10,233 research outputs found
Mass-Gaps and Spin Chains for (Super) Membranes
We present a method for computing the non-perturbative mass-gap in the theory
of Bosonic membranes in flat background spacetimes with or without background
fluxes. The computation of mass-gaps is carried out using a matrix
regularization of the membrane Hamiltonians. The mass gap is shown to be
naturally organized as an expansion in a 'hidden' parameter, which turns out to
be : d being the related to the dimensionality of the background
space. We then proceed to develop a large perturbation theory for the
membrane/matrix-model Hamiltonians around the quantum/mass corrected effective
potential. The same parameter that controls the perturbation theory for the
mass gap is also shown to control the Hamiltonian perturbation theory around
the effective potential. The large perturbation theory is then translated
into the language of quantum spin chains and the one loop spectra of various
Bosonic matrix models are computed by applying the Bethe ansatz to the one-loop
effective Hamiltonians for membranes in flat space times. Apart from membranes
in flat spacetimes, the recently proposed matrix models (hep-th/0607005) for
non-critical membranes in plane wave type spacetimes are also analyzed within
the paradigm of quantum spin chains and the Bosonic sectors of all the models
proposed in (hep-th/0607005) are diagonalized at the one-loop level.Comment: 36 Page
Extended Supersymmetries and the Dirac Operator
We consider supersymmetric quantum mechanical systems in arbitrary dimensions
on curved spaces with nontrivial gauge fields. The square of the Dirac operator
serves as Hamiltonian. We derive a relation between the number of supercharges
that exist and restrictions on the geometry of the underlying spaces as well as
the admissible gauge field configurations. From the superalgebra with two or
more real supercharges we infer the existence of integrability conditions and
obtain a corresponding superpotential. This potential can be used to deform the
supercharges and to determine zero modes of the Dirac operator. The general
results are applied to the Kahler spaces CP^n.Comment: 22 pages, no figure
Higher Spins in Hyper-Superspace
We extend the results of arXiv:1401.1645 on the generalized conformal
Sp(2n)-structure of infinite multiplets of higher spin fields, formulated in
spaces with extra tensorial directions (hyperspaces), to the description of
OSp(1|2n)-invariant infinite-dimensional higher-spin supermultiplets formulated
in terms of scalar superfields on flat hyper-superspaces and on OSp(1|n)
supergroup manifolds. We find generalized superconformal transformations
relating the superfields and their equations of motion in flat hyper-superspace
with those on the OSp(1|n) supermanifold. We then use these transformations to
relate the two-, three- and four-point correlation functions of the scalar
superfields on flat hyperspace, derived by requiring the OSp(1|2n) invariance
of the correlators, to correlation functions on the OSp(1|n) group manifold. As
a byproduct, for the simplest particular case of a conventional N=1, D=3
superconformal theory of scalar superfields, we also derive correlation
functions of component fields of the scalar supermultiplet including those of
auxiliary fields.Comment: 25 pages, discussion in section 4.1 improved, references added;
subsection 2.4 and conclusions expanded, typos corrected, references added,
published versio
M-theory moduli spaces and torsion-free structures
Motivated by the description of M-theory compactifications to
four-dimensions given by Exceptional Generalized Geometry, we propose a way to
geometrize the M-theory fluxes by appropriately relating the compactification
space to a higher-dimensional manifold equipped with a torsion-free structure.
