269 research outputs found
EXTENDED SUPERCONFORMAL SYMMETRY, FREUDENTHAL TRIPLE SYSTEMS AND GAUGED WZW MODELS
We review the construction of extended ( N=2 and N=4 ) superconformal
algebras over triple systems and the gauged WZW models invariant under them.
The N=2 superconformal algebras (SCA) realized over Freudenthal triple systems
(FTS) admit extension to ``maximal'' N=4 SCA's with SU(2)XSU(2)XU(1) symmetry.
A detailed study of the construction and classification of N=2 and N=4 SCA's
over Freudenthal triple systems is given. We conclude with a study and
classification of gauged WZW models with N=4 superconformal symmetry.Comment: Invited talk presented at the Gursey Memorial Conference I in
Istanbul, Turkiye (June 6-10, 1994). To appear in the proceedings of the
conference. (21 pages. Latex document.
Unified Maxwell-Einstein and Yang-Mills-Einstein Supergravity Theories in Five Dimensions
Unified N=2 Maxwell-Einstein supergravity theories (MESGTs) are supergravity
theories in which all the vector fields, including the graviphoton, transform
in an irreducible representation of a simple global symmetry group of the
Lagrangian. As was established long time ago, in five dimensions there exist
only four unified Maxwell-Einstein supergravity theories whose target manifolds
are symmetric spaces. These theories are defined by the four simple Euclidean
Jordan algebras of degree three. In this paper, we show that, in addition to
these four unified MESGTs with symmetric target spaces, there exist three
infinite families of unified MESGTs as well as another exceptional one. These
novel unified MESGTs are defined by non-compact (Minkowskian) Jordan algebras,
and their target spaces are in general neither symmetric nor homogeneous. The
members of one of these three infinite families can be gauged in such a way as
to obtain an infinite family of unified N=2 Yang-Mills-Einstein supergravity
theories, in which all vector fields transform in the adjoint representation of
a simple gauge group of the type SU(N,1). The corresponding gaugings in the
other two infinite families lead to Yang-Mills-Einstein supergravity theories
coupled to tensor multiplets.Comment: Latex 2e, 28 pages. v2: reference added, footnote 14 enlarge
Superconformal symmetry and maximal supergravity in various dimensions
In this paper we explore the relation between conformal superalgebras with 64
supercharges and maximal supergravity theories in three, four and six
dimensions using twistorial oscillator techniques. The massless fields of N=8
supergravity in four dimensions were shown to fit into a CPT-self-conjugate
doubleton supermultiplet of the conformal superalgebra SU(2,2|8) a long time
ago. We show that the fields of maximal supergravity in three dimensions can
similarly be fitted into the super singleton multiplet of the conformal
superalgebra OSp(16|4,R), which is related to the doubleton supermultiplet of
SU(2,2|8) by dimensional reduction. Moreover, we construct the ultra-short
supermultiplet of the six-dimensional conformal superalgebra OSp(8*|8) and show
that its component fields can be organized in an on-shell superfield. The
ultra-short OSp(8*|8) multiplet reduces to the doubleton supermultiplet of
SU(2,2|8) upon dimensional reduction. We discuss the possibility of a chiral
maximal (4,0) six-dimensional supergravity theory with USp(8) R-symmetry that
reduces to maximal supergravity in four dimensions and is different from
six-dimensional (2,2) maximal supergravity, whose fields cannot be fitted into
a unitary supermultiplet of a simple conformal superalgebra. Such an
interacting theory would be the gravitational analog of the (2,0) theory.Comment: 54 pages, PDFLaTeX, Section 5 and several references added. Version
accepted for publication in JHE
Orbifolds and Flows from Gauged Supergravity
We examine orbifolds of the IIB string via gauged supergravity. For the
gravity duals of the A_{n-1} quiver gauge theories, we extract the massless
degrees of freedom and assemble them into multiplets of N=4 gauged supergravity
in five dimensions. We examine the embedding of the gauge group into the
isometry group of the scalar manifold, as well as the symmetries of the scalar
potential. From this we find that there is a large SU(1,n) symmetry group which
relates different RG flows in the dual quiver gauge theory. We find that this
symmetry implies an extension of the usual duality between ten-dimensional IIB
solutions which involves exchanging geometric moduli with background fluxes.Comment: 37 pages, harvma
Quantum Attractor Flows
Motivated by the interpretation of the Ooguri-Strominger-Vafa conjecture as a
holographic correspondence in the mini-superspace approximation, we study the
radial quantization of stationary, spherically symmetric black holes in four
dimensions. A key ingredient is the classical equivalence between the radial
evolution equation and geodesic motion of a fiducial particle on the moduli
space M^*_3 of the three-dimensional theory after reduction along the time
direction. In the case of N=2 supergravity, M^*_3 is a para-quaternionic-Kahler
manifold; in this case, we show that BPS black holes correspond to a particular
class of geodesics which lift holomorphically to the twistor space Z of M^*_3,
and identify Z as the BPS phase space. We give a natural quantization of the
BPS phase space in terms of the sheaf cohomology of Z, and compute the exact
wave function of a BPS black hole with fixed electric and magnetic charges in
this framework. We comment on the relation to the topological string amplitude,
extensions to N>2 supergravity theories, and applications to automorphic black
