Generalized Cartan Calculus in general dimension

Wang, Yi -Nan

doi:10.1007/JHEP07(2015)114

Title: Generalized Cartan Calculus in general dimension

Abstract

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.

Authors:

Wang, Yi -Nan ^[1]

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

Publication Date:: Wed Jul 22 00:00:00 EDT 2015

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

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

OSTI Identifier:: 1254829

Grant/Contract Number:: SC00012567

Resource Type:: Accepted Manuscript

Journal Name:: Journal of High Energy Physics (Online)

Additional Journal Information:: Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2015; Journal Issue: 7; Journal ID: ISSN 1029-8479

Publisher:: Springer Berlin

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; differential and algebraic geometry; string duality; space-time symmetries; supergravity models

Citation Formats


                    Wang, Yi -Nan. Generalized Cartan Calculus in general dimension.  United States: N. p., 2015. 
Web.  doi:10.1007/JHEP07(2015)114.

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                    Wang, Yi -Nan. Generalized Cartan Calculus in general dimension.  United States.  https://doi.org/10.1007/JHEP07(2015)114

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                    Wang, Yi -Nan. Wed .  
"Generalized Cartan Calculus in general dimension".  United States.  https://doi.org/10.1007/JHEP07(2015)114.  https://www.osti.gov/servlets/purl/1254829.

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@article{osti_1254829,

  title        = {Generalized Cartan Calculus in general dimension},

  author       = {Wang, Yi -Nan},

  abstractNote = {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.},

  doi          = {10.1007/JHEP07(2015)114},

  journal      = {Journal of High Energy Physics (Online)},

  number       = 7,

  volume       = 2015,

  place        = {United States},

  year         = {Wed Jul 22 00:00:00 EDT 2015},

  month        = {Wed Jul 22 00:00:00 EDT 2015}

}

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Works referenced in this record:

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Title: Generalized Cartan Calculus in general dimension

Abstract

Citation Formats

The N = 8 supergravity theory. I. The lagrangian journal, December 1978

The SO(8) supergravity journal, November 1979

Hidden symmetry in d = 11 supergravity journal, May 1985

d = 11 supergravity with local SU(8) invariance journal, September 1986

Hidden symmetries, central charges and all that journal, August 2001

An exceptional geometry for d = 11 supergravity? journal, September 2000

E 11 and M theory journal, October 2001

Borcherds symmetries in M-theory journal, April 2002

E 10 and a Small Tension Expansion of M Theory journal, November 2002

E11, SL(32) and central charges journal, November 2003

Generalised geometry for M-theory journal, July 2007

Generalized E 7(7) coset dynamics and D = 11 supergravity journal, March 2009

Generalized geometry and M theory journal, June 2011

SO(5,5) duality in M-theory and generalized geometry journal, May 2011

Duality invariant actions and generalised geometry journal, February 2012

$ {E_d}_{(d)}\times {{\mathbb{R}}^{+}} $ generalised geometry, connections and M theory journal, February 2014

Supergravity as generalised geometry II: E d(d) × ℝ+ and M theory journal, March 2014

The gauge structure of generalised diffeomorphisms journal, January 2013

Extended geometry and gauged maximal supergravity journal, June 2013

Gauged maximal supergravities and hierarchies of nonabelian vector-tensor systems journal, May 2005

Lectures on gauged supergravity and flux compactifications journal, October 2008

Non-gravitational exceptional supermultiplets journal, July 2013

Exceptional Form of D = 11 Supergravity journal, December 2013

Tensor hierarchy and generalized Cartan calculus in SL(3) × SL(2) exceptional field theory journal, April 2015

Exceptional field theory: SO(5,5) journal, June 2015

Supersymmetric E7(7) exceptional field theory journal, September 2014

Fermions and supersymmetry in E6(6) exceptional field theory journal, March 2015

Double field theory journal, September 2009

The gauge algebra of double field theory and Courant brackets journal, September 2009

Background independent action for double field theory journal, July 2010

Generalized metric formulation of double field theory journal, August 2010

Exceptional geometry and tensor fields journal, July 2013

(Non-)Abelian Gauged Supergravities in Nine Dimensions journal, October 2002

M-theory and gauged supergravities journal, February 2005

The power of M theory journal, January 1996

Lectures on superstring and M theory dualities journal, May 1997

M-theory and type IIB from a duality manifest action journal, January 2014

Gauged supergravities in 5 and 6 dimensions from generalised Scherk-Schwarz reductions journal, May 2013

Super-Poincare covariant quantization of the superstring journal, March 2000

Covariant Quantization of Superstrings Without Pure Spinor Constraints journal, October 2002

The gaugings of maximal D = 6 supergravity journal, March 2008

The gauge structure of exceptional field theories and the tensor hierarchy journal, April 2014

Consistent Kaluza-Klein truncations via exceptional field theory journal, January 2015

L∞ algebras and field theory: L∞ algebras and field theory journal, March 2017

Half-Maximal Supersymmetry from Exceptional Field Theory: Half-Maximal Supersymmetry from Exceptional Field Theory journal, October 2017

Locally non-geometric fluxes and missing momenta in M-theory journal, January 2018

The exceptional sigma model journal, April 2018

O-folds. Orientifolds and orbifolds in exceptional field theory journal, September 2018

