<i>E</i><sub>10</sub>orbifolds

Brown, Jeffrey; Helfgott, C.; Ganguli, Surya; Ganor, Ori

doi:10.1088/1126-6708/2005/06/057

Cited by 14 publications

(46 citation statements)

References 64 publications

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“…Because the rank of the gauge groups relevant to string theory in ten dimensions is 16, one might nevertheless argue that it is the algebra so(8, 8 + 16) ++ = so(8, 24) ++ and thus the maximal split algebra BE 10 that controls the weight pattern. Evidence for this comes from the billiard analysis [2] and was also given in [17]. The above study of quantum corrections for BE 10 would therefore again apply.…”

Section: General Considerationsmentioning

confidence: 75%

“…The correction term weight 10 which gave sensible results for D = 11 and IIA [see (17) and (32) and is non-isotropic for IIB in D = 10. This might be related to the difficulties with writing a covariant Lagrangian for the IIB supergravity theory in ten spacetime dimensions and we are therefore tempted to consider the situation after compactification of the theory on S 1 (coordinatized by x 1 ) to nine space-time dimensions (which is required to make the T-duality equivalence of IIA and IIB manifest), as is necessary in all string calculations of higher order effects in IIB theory.…”

Section: Iibmentioning

confidence: 99%

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Curvature corrections and Kac–Moody compatibility conditions

et al. 2006

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We study possible restrictions on the structure of curvature corrections to gravitational theories in the context of their corresponding Kac-Moody algebras, following the initial work on E 10 in Damour and Nicolai [Class Quant Grav 22:2849]. We first emphasize that the leading quantum corrections of M-theory can be naturally interpreted in terms of (non-gravity) fundamental weights of E 10 . We then heuristically explore the extent to which this remark can be generalized to all over-extended algebras by determining which curvature corrections are compatible with their weight structure, and by comparing these curvature terms with known results on the quantum corrections for the corresponding gravitational theories.

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Section: General Considerationsmentioning

confidence: 75%

Section: Iibmentioning

confidence: 99%

Curvature corrections and Kac–Moody compatibility conditions

et al. 2006

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“…Many important observations in favor of E 11 were made within the Cosmological Billiards in String Cosmology [27,28] (and references therein), as well as within the E 10 approach to M-theory [29]. Properties of imaginary roots of E 10 in correspondence with branes, higher order corrections to M-theory and orbifolds were studied in [19,18,30]. A correspondence between M(atrix)-theory and E 11 was reviewed in [21], and interesting observations on orbifolding E 11 were made in [75].…”

Section: Discussionmentioning

confidence: 99%

Duality-Symmetric Approach to General Relativity and Supergravity

Nurmagambetov¹

2006

SIGMA

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Abstract. We review the application of a duality-symmetric approach to gravity and supergravity with emphasizing benefits and disadvantages of the formulation. Contents of these notes includes: 1) Introduction with putting the accent on the role of dual gravity within M-theory; 2) Dualization of gravity with a cosmological constant in D = 3; 3) Onshell description of dual gravity in D > 3; 4) Construction of the duality-symmetric action for General Relativity with/without matter fields; 5) On-shell description of dual gravity in linearized approximation; 6) Brief summary of the paper.

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Section: Introductionmentioning

confidence: 99%

“…We will not present the relation of higher derivative corrections to the E 10 model which can be found in [14]. Related work in [15,16] discusses the role of imaginary roots of E 10 from a brane point of view and orbifolds.We note that already in [17,18] it was proposed that d = 11 supergravity is a non-linear realisation of the bigger group E 11 (and the conformal group via a Borisov-Ogievetsky-type construction [19]). The non-linear E 11 model is thus supposed to operate directly in eleven (or even more) dimensions, and is therefore very different from the one-dimensional E 10 model which we will present below.…”

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confidence: 99%

Maximal supergravities and theE₁₀model

Kleinschmidt

Nicolai

2006

J. Phys.: Conf. Ser.

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Abstract. The maximal rank hyperbolic Kac-Moody algebra e10 has been conjectured to play a prominent role in the unification of duality symmetries in string and M theory. We review some recent developments supporting this conjecture. IntroductionHidden symmetries of exceptional type in the reduction of supergravity theories were first discovered in maximal N = 8 supergravity in d = 4 [1,2]. The unexpected emergence of the coset E 7 /SU (8) describing the scalar sector of the theory was soon generalised to other dimensions and other theories [3]. The most prominent example remains the chain of hidden symmetries occurring in the dimensional reduction of d = 11 maximal supergravity on a torus T n . For 1 ≤ n ≤ 8 the scalars always in appear in group cosets which have become known as E n /K(E n ) where K(E n ) designates the maximal compact subgroup of E n . For n > 8 it was soon conjectured that the resulting symmetry groups become infinite-dimensional [4] and formulations using the centrally extended loop group E 9 [5, 6] and partial results on E 10 [7] have since been obtained.In an initially unrelated development, the study of the asymptotic behaviour of d = 11 supergravity (and IIA and IIB supergravity) near a space-like singularity also revealed evidence for infinite dimensional symmetries, and the hyperbolic Kac-Moody algebra E 10 , in particular. Namely, in this limit, the dynamics can be asymptotically described by a cosmological billiard taking place in the fundamental Weyl chamber of E 10 [8, 9]. The dynamical variables in this case are the spatial scale factors. This led the authors of [10] to propose a one-dimensional nonlinear σ-model based on a coset E 10 /K(E 10 ) and [10,11] uncovered a remarkable dynamical equivalence between a truncation of the bosonic d = 11 supergravity equations and a truncated version of this infinite-dimensional coset model. It is the aim of the present contribution to review this correspondence and similar correspondences to the d = 10 maximal supergravities which were derived in [12,13]. We will not present the relation of higher derivative corrections to the E 10 model which can be found in [14]. Related work in [15,16] discusses the role of imaginary roots of E 10 from a brane point of view and orbifolds.We note that already in [17,18] it was proposed that d = 11 supergravity is a non-linear realisation of the bigger group E 11 (and the conformal group via a Borisov-Ogievetsky-type construction [19]). The non-linear E 11 model is thus supposed to operate directly in eleven (or even more) dimensions, and is therefore very different from the one-dimensional E 10 model which we will present below. In addition, as will be discussed in section 5.3, space-time is thought to

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E₁₀orbifolds

Cited by 14 publications

References 64 publications

Curvature corrections and Kac–Moody compatibility conditions

Curvature corrections and Kac–Moody compatibility conditions

Duality-Symmetric Approach to General Relativity and Supergravity

Maximal supergravities and theE₁₀model

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E10orbifolds

Cited by 14 publications

References 64 publications

Curvature corrections and Kac–Moody compatibility conditions

Curvature corrections and Kac–Moody compatibility conditions

Duality-Symmetric Approach to General Relativity and Supergravity

Maximal supergravities and theE10model

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E₁₀orbifolds

Maximal supergravities and theE₁₀model