hole partition functions.Comment: 43 pages, 6 figures; v2: typos and references added; v3: published
version, minor change
The extremal black holes of N=4 supergravity from so(8,2+n) nilpotent orbits
We consider the stationary solutions of N=4 supergravity coupled to n vector
multiplets that define linear superpositions of non-interacting extremal black
holes. The most general solutions of this type are derived from the graded
decompositions of so(8,2+n) associated to its nilpotent orbits. We illustrate
the formalism by giving explicitly asymptotically Minkowski non-BPS solutions
of the most exotic class depending on 6+n harmonic functions.Comment: Corrected version for publication, references adde
Quaternionic and Octonionic Spinors. A Classification
Quaternionic and octonionic realizations of Clifford algebras and spinors are
classified and explicitly constructed in terms of recursive formulas. The most
general free dynamics in arbitrary signature space-times for both quaternionic
and octonionic spinors is presented. In the octonionic case we further provide
a systematic list of results and tables expressing, e.g., the relations of the
octonionic Clifford algebras with the cosets over the Lorentz algebras,
the identities satisfied by the higher-rank antisymmetric octonionic tensors
and so on. Applications of these results range from the classification of
octonionic generalized supersymmetries, the construction of octonionic
superstrings, as well as the investigations concerning the recently discovered
octonionic -superalgebra and its superconformal extension.Comment: 24 pages, LaTe
Spectra of PP-Wave Limits of M-/Superstring Theory on AdS_p x S^q Spaces
In this paper we show how one can obtain very simply the spectra of the
PP-wave limits of M-theory over AdS_7(4) x S^4(7) spaces and IIB superstring
theory over AdS_5 x S^5 from the oscillator construction of the Kaluza-Klein
spectra of these theories over the corresponding spaces. The PP-wave symmetry
superalgebras are obtained by taking the number P of ``colors'' of oscillators
to be large (infinite). In this large P limit, the symmetry superalgebra
osp(8*|4) of AdS_7 x S^4 and the symmetry superalgebra osp(8|4,R) of AdS_4 x
S^7 lead to isomorphic PP-wave algebras, which is the semi-direct sum of
su(4|2) with H^(18,16), while the symmetry superalgebra su(2,2|4) of AdS_5 x
S^5 leads to the semi-direct sum of [psu(2|2) + psu(2|2) + u(1)] with H^(16,16)
as its PP-wave algebra [H^(m,n) denoting a super-Heisenberg algebra with m
bosonic and n fermionic generators]. The zero mode spectra of M-theory or IIB
superstring theory in the PP-wave limit corresponds simply to the unitary
positive energy representations of these algebras whose lowest weight vector is
the Fock vacuum of all the oscillators. General positive energy supermultiplets
including those corresponding to higher modes can similarly be constructed by
the oscillator method.Comment: Typos corrected; references added; minor modifications to improve
presentation; 37 pages, LaTeX fil
Decoupling limits of N=4 super Yang-Mills on R x S^3
We find new decoupling limits of N=4 super Yang-Mills (SYM) on R x S^3 with
gauge group SU(N). These decoupling limits lead to decoupled theories that are
much simpler than the full N=4 SYM but still contain many of its interesting
features. The decoupling limits correspond to being in a near-critical region,
near a point with zero temperature and critical chemical potentials. The new
decoupling limits are found by generalizing the limits of hep-th/0605234 to
include not only the chemical potentials for the SU(4) R-symmetry of N=4 SYM
but also the chemical potentials corresponding to the SO(4) symmetry. In the
decoupled theories it is possible to take a strong coupling limit in a
controllable manner since the full effective Hamiltonian is known. For planar
N=4 SYM on R x S^3 all the decoupled theories correspond to fully integrable
spin chains. We study the thermodynamics of the decoupled theories and find the
Hagedorn temperature for small and large values of the effective coupling. We
find an alternative formulation of the decoupling limits in the microcanonical
ensemble. This leads to a characterization of certain regimes of weakly coupled
N=4 SYM in which there are string-like states. Finally, we find a similar
decoupling limit for pure Yang-Mills theory, which for the planar limit leads
to a fully integrable decoupled theory.Comment: 48 pages, 1 figure; added references, published versio
No N=4 Strings on Wolf Spaces
We generalize the standard supersymmetric Kazama-Suzuki coset
construction to the case by requiring the {\it non-linear}
(Goddard-Schwimmer) quasi-superconformal algebra to be realized on
cosets. The constraints that we find allow very simple geometrical
interpretation and have the Wolf spaces as their natural solutions. Our results
obtained by using components-level superconformal field theory methods are
fully consistent with standard results about supersymmetric
two-dimensional non-linear sigma-models and WZNW models on Wolf spaces.
We construct the actions for the latter and express the quaternionic structure,
appearing in the coset solution, in terms of the symplectic structure
associated with the underlying Freudenthal triple system. Next, we gauge the
QSCA and build a quantum BRST charge for the string propagating on
a Wolf space. Surprisingly, the BRST charge nilpotency conditions rule out the
non-trivial Wolf spaces as consistent string backgrounds.Comment: 31 pages, LaTeX, special macros are include
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