1,287 research outputs found
Missing Modules, the Gnome Lie Algebra, and
We study the embedding of Kac-Moody algebras into Borcherds (or generalized
Kac-Moody) algebras which can be explicitly realized as Lie algebras of
physical states of some completely compactified bosonic string. The extra
``missing states'' can be decomposed into irreducible highest or lowest weight
``missing modules'' w.r.t. the relevant Kac-Moody subalgebra; the corresponding
lowest weights are associated with imaginary simple roots whose multiplicities
can be simply understood in terms of certain polarization states of the
associated string. We analyse in detail two examples where the momentum lattice
of the string is given by the unique even unimodular Lorentzian lattice
or , respectively. The former leads to the Borcherds
algebra , which we call ``gnome Lie algebra", with maximal Kac-Moody
subalgebra . By the use of the denominator formula a complete set of
imaginary simple roots can be exhibited, whereas the DDF construction provides
an explicit Lie algebra basis in terms of purely longitudinal states of the
compactified string in two dimensions. The second example is the Borcherds
algebra , whose maximal Kac-Moody subalgebra is the hyperbolic algebra
. The imaginary simple roots at level 1, which give rise to irreducible
lowest weight modules for , can be completely characterized;
furthermore, our explicit analysis of two non-trivial level-2 root spaces leads
us to conjecture that these are in fact the only imaginary simple roots for
.Comment: 31 pages, LaTeX2e, AMS packages, PSTRICK
A perturbative expansion scheme for supermembrane and matrix theory
We reconsider the supermembrane in a Minkowski background and in the light-cone gauge as a one-dimensional gauge theory of area preserving diffeomorphisms (APDs). Keeping the membrane tension as an independent parameter we show that is proportional to the gauge coupling of this gauge theory, such that the small (large) tension limit of the supermembrane corresponds to the weak (strong) coupling limit of the APD gauge theory and its SU matrix model approximation. A perturbative linearization of the supersymmetric theory suitable for a quantum mechanical path-integral treatment can be achieved by formulating a Nicolai map for the matrix model, which we work out explicitly to . The corresponding formulae remain well-defined in the limit , i.e. for the supermembrane theory itself. Furthermore we show that the map has improved convergence properties in comparison with the usual perturbative expansions because its Jacobian admits an expansion in with a non-zero radius of convergence. Possible implications for unsolved issues with the matrix model of M theory are also mentioned
AdS vacua and RG flows in three dimensional gauged supergravities
We study supersymmetric vacua in N=4 and N=8, three dimensional
gauged supergravities, with scalar manifolds and , non-semisimple Chern-Simons
gaugings and ,
respectively. These are in turn equivalent to SO(4) and
Yang-Mills theories coupled to supergravity. For the N=4 case, we study
renormalization group flows between UV and IR vacua with the same
amount of supersymmetry: in one case, with (3,1) supersymmetry, we can find an
analytic solution whereas in another, with (2,0) supersymmetry, we give a
numerical solution. In both cases, the flows turn out to be v.e.v. flows, i.e.
they are driven by the expectation value of a relevant operator in the dual
. These provide examples of v.e.v. flows between two vacua
within a gauged supergravity framework.Comment: 35 pages in JHEP form, 3 figures, typos corrected, references adde
CXCL12 inhibits expression of the NMDA receptor\u27s NR2B subunit through a histone deacetylase-dependent pathway contributing to neuronal survival
Entangling photons via the double quantum Zeno effect
We propose a scheme for entangling two photons via the quantum Zeno effect,
which describes the inhibition of quantum evolution by frequent measurements
and is based on the difference between summing amplitudes and probabilities.
For a given error probability , our scheme requires that the
one-photon loss rate and the two-photon absorption rate
in some medium satisfy , which is significantly improved in comparison to previous
approaches. Again based on the quantum Zeno effect, as well as coherent
excitations, we present a possibility to fulfill this requirement in an
otherwise linear optics set-up.Comment: 4 pages RevTeX, 2 figure
On Dimensional Degression in AdS(d)
We analyze the pattern of fields in d+1 dimensional anti-de Sitter space in
terms of those in d dimensional anti-de Sitter space. The procedure, which is
neither dimensional reduction nor dimensional compactification, is called
dimensional degression. The analysis is performed group-theoretically for all
totally symmetric bosonic and fermionic representations of the anti-de Sitter
algebra. The field-theoretical analysis is done for a massive scalar field in
AdS(d+d) and massless spin one-half, spin one, and spin two fields in
AdS(d+1). The mass spectra of the resulting towers of fields in AdS(d) are
found. For the scalar field case, the obtained results extend to the shadow
sector those obtained by Metsaev in [1] by a different method.Comment: 30 page
Gauged diffeomorphisms and hidden symmetries in Kaluza-Klein theories
We analyze the symmetries that are realized on the massive Kaluza-Klein modes
in generic D-dimensional backgrounds with three non-compact directions. For
this we construct the unbroken phase given by the decompactification limit, in
which the higher Kaluza-Klein modes are massless. The latter admits an
infinite-dimensional extension of the three-dimensional diffeomorphism group as
local symmetry and, moreover, a current algebra associated to SL(D-2,R)
together with the diffeomorphism algebra of the internal manifold as global
symmetries. It is shown that the `broken phase' can be reconstructed by gauging
a certain subgroup of the global symmetries. This deforms the three-dimensional
diffeomorphisms to a gauged version, and it is shown that they can be governed
by a Chern-Simons theory, which unifies the spin-2 modes with the Kaluza-Klein
vectors. This provides a reformulation of D-dimensional Einstein gravity, in
which the physical degrees of freedom are described by the scalars of a gauged
non-linear sigma model based on SL(D-2,R)/SO(D-2), while the metric appears in
a purely topological Chern-Simons form.Comment: 23 pages, minor changes, v3: published versio
Kaluza-Klein supergravity on AdS_3 x S^3
We construct a Chern-Simons type gauged N=8 supergravity in three spacetime
dimensions with gauge group SO(4) x T_\infty over the infinite dimensional
coset space SO(8,\infty)/(SO(8) x SO(\infty)), where T_\infty is an infinite
dimensional translation subgroup of SO(8,\infty). This theory describes the
effective interactions of the (infinitely many) supermultiplets contained in
the two spin-1 Kaluza-Klein towers arising in the compactification of N=(2,0)
supergravity in six dimensions on AdS_3 x S^3 with the massless supergravity
multiplet. After the elimination of the gauge fields associated with T_\infty,
one is left with a Yang Mills type gauged supergravity with gauge group SO(4),
and in the vacuum the symmetry is broken to the (super-)isometry group of AdS_3
x S^3, with infinitely many fields acquiring masses by a variant of the
Brout-Englert-Higgs effect.Comment: LaTeX2e, 24 pages; v2: references update
Effective Actions for Massive Kaluza-Klein States on AdS_3 x S^3 x S^3
We construct the effective supergravity actions for the lowest massive
Kaluza-Klein states on the supersymmetric background AdS_3 x S^3 x S^3. In
particular, we describe the coupling of the supergravity multiplet to the
lowest massive spin-3/2 multiplet which contains 256 physical degrees of
freedom and includes the moduli of the theory. The effective theory is realized
as the broken phase of a particular gauging of the maximal three-dimensional
supergravity with gauge group SO(4) x SO(4). Its ground state breaks half of
the supersymmetries leading to 8 massive gravitinos acquiring mass in a super
Higgs effect. The holographic boundary theory realizes the large N=(4,4)
superconformal symmetry.Comment: 31 pages, v2: minor change
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