Generalized Cartan Calculus in general dimension

Wang, Yi -Nan

doi:10.1007/JHEP07(2015)114

Title: Generalized Cartan Calculus in general dimension

Journal Article · Wed Jul 22 00:00:00 EDT 2015 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/JHEP07(2015)114· OSTI ID:1254829

Wang, Yi -Nan ^[1]

Massachusetts Institute of Technology, Cambridge, MA (United States)

We develop the generalized Cartan Calculus for the groups G = SL(2,R) × R⁺, SL(5,R) and SO(5,5). They are the underlying algebraic structures of d=9,7,6 exceptional field theory, respectively. These algebraic identities are needed for the "tensor hierarchy" structure in exceptional field theory. The validity of Poincar\'e lemmas in this new differential geometry is also discussed. Lastly, we explore some possible extension of the generalized Cartan calculus beyond the exceptional series.

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Research Organization:: Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), High Energy Physics (HEP)

Grant/Contract Number:: SC00012567

OSTI ID:: 1254829

Journal Information:: Journal of High Energy Physics (Online), Vol. 2015, Issue 7; ISSN 1029-8479

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 21 works

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References (43)

The N = 8 supergravity theory. I. The lagrangian Cremmer, E.; Julia, B. Physics Letters B, Vol. 80, Issue 1-2 https://doi.org/10.1016/0370-2693(78)90303-9	journal	December 1978
The SO(8) supergravity Cremmer, E.; Julia, B. Nuclear Physics B, Vol. 159, Issue 1-2 https://doi.org/10.1016/0550-3213(79)90331-6	journal	November 1979
Hidden symmetry in d = 11 supergravity De Wit, B.; Nicolai, H. Physics Letters B, Vol. 155, Issue 1-2 https://doi.org/10.1016/0370-2693(85)91030-5	journal	May 1985
d = 11 supergravity with local SU(8) invariance De Wit, B.; Nicolai, H. Nuclear Physics B, Vol. 274, Issue 2 https://doi.org/10.1016/0550-3213(86)90290-7	journal	September 1986
Hidden symmetries, central charges and all that Wit, B. de; Nicolai, H. Classical and Quantum Gravity, Vol. 18, Issue 16 https://doi.org/10.1088/0264-9381/18/16/302	journal	August 2001
An exceptional geometry for d = 11 supergravity? Koepsell, K.; Nicolai, H.; Samtleben, H. Classical and Quantum Gravity, Vol. 17, Issue 18 https://doi.org/10.1088/0264-9381/17/18/308	journal	September 2000
E ₁₁ and M theory West, P. Classical and Quantum Gravity, Vol. 18, Issue 21 https://doi.org/10.1088/0264-9381/18/21/305	journal	October 2001
Borcherds symmetries in M-theory Henry-Labordère, Pierre; Julia, Bernard; Paulot, Louis Journal of High Energy Physics, Vol. 2002, Issue 04 https://doi.org/10.1088/1126-6708/2002/04/049	journal	April 2002
$E_{10}$ and a Small Tension Expansion of M Theory Damour, T.; Henneaux, M.; Nicolai, H. Physical Review Letters, Vol. 89, Issue 22 https://doi.org/10.1103/PhysRevLett.89.221601	journal	November 2002
E11, SL(32) and central charges West, Peter Physics Letters B, Vol. 575, Issue 3-4 https://doi.org/10.1016/j.physletb.2003.09.059	journal	November 2003
Generalised geometry for M-theory Hull, Christopher M. Journal of High Energy Physics, Vol. 2007, Issue 07 https://doi.org/10.1088/1126-6708/2007/07/079	journal	July 2007
