554 research outputs found
The Minimal Unitary Representation of E_8(8)
We give a new construction of the minimal unitary representation of the
exceptional group E_8(8) on a Hilbert space of complex functions in 29
variables. Due to their manifest covariance with respect to the E_7(7) subgroup
of E_8(8) our formulas are simpler than previous realizations, and thus well
suited for applications in superstring and M theory.Comment: 24 pages, 1 figure, version to be published in ATM
Domain Wall World(s)
Gravitational properties of domain walls in fundamental theory and their
implications for the trapping of gravity are reviewed. In particular, the
difficulties to embed gravity trapping configurations within gauged
supergravity is reviewed and the status of the domain walls obtained via the
breathing mode of sphere reduced Type IIB supergravity is presented.Comment: 11 pages, Based on talk given at Strings 2000 Minor corrections,
references adde
Conformal and Quasiconformal Realizations of Exceptional Lie Groups
We present a nonlinear realization of E_8 on a space of 57 dimensions, which
is quasiconformal in the sense that it leaves invariant a suitably defined
``light cone'' in 57 dimensions. This realization, which is related to the
Freudenthal triple system associated with the unique exceptional Jordan algebra
over the split octonions, contains previous conformal realizations of the lower
rank exceptional Lie groups on generalized space times, and in particular a
conformal realization of E_7 on a 27 dimensional vector space which we exhibit
explicitly. Possible applications of our results to supergravity and M-Theory
are briefly mentioned.Comment: 21 pages, 1 figure. Revised version. Connection between SU(8) and
SL(8,R) bases clarified; formulas corrected; references adde
Intertwining Operator Realization of the AdS/CFT Correspondence
We give a group-theoretic interpretation of the AdS/CFT correspondence as
relation of representation equivalence between representations of the conformal
group describing the bulk AdS fields and the coupled boundary fields
and . We use two kinds of equivalences. The first kind is
equivalence between bulk fields and boundary fields and is established here.
The second kind is the equivalence between coupled boundary fields. Operators
realizing the first kind of equivalence for special cases were given by Witten
and others - here they are constructed in a more general setting from the
requirement that they are intertwining operators. The intertwining operators
realizing the second kind of equivalence are provided by the standard conformal
two-point functions. Using both equivalences we find that the bulk field has in
fact two boundary fields, namely, the coupled boundary fields. Thus, from the
viewpoint of the bulk-boundary correspondence the coupled fields are on an
equal footing. Our setting is more general since our bulk fields are described
by representations of the Euclidean conformal group , induced from
representations of the maximal compact subgroup of . From
these large reducible representations we can single out representations which
are equivalent to conformal boundary representations labelled by the conformal
weight and by arbitrary representations of the Euclidean Lorentz group
, such that is contained in the restriction of to .
