202 research outputs found
Seven Dimensional Octonionic Yang-Mills Instanton and its Extension to an Heterotic String Soliton
We construct an octonionic instanton solution to the seven dimensional
Yang-Mills theory based on the exceptional gauge group which is the
automorphism group of the division algebra of octonions. This octonionic
instanton has an extension to a solitonic two-brane solution of the low energy
effective theory of the heterotic string that preserves two of the sixteen
supersymmetries and hence corresponds to space-time supersymmetry in the
(2+1) dimensions transverse to the seven dimensions where the Yang-Mills
instanton is defined.Comment: 7 pages, Latex document. This is the final version that appeared in
Phys. Lett. B that includes an extra paragraph about the physical properties
of the octonionic two-brane. We have also put an addendum regarding some
related references that were brought to our attention recentl
Harmonic Superspace, Minimal Unitary Representations and Quasiconformal Groups
We show that there is a remarkable connection between the harmonic superspace
(HSS) formulation of N=2, d=4 supersymmetric quaternionic Kaehler sigma models
that couple to N=2 supergravity and the minimal unitary representations of
their isometry groups. In particular, for N=2 sigma models with quaternionic
symmetric target spaces of the form G/HXSU(2) we establish a one-to-one mapping
between the Killing potentials that generate the isometry group G under Poisson
brackets in the HSS formulation and the generators of the minimal unitary
representation of G obtained by quantization of its geometric realization as a
quasiconformal group. Quasiconformal extensions of U-duality groups of four
dimensional N=2, d=4 Maxwell-Einstein supergravity theories (MESGT) had been
proposed as spectrum generating symmetry groups earlier. We discuss some of the
implications of our results, in particular, for the BPS black hole spectra of
4d, N=2 MESGTs.Comment: 20 pages; Latex file: references added; minor cosmetic change
Minimal unitary representation of SU(2,2) and its deformations as massless conformal fields and their supersymmetric extensions
We study the minimal unitary representation (minrep) of SO(4,2) over an
Hilbert space of functions of three variables, obtained by quantizing its
quasiconformal action on a five dimensional space. The minrep of SO(4,2), which
coincides with the minrep of SU(2,2) similarly constructed, corresponds to a
massless conformal scalar in four spacetime dimensions. There exists a
one-parameter family of deformations of the minrep of SU(2,2). For positive
(negative) integer values of the deformation parameter \zeta one obtains
positive energy unitary irreducible representations corresponding to massless
conformal fields transforming in (0,\zeta/2) ((-\zeta/2,0)) representation of
the SL(2,C) subgroup. We construct the supersymmetric extensions of the minrep
of SU(2,2) and its deformations to those of SU(2,2|N). The minimal unitary
supermultiplet of SU(2,2|4), in the undeformed case, simply corresponds to the
massless N=4 Yang-Mills supermultiplet in four dimensions. For each given
non-zero integer value of \zeta, one obtains a unique supermultiplet of
massless conformal fields of higher spin. For SU(2,2|4) these supermultiplets
are simply the doubleton supermultiplets studied in arXiv:hep-th/9806042.Comment: Revised with an extended introduction and additional references.
Typos corrected. 49 pages; Latex fil
Minimal unitary representation of SO*(8) = SO(6,2) and its SU(2) deformations as massless 6D conformal fields and their supersymmetric extensions
We study the minimal unitary representation (minrep) of SO(6,2) over an
Hilbert space of functions of five variables, obtained by quantizing its
quasiconformal realization. The minrep of SO(6,2), which coincides with the
minrep of SO*(8) similarly constructed, corresponds to a massless conformal
scalar field in six spacetime dimensions. There exists a family of
"deformations" of the minrep of SO*(8) labeled by the spin t of an SU(2)_T
subgroup of the little group SO(4) of lightlike vectors. These deformations
labeled by t are positive energy unitary irreducible representations of SO*(8)
that describe massless conformal fields in six dimensions. The SU(2)_T spin t
is the six dimensional counterpart of U(1) deformations of the minrep of 4D
conformal group SU(2,2) labeled by helicity. We also construct the
supersymmetric extensions of the minimal unitary representation of SO*(8) to
minimal unitary representations of OSp(8*|2N) that describe massless six
dimensional conformal supermultiplets. The minimal unitary supermultiplet of
OSp(8*|4) is the massless supermultiplet of (2,0) conformal field theory that
is believed to be dual to M-theory on AdS_7 x S^4.Comment: Revised with modified notation; Typos corrected; 58 pages; Latex fil
Generalized spacetimes defined by cubic forms and the minimal unitary realizations of their quasiconformal groups
We study the symmetries of generalized spacetimes and corresponding phase
spaces defined by Jordan algebras of degree three. The generic Jordan family of
formally real Jordan algebras of degree three describe extensions of the
Minkowskian spacetimes by an extra "dilatonic" coordinate, whose rotation,
Lorentz and conformal groups are SO(d-1), SO(d-1,1) XSO(1,1) and
SO(d,2)XSO(2,1), respectively. The generalized spacetimes described by simple
Jordan algebras of degree three correspond to extensions of Minkowskian
spacetimes in the critical dimensions (d=3,4,6,10) by a dilatonic and extra
(2,4,8,16) commuting spinorial coordinates, respectively. The Freudenthal
triple systems defined over these Jordan algebras describe conformally
covariant phase spaces. Following hep-th/0008063, we give a unified geometric
realization of the quasiconformal groups that act on their conformal phase
spaces extended by an extra "cocycle" coordinate. For the generic Jordan family
the quasiconformal groups are SO(d+2,4), whose minimal unitary realizations are
given. The minimal unitary representations of the quasiconformal groups F_4(4),
E_6(2), E_7(-5) and E_8(-24) of the simple Jordan family were given in our
earlier work hep-th/0409272.Comment: A typo in equation (37) corrected and missing titles of some
references added. Version to be published in JHEP. 38 pages, latex fil
Real forms of nonlinear superconformal and quasi-superconformal algebras and their unified realization
We give a complete classification of the real forms of simple nonlinear
superconformal algebras (SCA) and quasi-superconformal algebras (QSCA) and
present a unified realization of these algebras with simple symmetry groups.