Generalized E ₇₍₇₎ coset dynamics and D = 11 supergravity Hillmann, Christian Journal of High Energy Physics, Vol. 2009, Issue 03 https://doi.org/10.1088/1126-6708/2009/03/135	journal	March 2009
Generalized geometry and M theory Berman, David S.; Perry, Malcolm J. Journal of High Energy Physics, Vol. 2011, Issue 6 https://doi.org/10.1007/JHEP06(2011)074	journal	June 2011
SO(5,5) duality in M-theory and generalized geometry Berman, David S.; Godazgar, Hadi; Perry, Malcolm J. Physics Letters B, Vol. 700, Issue 1 https://doi.org/10.1016/j.physletb.2011.04.046	journal	May 2011
Duality invariant actions and generalised geometry Berman, David S.; Godazgar, Hadi; Perry, Malcolm J. Journal of High Energy Physics, Vol. 2012, Issue 2 https://doi.org/10.1007/JHEP02(2012)108	journal	February 2012
$ {E_d}_{(d)}\times {{\mathbb{R}}^{+}} $ generalised geometry, connections and M theory Coimbra, André; Strickland-Constable, Charles; Waldram, Daniel Journal of High Energy Physics, Vol. 2014, Issue 2 https://doi.org/10.1007/JHEP02(2014)054	journal	February 2014
Supergravity as generalised geometry II: E d(d) × ℝ+ and M theory Coimbra, André; Strickland-Constable, Charles; Waldram, Daniel Journal of High Energy Physics, Vol. 2014, Issue 3 https://doi.org/10.1007/JHEP03(2014)019	journal	March 2014
The gauge structure of generalised diffeomorphisms Berman, David S.; Cederwall, Martin; Kleinschmidt, Axel Journal of High Energy Physics, Vol. 2013, Issue 1 https://doi.org/10.1007/JHEP01(2013)064	journal	January 2013
Extended geometry and gauged maximal supergravity Aldazabal, G.; Graña, M.; Marqués, D. Journal of High Energy Physics, Vol. 2013, Issue 6 https://doi.org/10.1007/JHEP06(2013)046	journal	June 2013
Gauged maximal supergravities and hierarchies of nonabelian vector-tensor systems de Wit, B.; Samtleben, H. Fortschritte der Physik, Vol. 53, Issue 5-6 https://doi.org/10.1002/prop.200510202	journal	May 2005
Lectures on gauged supergravity and flux compactifications Samtleben, Henning Classical and Quantum Gravity, Vol. 25, Issue 21 https://doi.org/10.1088/0264-9381/25/21/214002	journal	October 2008
Non-gravitational exceptional supermultiplets Cederwall, Martin Journal of High Energy Physics, Vol. 2013, Issue 7 https://doi.org/10.1007/JHEP07(2013)025	journal	July 2013
Exceptional Form of $D = 11$ Supergravity Hohm, Olaf; Samtleben, Henning Physical Review Letters, Vol. 111, Issue 23 https://doi.org/10.1103/PhysRevLett.111.231601	journal	December 2013
Tensor hierarchy and generalized Cartan calculus in SL(3) × SL(2) exceptional field theory Hohm, Olaf; Wang, Yi-Nan Journal of High Energy Physics, Vol. 2015, Issue 4 https://doi.org/10.1007/JHEP04(2015)050	journal	April 2015
Exceptional field theory: SO(5,5) Abzalov, Aidar; Bakhmatov, Ilya; Musaev, Edvard T. Journal of High Energy Physics, Vol. 2015, Issue 6 https://doi.org/10.1007/JHEP06(2015)088	journal	June 2015
Supersymmetric E7(7) exceptional field theory Godazgar, Hadi; Godazgar, Mahdi; Hohm, Olaf Journal of High Energy Physics, Vol. 2014, Issue 9 https://doi.org/10.1007/JHEP09(2014)044	journal	September 2014
Fermions and supersymmetry in E6(6) exceptional field theory Musaev, Edvard T.; Samtleben, Henning Journal of High Energy Physics, Vol. 2015, Issue 3 https://doi.org/10.1007/JHEP03(2015)027	journal	March 2015
