190 research outputs found
U-duality (sub-)groups and their topology
We discuss some consequences of the fact that symmetry groups appearing in
compactified (super-)gravity may be non-simply connected. The possibility to
add fermions to a theory results in a simple criterion to decide whether a
3-dimensional coset sigma model can be interpreted as a dimensional reduction
of a higher dimensional theory. Similar criteria exist for higher dimensional
sigma models, though less decisive. Careful examination of the topology of
symmetry groups rules out certain proposals for M-theory symmetries, which are
not ruled out at the level of the algebra's. We conclude with an observation on
the relation between the ``generalized holonomy'' proposal, and the actual
symmetry groups resulting from E_10 and E_11 conjectures.Comment: LaTeX, 8 pages, 2 tables, 1 figure, uses IOP-style files. Contributed
to the proceedings of the RTN-workshop ``The quantum structure of space-time
and the geometrical nature of the fundamental interactions,'', Copenhagen,
Denmark, september 200
The topology of U-duality (sub-)groups
We discuss the topology of the symmetry groups appearing in compactified
(super-)gravity, and discuss two applications. First, we demonstrate that for 3
dimensional sigma models on a symmetric space G/H with G non-compact and H the
maximal compact subgroup of G, the possibility of oxidation to a higher
dimensional theory can immediately be deduced from the topology of H. Second,
by comparing the actual symmetry groups appearing in maximal supergravities
with the subgroups of SL(32,R) and Spin(32), we argue that these groups cannot
serve as a local symmetry group for M-theory in a formulation of de Wit-Nicolai
type.Comment: 18 pages, LaTeX, 1 figure, 2 table
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
Generalised Geometry for M-Theory
Generalised geometry studies structures on a d-dimensional manifold with a
metric and 2-form gauge field on which there is a natural action of the group
SO(d,d). This is generalised to d-dimensional manifolds with a metric and
3-form gauge field on which there is a natural action of the group .
This provides a framework for the discussion of M-theory solutions with flux. A
different generalisation is to d-dimensional manifolds with a metric, 2-form
gauge field and a set of p-forms for either odd or even on which there is a
natural action of the group . This is useful for type IIA or IIB
string solutions with flux. Further generalisations give extended tangent
bundles and extended spin bundles relevant for non-geometric backgrounds.
Special structures that arise for supersymmetric backgrounds are discussed.Comment: 31 page
An E9 multiplet of BPS states
We construct an infinite E9 multiplet of BPS states for 11D supergravity. For
each positive real root of E9 we obtain a BPS solution of 11D supergravity, or
of its exotic counterparts, depending on two non-compact transverse space
variables. All these solutions are related by U-dualities realised via E9 Weyl
transformations in the regular embedding of E9 in E10, E10 in E11. In this way
we recover the basic BPS solutions, namely the KK-wave, the M2 brane, the M5
brane and the KK6-monopole, as well as other solutions admitting eight
longitudinal space dimensions. A novel technique of combining Weyl reflexions
with compensating transformations allows the construction of many new BPS
solutions, each of which can be mapped to a solution of a dual effective action
of gravity coupled to a certain higher rank tensor field. For real roots of E10
which are not roots of E9, we obtain additional BPS solutions transcending 11D
supergravity (as exemplified by the lowest level solution corresponding to the
M9 brane). The relation between the dual formulation and the one in terms of
the original 11D supergravity fields has significance beyond the realm of BPS
solutions. We establish the link with the Geroch group of general relativity,
and explain how the E9 duality transformations generalize the standard Hodge
dualities to an infinite set of `non-closing dualities'.Comment: 76 pages, 6 figure
Dirichlet Branes on Orientifolds
We consider the classification of BPS and non-BPS D-branes in orientifold
models. In particular we construct all stable BPS and non-BPS D-branes in the
Gimon-Polchinski (GP) and Dabholkar-Park-Blum-Zaffaroni (DPBZ) orientifolds and
determine their stability regions in moduli space as well as decay products. We
find several kinds of integrally and torsion charged non-BPS D-branes. Certain
of these are found to have projective representations of the orientifold
GSO group on the Chan-Paton factors. It is found that the GP
orientifold is not described by equivariant orthogonal K-theory as may have
been at first expected. Instead a twisted version of this K-theory is expected
to be relevant.Comment: 33 pages, LaTeX, 5 figures. v2 typos corrected, references included,
(4,s)-branes re-examine
Super-Ehlers in Any Dimension
We classify the enhanced helicity symmetry of the Ehlers group to extended
supergravity theories in any dimension. The vanishing character of the
pseudo-Riemannian cosets occurring in this analysis is explained in terms of
Poincar\'e duality. The latter resides in the nature of regularly embedded
quotient subgroups which are non-compact rank preserving.Comment: 1+55 pages; 15 Tables, 6 Figures; v2 : some clarifications added in
Sec. 1 and in App.
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
Hyperbolic billiards of pure D=4 supergravities
We compute the billiards that emerge in the Belinskii-Khalatnikov-Lifshitz
(BKL) limit for all pure supergravities in D=4 spacetime dimensions, as well as
for D=4, N=4 supergravities coupled to k (N=4) Maxwell supermultiplets. We find
that just as for the cases N=0 and N=8 investigated previously, these billiards
can be identified with the fundamental Weyl chambers of hyperbolic Kac-Moody
algebras. Hence, the dynamics is chaotic in the BKL limit. A new feature
arises, however, which is that the relevant Kac-Moody algebra can be the
Lorentzian extension of a twisted affine Kac-Moody algebra, while the N=0 and
N=8 cases are untwisted. This occurs for N=5, N=3 and N=2. An understanding of
this property is provided by showing that the data relevant for determining the
billiards are the restricted root system and the maximal split subalgebra of
the finite-dimensional real symmetry algebra characterizing the toroidal
reduction to D=3 spacetime dimensions. To summarize: split symmetry controls
chaos.Comment: 21 page
Counting supersymmetric branes
Maximal supergravity solutions are revisited and classified, with particular
emphasis on objects of co-dimension at most two. This class of solutions
includes branes whose tension scales with g_s^{-\sigma} for \sigma>2. We
present a group theory derivation of the counting of these objects based on the
corresponding tensor hierarchies derived from E11 and discrete T- and U-duality
transformations. This provides a rationale for the wrapping rules that were
recently discussed for \sigma<4 in the literature and extends them. Explicit
supergravity solutions that give rise to co-dimension two branes are
constructed and analysed.Comment: 1+33 pages. To the memory of Laurent Houart. v2: Published version
with added reference
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