field redefinitions and heterotic supergravity, JHEP 12 (2014) 008 [arXiv:1409.3347] [INSPIRE].
H. Lü, C.N. Pope and K.S. Stelle, M theory/heterotic duality: a Kaluza-Klein perspective, Nucl. Phys. B 548 (1999) 87 [hep-th/9810159] [INSPIRE].
B.R. Greene, A.D. Shapere, C. Vafa and S.-T. Yau, Stringy cosmic strings and noncompact Calabi-Yau manifolds, Nucl. Phys. B 337 (1990) 1 [INSPIRE].
S. Sasaki and M. Yata, Non-geometric five-branes in heterotic supergravity, JHEP 11 (2016) 064 [arXiv:1608.01436] [INSPIRE].
O. Hohm, A. Sen and B. Zwiebach, Heterotic effective action and duality symmetries revisited, JHEP 02 (2015) 079 [arXiv:1411.5696] [INSPIRE].
S. J. Rey, The confining phase of superstrings and axionic strings, Phys. Rev. D 43 (1991) 526.
S.J. Rey, Axionic string instantons and their low-energy implications, in the proceedings of the Workshop on Superstrings and Particle Theory, November 8-1, Tuscaloosa, U.S.A. (1989).
S.J. Rey, On string theory and axionic strings and instantons, in the proceedingsof The Vancouver meeting: Particles and Fields ’91, August 18-22, Vancouver, Canada (1991).
C.G. Callan Jr., J.A. Harvey and A. Strominger, Worldbrane actions for string solitons, Nucl. Phys. B 367 (1991) 60 [INSPIRE].
E. Bergshoeff and M. de Roo, Supersymmetric Chern-Simons terms in ten-dimensions, Phys. Lett. B 218 (1989) 210 [INSPIRE].
E.A. Bergshoeff and M. de Roo, The quartic effective action of the heterotic string and supersymmetry, Nucl. Phys. B 328 (1989) 439 [INSPIRE].
C.G. Callan Jr., J.A. Harvey and A. Strominger, World sheet approach to heterotic instantons and solitons, Nucl. Phys. B 359 (1991) 611 [INSPIRE].
H. Godazgar, M. Godazgar and M.J. Perry, E 8 duality and dual gravity, JHEP 06 (2013) 044 [arXiv:1303.2035] [INSPIRE].
C.D.A. Blair, Conserved currents of double field theory, JHEP 04 (2016) 180 [arXiv:1507.07541] [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].
U. Naseer, Canonical formulation and conserved charges of double field theory, JHEP 10 (2015) 158 [arXiv:1508.00844] [INSPIRE].
I. Bakhmatov, A. Kleinschmidt and E.T. Musaev, Non-geometric branes are DFT monopoles, JHEP 10 (2016) 076 [arXiv:1607.05450] [INSPIRE].
I. Jeon, K. Lee and J.-H. Park, Stringy differential geometry, beyond Riemann, Phys. Rev. D 84 (2011) 044022 [arXiv:1105.6294] [INSPIRE].
K. Lee, Quadratic α ′ -corrections to heterotic double field theory, Nucl. Phys. B 899 (2015) 594 [arXiv:1504.00149] [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].
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, 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].
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: 1612.08738
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
Lee, K., Rey, SJ. & Sakatani, Y. Effective action for non-geometric fluxes duality covariant actions. J. High Energ. Phys. 2017, 75 (2017). https://doi.org/10.1007/JHEP07(2017)075
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP07(2017)075