75 research outputs found
Kac-Moody Symmetries of Ten-dimensional Non-maximal Supergravity Theories
A description of the bosonic sector of ten-dimensional N=1 supergravity as a
non-linear realisation is given. We show that if a suitable extension of this
theory were invariant under a Kac-Moody algebra, then this algebra would have
to contain a rank eleven Kac-Moody algebra, that can be identified to be a
particular real form of very-extended D_8. We also describe the extension of
N=1 supergravity coupled to an abelian vector gauge field as a non-linear
realisation, and find the Kac-Moody algebra governing the symmetries of this
theory to be very-extended B_8. Finally, we discuss the related points for the
N=1 supergravity coupled to an arbitrary number of abelian vector gauge fields
A class of Lorentzian Kac-Moody algebras
We consider a natural generalisation of the class of hyperbolic Kac-Moody
algebras. We describe in detail the conditions under which these algebras are
Lorentzian. We also construct their fundamental weights, and analyse whether
they possess a real principal so(1,2) subalgebra. Our class of algebras include
the Lorentzian Kac-Moody algebras that have recently been proposed as
symmetries of M-theory and the closed bosonic string.Comment: 40 pages TeX, 5 eps-figure
Curvature corrections and Kac-Moody compatibility conditions
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 E10 in Class. Quant. Grav. 22 (2005)
2849. We first emphasize that the leading quantum corrections of M-theory can
be naturally interpreted in terms of (non-gravity) fundamental weights of E10.
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.Comment: 27 page
Sugawara-type constraints in hyperbolic coset models
In the conjectured correspondence between supergravity and geodesic models on
infinite-dimensional hyperbolic coset spaces, and E10/K(E10) in particular, the
constraints play a central role. We present a Sugawara-type construction in
terms of the E10 Noether charges that extends these constraints infinitely into
the hyperbolic algebra, in contrast to the truncated expressions obtained in
arXiv:0709.2691 that involved only finitely many generators. Our extended
constraints are associated to an infinite set of roots which are all imaginary,
and in fact fill the closed past light-cone of the Lorentzian root lattice. The
construction makes crucial use of the E10 Weyl group and of the fact that the
E10 model contains both D=11 supergravity and D=10 IIB supergravity. Our
extended constraints appear to unite in a remarkable manner the different
canonical constraints of these two theories. This construction may also shed
new light on the issue of `open constraint algebras' in traditional canonical
approaches to gravity.Comment: 49 page
Duality Symmetries and G^{+++} Theories
We show that the non-linear realisations of all the very extended algebras
G^{+++}, except the B and C series which we do not consider, contain fields
corresponding to all possible duality symmetries of the on-shell degrees of
freedom of these theories. This result also holds for G_2^{+++} and we argue
that the non-linear realisation of this algebra accounts precisely for the form
fields present in the corresponding supersymmetric theory. We also find a
simple necessary condition for the roots to belong to a G^{+++} algebra.Comment: 35 pages. v2: 2 appendices added, other minor corrections. v3: tables
corrected, other minor changes, one appendix added, refs. added. Version
published in Class. Quant. Gra
Time-like T-duality algebra
When compactifying M- or type II string-theories on tori of indefinite
space-time signature, their low energy theories involve sigma models on
E_{n(n)}/H_n, where H_n is a not necessarily compact subgroup of E_{n(n)} whose
complexification is identical to the complexification of the maximal compact
subgroup of E_{n(n)}. We discuss how to compute the group H_n. For finite
dimensional E_{n(n)}, a formula derived from the theory of real forms of E_n
algebra's gives the possible groups immediately. A few groups that have not
appeared in the literature are found. For n=9,10,11 we compute and describe the
relevant real forms of E_n and H_n. A given H_n can correspond to multiple
signatures for the compact torus. We compute the groups H_n for all
compactifications of M-, M*-, and M'-theories, and type II-, II*- and
II'-theories on tori of arbitrary signature, and collect them in tables that
outline the dualities between them. In an appendix we list cosets G/H, with G
split and H a subgroup of G, that are relevant to timelike toroidal
compactifications and oxidation of theories with enhanced symmetries.Comment: LaTeX, 37 pages, 1 eps-figure, uses JHEP.cls; v2. corrected typo's in
tables 16 and 17, minor changes to tex
Massive Type II in Double Field Theory
We provide an extension of the recently constructed double field theory
formulation of the low-energy limits of type II strings, in which the RR fields
can depend simultaneously on the 10-dimensional space-time coordinates and
linearly on the dual winding coordinates. For the special case that only the RR
one-form of type IIA carries such a dependence, we obtain the massive
deformation of type IIA supergravity due to Romans. For T-dual configurations
we obtain a `massive' but non-covariant formulation of type IIB, in which the
10-dimensional diffeomorphism symmetry is deformed by the mass parameter.Comment: 21 page
E_{11} origin of Brane charges and U-duality multiplets
We derive general equations which determine the decomposition of the G^{+++}
multiplet of brane charges into the sub-algebras that arise when the
non-linearly realised G^{+++} theory is dimensionally reduced on a torus. We
apply this to calculate the low level E_8 multiplets of brane charges that
arise when the E_{8}^{+++}, or E_{11}, non-linearly realised theory is
dimensionally reduced to three dimensions on an eight dimensional torus. We
find precise agreement with the U-duality multiplet of brane charges previously
calculated, thus providing a natural eleven dimensional origin for the
"mysterious" brane charges found that do not occur as central charges in the
supersymmetry algebra. We also discuss the brane charges in nine dimensions and
how they arise from the IIA and IIB theories.Comment: 30 pages, plain te
Diagrammar and metamorphosis of coset symmetries in dimensionally reduced type IIB supergravity
Studying the reduction of type IIB supergravity from ten to three space-time
dimensions we describe the metamorphosis of Dynkin diagram for gravity line
"caterpillar" into a type IIB supergravity "dragonfly" that is triggered by
inclusion of scalars and antisymmetric tensor fields. The final diagram
corresponds to type IIB string theory E8 global symmetry group which is the
subgroup of the conjectured E11 hidden symmetry group. Application of the
results for getting the type IIA/IIB T-duality rules and for searching for type
IIB vacua solutions is considered.Comment: 9 pp, 7 figs, LATEX; to be published in JETP Let
E10 and SO(9,9) invariant supergravity
We show that (massive) D=10 type IIA supergravity possesses a hidden rigid
SO(9,9) symmetry and a hidden local SO(9) x SO(9) symmetry upon dimensional
reduction to one (time-like) dimension. We explicitly construct the associated
locally supersymmetric Lagrangian in one dimension, and show that its bosonic
sector, including the mass term, can be equivalently described by a truncation
of an E10/K(E10) non-linear sigma-model to the level \ell<=2 sector in a
decomposition of E10 under its so(9,9) subalgebra. This decomposition is
presented up to level 10, and the even and odd level sectors are identified
tentatively with the Neveu--Schwarz and Ramond sectors, respectively. Further
truncation to the level \ell=0 sector yields a model related to the reduction
of D=10 type I supergravity. The hyperbolic Kac--Moody algebra DE10, associated
to the latter, is shown to be a proper subalgebra of E10, in accord with the
embedding of type I into type IIA supergravity. The corresponding decomposition
of DE10 under so(9,9) is presented up to level 5.Comment: 1+39 pages LaTeX2e, 2 figures, 2 tables, extended tables obtainable
by downloading sourc
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