Particle actions and brane tensions from double and exceptional geometry journal, October 2017

$$L_{\infty }$$ L ∞ Algebras for Extended Geometry from Borcherds Superalgebras journal, April 2019

An action for F-theory: $\mathrm{SL}(2){{\mathbb{R}}}^{+}$ exceptional field theory journal, September 2016

Higher curvature Bianchi identities, generalized geometry, and L ∞ algebras journal, November 2019

An Action for F-theory: $\mathrm{SL}(2) \times \mathbb{R}^+$ Exceptional Field Theory text, January 2015

Particle actions and brane tensions from double and exceptional geometry text, January 2017

Locally non-geometric fluxes and missing momenta in M-theory text, January 2017

The Exceptional Sigma Model text, January 2018

O-folds: Orientifolds and Orbifolds in Exceptional Field Theory text, January 2018

The N = 8 supergravity theory. I. The lagrangian
journal, December 1978

The SO(8) supergravity
journal, November 1979

Hidden symmetry in d = 11 supergravity
journal, May 1985

d = 11 supergravity with local SU(8) invariance
journal, September 1986

Hidden symmetries, central charges and all that
journal, August 2001

An exceptional geometry for d = 11 supergravity?
journal, September 2000

E ₁₁ and M theory
journal, October 2001

Borcherds symmetries in M-theory
journal, April 2002

$E_{10}$ and a Small Tension Expansion of M Theory
journal, November 2002

E11, SL(32) and central charges
journal, November 2003

Generalised geometry for M-theory
journal, July 2007

Generalized E ₇₍₇₎ coset dynamics and D = 11 supergravity
journal, March 2009

Generalized geometry and M theory
journal, June 2011

SO(5,5) duality in M-theory and generalized geometry
journal, May 2011

Duality invariant actions and generalised geometry
journal, February 2012

$ {E_d}_{(d)}\times {{\mathbb{R}}^{+}} $ generalised geometry, connections and M theory
journal, February 2014

Supergravity as generalised geometry II: E d(d) × ℝ+ and M theory
journal, March 2014

The gauge structure of generalised diffeomorphisms
journal, January 2013

Extended geometry and gauged maximal supergravity
journal, June 2013

Gauged maximal supergravities and hierarchies of nonabelian vector-tensor systems
journal, May 2005

Lectures on gauged supergravity and flux compactifications
journal, October 2008

Non-gravitational exceptional supermultiplets
journal, July 2013

Exceptional Form of $D = 11$ Supergravity
journal, December 2013

Tensor hierarchy and generalized Cartan calculus in SL(3) × SL(2) exceptional field theory
journal, April 2015

Exceptional field theory: SO(5,5)
journal, June 2015

Supersymmetric E7(7) exceptional field theory
journal, September 2014

Fermions and supersymmetry in E6(6) exceptional field theory
journal, March 2015

Double field theory
journal, September 2009

The gauge algebra of double field theory and Courant brackets
journal, September 2009

Background independent action for double field theory
journal, July 2010

Generalized metric formulation of double field theory
journal, August 2010

Exceptional geometry and tensor fields
journal, July 2013

(Non-)Abelian Gauged Supergravities in Nine Dimensions
journal, October 2002

M-theory and gauged supergravities
journal, February 2005

The power of M theory
journal, January 1996

Lectures on superstring and M theory dualities
journal, May 1997

M-theory and type IIB from a duality manifest action
journal, January 2014

Gauged supergravities in 5 and 6 dimensions from generalised Scherk-Schwarz reductions
journal, May 2013

Super-Poincare covariant quantization of the superstring
journal, March 2000

Covariant Quantization of Superstrings Without Pure Spinor Constraints
journal, October 2002

The gaugings of maximal D = 6 supergravity
journal, March 2008

The gauge structure of exceptional field theories and the tensor hierarchy
journal, April 2014

Consistent Kaluza-Klein truncations via exceptional field theory
journal, January 2015

L∞ algebras and field theory: L∞ algebras and field theory
journal, March 2017

Half-Maximal Supersymmetry from Exceptional Field Theory: Half-Maximal Supersymmetry from Exceptional Field Theory
journal, October 2017

Locally non-geometric fluxes and missing momenta in M-theory
journal, January 2018

The exceptional sigma model
journal, April 2018

O-folds. Orientifolds and orbifolds in exceptional field theory
journal, September 2018

Particle actions and brane tensions from double and exceptional geometry
journal, October 2017

$$L_{\infty }$$ L ∞ Algebras for Extended Geometry from Borcherds Superalgebras
journal, April 2019

An action for F-theory: $\mathrm{SL}(2){{\mathbb{R}}}^{+}$ exceptional field theory
journal, September 2016

Higher curvature Bianchi identities, generalized geometry, and $L_{\infty}$ algebras
journal, November 2019

An Action for F-theory: $\mathrm{SL}(2) \times \mathbb{R}^+$ Exceptional Field Theory
text, January 2015

Particle actions and brane tensions from double and exceptional geometry
text, January 2017

Locally non-geometric fluxes and missing momenta in M-theory
text, January 2017

The Exceptional Sigma Model
text, January 2018

O-folds: Orientifolds and Orbifolds in Exceptional Field Theory
text, January 2018