This classification is achieved by establishing a correspondence between simple
nonlinear QSCA's and SCA's and quaternionic and super-quaternionic symmetric
spaces of simple Lie groups and Lie supergroups, respectively. The unified
realization involves a dimension zero boson (dilaton), dimension one symmetry
currents and dimension 1/2 free bosons for QSCA'a and dimension 1/2 free
fermions for SCA's. The dimension 1/2 free bosons and fermions are associated
with the quaternionic and super-quaternionic symmetric spaces of corresponding
Lie groups and Lie supergroups, respectively. We conclude with a discussion of
possible applications of our results.Comment: A paragraph together with a few new references added. Version to
appear in Nuclear Physics B. 36 pages, latex fil
Spectrum Generating Conformal and Quasiconformal U-Duality Groups, Supergravity and Spherical Vectors
After reviewing the algebraic structures that underlie the geometries of N=2
Maxwell-Einstein supergravity theories (MESGT) in five and four dimensions with
symmetric scalar manifolds, we give a unified realization of their three
dimensional U-duality groups as spectrum generating quasiconformal groups. They
are F_{4(4)}, E_{6(2)}, E_{7(-5)}, E_{8(-24)} and SO(n+2,4). Our formulation is
covariant with respect to U-duality symmetry groups of corresponding five
dimensional supergravity theories, which are SL(3,R), SL(3,C), SU*(6), E_{6(6)}
and SO(n-1,1)X SO(1,1), respectively. We determine the spherical vectors of
quasiconformal realizations of all these groups twisted by a unitary character.
We also give their quadratic Casimir operators and determine their values. Our
work lays the algebraic groundwork for constructing the unitary representations
of these groups induced by their geometric quasiconformal actions, which
include the quaternionic discrete series. For rank 2 cases, SU(2,1) and
G_{2(2)}, corresponding to simple N=2 supergravity in four and five dimensions,
this program was carried out in arXiv:0707.1669. We also discuss the
corresponding algebraic structures underlying symmetries of matter coupled N=4
and N>4 supergravity theories. They lead to quasiconformal realizations of
split real forms of U-duality groups as a straightforward extension of the
quaternionic real forms.Comment: Section 4 is split with the addition of a subsection on quadratic
Casimir operators; references added; typos corrected. Latex file; 53 page
Orbits of Exceptional Groups, Duality and BPS States in String Theory
We give an invariant classification of orbits of the fundamental
representations of exceptional groups and which classify
BPS states in string and M theories toroidally compactified to d=4 and d=5. The
exceptional Jordan algebra and the exceptional Freudenthal triple system and
their cubic and quartic invariants play a major role in this classification.
The cubic and quartic invariants correspond to the black hole entropy in d=5
and d=4, respectively. The classification of BPS states preserving different
numbers of supersymmetries is in close parallel to the classification of the
little groups and the orbits of timelike, lightlike and space-like vectors in
Minkowski space. The orbits of BPS black holes in N=2 Maxwell-Einstein
supergravity theories in d=4 and d=5 with symmetric space geometries are also
classified including the exceptional N=2 theory that has and
as its symmety in the respective dimensions.Comment: New references and two tables added, a new section on the orbits of
N=2 Maxwell-Einstein supergravity theories in d=4 and d=5 included and some
minor changes were made in other sections. 17 pages. Latex fil
Oscillator Construction of Spectra of PP-Wave Superalgebras in Eleven Dimensions
After reviewing the oscillator realization of the symmetry superalgebra of
the BMN matrix model on its maximally supersymmetric plane-wave background and
the construction of its zero-mode spectrum, we study a large number of
non-maximally supersymmetric pp-wave algebras in eleven dimensions which are
obtained by various restrictions from the maximally supersymmetric case (BMN
model). We also show how to obtain their zero-mode spectra, which we explicitly
construct in some chosen examples. Except for some `exotic' or degenerate
special cases, we believe our study covers all possible interesting pp-wave
superalgebras of this kind in eleven dimensions.Comment: 48 pages; latex fil
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