Thus, our boundary-to-bulk operators can be compared with those in the
literature only when for a fixed we consider a 'minimal' representation
containing .Comment: 25 pages, TEX file using harvmac.tex; v2: misprints corrected; to
appear in Nuclear Physics
Explicit Orbit Classification of Reducible Jordan Algebras and Freudenthal Triple Systems
We determine explicit orbit representatives of reducible Jordan algebras and
of their corresponding Freudenthal triple systems. This work has direct
application to the classification of extremal black hole solutions of N = 2, 4
locally supersymmetric theories of gravity coupled to an arbitrary number of
Abelian vector multiplets in D = 4, 5 space-time dimensions.Comment: 18 pages. Updated to match published versio
Fake Supergravity and Domain Wall Stability
We review the generalized Witten-Nester spinor stability argument for flat
domain wall solutions of gravitational theories. Neither the field theory nor
the solution need be supersymmetric. Nor is the space-time dimension
restricted. We develop the non-trivial extension required for AdS-sliced domain
walls and apply this to show that the recently proposed "Janus" solution of
Type IIB supergravity is stable non-perturbatively for a broad class of
deformations. Generalizations of this solution to arbitrary dimension and a
simple curious linear dilaton solution of Type IIB supergravity are byproducts
of this work.Comment: 37 pages, 3 figures, v2: minor corrections, references and
acknowledgments adde
Lectures on Spectrum Generating Symmetries and U-duality in Supergravity, Extremal Black Holes, Quantum Attractors and Harmonic Superspace
We review the underlying algebraic structures of supergravity theories with
symmetric scalar manifolds in five and four dimensions, orbits of their
extremal black hole solutions and the spectrum generating extensions of their
U-duality groups. For 5D, N=2 Maxwell-Einstein supergravity theories (MESGT)
defined by Euclidean Jordan algebras, J, the spectrum generating symmetry
groups are the conformal groups Conf(J) of J which are isomorphic to their
U-duality groups in four dimensions. Similarly, the spectrum generating
symmetry groups of 4D, N=2 MESGTs are the quasiconformal groups QConf(J)
associated with J that are isomorphic to their U-duality groups in three
dimensions. We then review the work on spectrum generating symmetries of
spherically symmetric stationary 4D BPS black holes, based on the equivalence
of their attractor equations and the equations for geodesic motion of a
fiducial particle on the target spaces of corresponding 3D supergravity
theories obtained by timelike reduction. We also discuss the connection between
harmonic superspace formulation of 4D, N=2 sigma models coupled to supergravity
and the minimal unitary representations of their isometry groups obtained by
quantizing their quasiconformal realizations. We discuss the relevance of this
connection to spectrum generating symmetries and conclude with a brief summary
of more recent results.Comment: 55 pages; Latex fil
M-Theory on (K3 X S^1)/Z_2
We analyze -theory compactified on where the
changes the sign of the three form gauge field, acts on as a parity
transformation and on K3 as an involution with eight fixed points preserving
SU(2) holonomy. At a generic point in the moduli space the resulting theory has
as its low energy limit N=1 supergravity theory in six dimensions with eight
vector, nine tensor and twenty hypermultiplets. The gauge symmetry can be
enhanced (e.g. to ) at special points in the moduli space. At other
special points in the moduli space tensionless strings appear in the theory.Comment: LaTeX file, 11 page
Strings, Black Holes, and Quantum Information
We find multiple relations between extremal black holes in string theory and
2- and 3-qubit systems in quantum information theory. We show that the entropy
of the axion-dilaton extremal black hole is related to the concurrence of a
2-qubit state, whereas the entropy of the STU black holes, BPS as well as
non-BPS, is related to the 3-tangle of a 3-qubit state. We relate the 3-qubit
states with the string theory states with some number of D-branes. We identify
a set of "large" black holes with the maximally entangled GHZ-class of states
and "small" black holes with separable, bipartite and W states. We sort out the
relation between 3-qubit states, twistors, octonions, and black holes. We give
a simple expression for the entropy and the area of stretched horizon of
"small'' black holes in terms of a norm and 2-tangles of a 3-qubit system.
Finally, we show that the most general expression for the black hole and black
ring entropy in N=8 supergravity/M-theory, which is given by the famous quartic
Cartan E_{7(7)} invariant, can be reduced to Cayley's hyperdeterminant
describing the 3-tangle of a 3-qubit state.Comment: 31 pages, 10 figures. A version to appear in Physical Revie
Generalized Attractors in Five-Dimensional Gauged Supergravity
In this paper we study generalized attractors in N=2 gauged supergravity
theory in five dimensions coupled to arbitrary number of hyper, vector and
tensor multiplets. We look for attractor solutions with constant anholonomy
coefficients. By analyzing the equations of motion we derive the attractor
potential. We further show that the generalized attractor potential can be
obtained from the fermionic shifts. We study some simple examples and show that
constant anholonomy gives rise to homogeneous black branes in five dimensions.Comment: 30 pages, no figures,V3 minor revisions, to appear in JHE
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