As a non-trivial example of this proposal, we construct a bijection from the
set of -structures on an eight-dimensional -bundle to the set
of -structures on the base space, fully characterizing the
-torsion clases when the total space is equipped with a torsion-free
-structure. Finally, we elaborate on how the higher-dimensional
manifold and its moduli space of torsion-free structures can be used to obtain
information about the moduli space of M-theory compactifications.Comment: 24 pages. Typos fixed. Minor clarifications adde
Supersymmetric Higher Spin Theories
We revisit the higher spin extensions of the anti de Sitter algebra in four
dimensions that incorporate internal symmetries and admit representations that
contain fermions, classified long ago by Konstein and Vasiliev. We construct
the , Euclidean and Kleinian version of these algebras, as well as the
corresponding fully nonlinear Vasiliev type higher spin theories, in which the
reality conditions we impose on the master fields play a crucial role. The
supersymmetric higher spin theory in , on which we elaborate
further, is included in this class of models. A subset of Konstein-Vasiliev
algebras are the higher spin extensions of the superalgebras
for mod 4 and can be realized using
fermionic oscillators. We tensor the higher superalgebras of the latter kind
with appropriate internal symmetry groups and show that the mod 4
higher spin algebras are isomorphic to those with mod 4. We
describe the fully nonlinear higher spin theories based on these algebras as
well, and we elaborate further on the supersymmetric theory,
providing two equivalent descriptions one of which exhibits manifestly its
relation to the supersymmetric higher spin theory.Comment: 30 pages. Contribution to J. Phys. A special volume on "Higher Spin
Theories and AdS/CFT" edited by M. R. Gaberdiel and M. Vasilie
Grassmannians,Calibrations and Five-Brane Intersections
We present a geometric construction of a new class of hyper-Kahler manifolds
with torsion. This involves the superposition of the four-dimensional
hyper-Kahler geometry with torsion associated with the NS-5-brane along
quaternionic planes in quaternionic k-space, \bH^k. We find the moduli space
of these geometries and show that it can be constructed using the bundle space
of the canonical quaternionic line bundle over a quaternionic projective space.
We also investigate several special cases which are associated with certain
classes of quaternionic planes in \bH^k. We then show that the
eight-dimensional geometries we have found can be constructed using
quaternionic calibrations. We generalize our construction to superpose the same
four-dimensional hyper-Kahler geometry with torsion along complex planes in
\bC^{2k}. We find that the resulting geometry is Kahler with torsion. The
moduli space of these geometries is also investigated. In addition, the
applications of these new geometries to M-theory and sigma models are
presented. In particular, we find new solutions of IIA supergravity with the
interpretation of intersecting NS-5-branes at Sp(2)-angles on a string and show
that they preserve 3/32, 1/8, 5/32 and 3/16 of supersymmetry. We also show that
two-dimensional sigma models with target spaces the above manifolds have (p,q)
extended supersymmetry.Comment: 39 pages, phyzzx; a previously undetermined fraction of supersymmetry
has now been fixed; a table has been replaced; version submitted for
publication in CM
Hamiltonian reduction and supersymmetric mechanics with Dirac monopole
We apply the technique of Hamiltonian reduction for the construction of
three-dimensional supersymmetric mechanics specified by the
presence of a Dirac monopole. For this purpose we take the conventional supersymmetric mechanics on the four-dimensional conformally-flat spaces
and perform its Hamiltonian reduction to three-dimensional system. We formulate
the final system in the canonical coordinates, and present, in these terms, the
explicit expressions of the Hamiltonian and supercharges. We show that, besides
a magnetic monopole field, the resulting system is specified by the presence of
a spin-orbit coupling term. A comparison with previous work is also carried
out.Comment: 9 pages, LaTeX file, PACS numbers: 11.30.Pb, 03.65.-w, accepted for
publication in PRD; minor changes in the Conclusion, the Bibliography and the
Acknowledgemen
Towards an M5-Brane Model I: A 6d Superconformal Field Theory
We present an action for a six-dimensional superconformal field theory
containing a non-abelian tensor multiplet. All of the ingredients of this
action have been available in the literature. We bring these pieces together by
choosing the string Lie 2-algebra as a gauge structure, which we motivated in
previous work. The kinematical data contains a connection on a categorified
principal bundle, which is the appropriate mathematical description of the
parallel transport of self-dual strings. Our action can be written down for
each of the simply laced Dynkin diagrams, and each case reduces to a
four-dimensional supersymmetric Yang--Mills theory with corresponding gauge Lie
algebra. Our action also reduces nicely to an M2-brane model which is a
deformation of the ABJM model. While this action is certainly not the desired
M5-brane model, we regard it as a key stepping stone towards a potential
construction of the (2,0)-theory.Comment: 1+39 pages, v3: minor improvements, published versio
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