Double field theory Hull, Chris; Zwiebach, Barton Journal of High Energy Physics, Vol. 2009, Issue 09 https://doi.org/10.1088/1126-6708/2009/09/099	journal	September 2009
The gauge algebra of double field theory and Courant brackets Hull, Chris; Zwiebach, Barton Journal of High Energy Physics, Vol. 2009, Issue 09 https://doi.org/10.1088/1126-6708/2009/09/090	journal	September 2009
Background independent action for double field theory Hohm, Olaf; Hull, Chris; Zwiebach, Barton Journal of High Energy Physics, Vol. 2010, Issue 7 https://doi.org/10.1007/JHEP07(2010)016	journal	July 2010
Generalized metric formulation of double field theory Hohm, Olaf; Hull, Chris; Zwiebach, Barton Journal of High Energy Physics, Vol. 2010, Issue 8 https://doi.org/10.1007/JHEP08(2010)008	journal	August 2010
Exceptional geometry and tensor fields Cederwall, Martin; Edlund, Joakim; Karlsson, Anna Journal of High Energy Physics, Vol. 2013, Issue 7 https://doi.org/10.1007/JHEP07(2013)028	journal	July 2013
(Non-)Abelian Gauged Supergravities in Nine Dimensions Bergshoeff, Eric; Wit, Tim de; Gran, Ulf Journal of High Energy Physics, Vol. 2002, Issue 10 https://doi.org/10.1088/1126-6708/2002/10/061	journal	October 2002
M-theory and gauged supergravities Roest, D. Fortschritte der Physik, Vol. 53, Issue 2 https://doi.org/10.1002/prop.200410192	journal	February 2005
The power of M theory Schwarz, John H. Physics Letters B, Vol. 367, Issue 1-4 https://doi.org/10.1016/0370-2693(95)01429-2	journal	January 1996
Lectures on superstring and M theory dualities Schwarz, John H. Nuclear Physics B - Proceedings Supplements, Vol. 55, Issue 2 https://doi.org/10.1016/S0920-5632(97)00070-4	journal	May 1997
M-theory and type IIB from a duality manifest action Blair, Chris D. A.; Malek, Emanuel; Park, Jeong-Hyuck Journal of High Energy Physics, Vol. 2014, Issue 1 https://doi.org/10.1007/JHEP01(2014)172	journal	January 2014
Gauged supergravities in 5 and 6 dimensions from generalised Scherk-Schwarz reductions Musaev, Edvard T. Journal of High Energy Physics, Vol. 2013, Issue 5 https://doi.org/10.1007/JHEP05(2013)161	journal	May 2013
Super-Poincare covariant quantization of the superstring Berkovits, Nathan Journal of High Energy Physics, Vol. 2000, Issue 04 https://doi.org/10.1088/1126-6708/2000/04/018	journal	March 2000
Covariant Quantization of Superstrings Without Pure Spinor Constraints Grassi, Pietro Antonio; Nieuwenhuizen, Peter van; Policastro, Giuseppe Journal of High Energy Physics, Vol. 2002, Issue 10 https://doi.org/10.1088/1126-6708/2002/10/054	journal	October 2002
The gaugings of maximal D = 6 supergravity Bergshoeff, E.; Samtleben, H.; Sezgin, E. Journal of High Energy Physics, Vol. 2008, Issue 03 https://doi.org/10.1088/1126-6708/2008/03/068	journal	March 2008
The gauge structure of exceptional field theories and the tensor hierarchy Aldazabal, G.; Graña, M.; Marqués, D. Journal of High Energy Physics, Vol. 2014, Issue 4 https://doi.org/10.1007/JHEP04(2014)049	journal	April 2014
Consistent Kaluza-Klein truncations via exceptional field theory Hohm, Olaf; Samtleben, Henning Journal of High Energy Physics, Vol. 2015, Issue 1 https://doi.org/10.1007/JHEP01(2015)131	journal	January 2015

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