346 research outputs found
Quantum affine Cartan matrices, Poincare series of binary polyhedral groups, and reflection representations
We first review some invariant theoretic results about the finite subgroups
of SU(2) in a quick algebraic way by using the McKay correspondence and quantum
affine Cartan matrices. By the way it turns out that some parameters
(a,b,h;p,q,r) that one usually associates with such a group and hence with a
simply-laced Coxeter-Dynkin diagram have a meaningful definition for the
non-simply-laced diagrams, too, and as a byproduct we extend Saito's formula
for the determinant of the Cartan matrix to all cases. Returning to invariant
theory we show that for each irreducible representation i of a binary
tetrahedral, octahedral, or icosahedral group one can find a homomorphism into
a finite complex reflection group whose defining reflection representation
restricts to i.Comment: 19 page
Liouville integrability of a class of integrable spin Calogero-Moser systems and exponents of simple Lie algebras
In previous work, we introduced a class of integrable spin Calogero-Moser
systems associated with the classical dynamical r-matrices with spectral
parameter, as classified by Etingof and Varchenko for simple Lie algebras. Here
the main purpose is to establish the Liouville integrability of these systems
by a uniform method
Z_2-gradings of Clifford algebras and multivector structures
Let Cl(V,g) be the real Clifford algebra associated to the real vector space
V, endowed with a nondegenerate metric g. In this paper, we study the class of
Z_2-gradings of Cl(V,g) which are somehow compatible with the multivector
structure of the Grassmann algebra over V. A complete characterization for such
Z_2-gradings is obtained by classifying all the even subalgebras coming from
them. An expression relating such subalgebras to the usual even part of Cl(V,g)
is also obtained. Finally, we employ this framework to define spinor spaces,
and to parametrize all the possible signature changes on Cl(V,g) by
Z_2-gradings of this algebra.Comment: 10 pages, LaTeX; v2 accepted for publication in J. Phys.
The Schouten-Nijenhuis bracket, cohomology and generalized Poisson structures
Newly introduced generalized Poisson structures based on suitable
skew-symmetric contravariant tensors of even order are discussed in terms of
the Schouten-Nijenhuis bracket. The associated `Jacobi identities' are
expressed as conditions on these tensors, the cohomological contents of which
is given. In particular, we determine the linear generalized Poisson structures
which can be constructed on the dual spaces of simple Lie algebras.Comment: 29 pages. Plain TeX. Phyzzx needed. An example and some references
added. To appear in J. Phys.
Local BRST cohomology in the antifield formalism: II. Application to Yang-Mills theory
Yang-Mills models with compact gauge group coupled to matter fields are
considered. The general tools developed in a companion paper are applied to
compute the local cohomology of the BRST differential modulo the exterior
spacetime derivative for all values of the ghost number, in the space of
polynomials in the fields, the ghosts, the antifields (=sources for the BRST
variations) and their derivatives. New solutions to the consistency conditions
depending non trivially on the antifields are exhibited. For a
semi-simple gauge group, however, these new solutions arise only at ghost
number two or higher. Thus at ghost number zero or one, the inclusion of the
antifields does not bring in new solutions to the consistency condition
besides the already known ones. The analysis does not use power
counting and is purely cohomological. It can be easily extended to more general
actions containing higher derivatives of the curvature, or Chern-Simons terms.Comment: 30 pages Latex file, ULB-TH-94/07, NIKHEF-H 94-1
Generalized Weierstrass Relations and Frobenius reciprocity
This article investigates local properties of the further generalized
Weierstrass relations for a spin manifold immersed in a higher dimensional
spin manifold from viewpoint of study of submanifold quantum mechanics. We
show that kernel of a certain Dirac operator defined over , which we call
submanifold Dirac operator, gives the data of the immersion. In the derivation,
the simple Frobenius reciprocity of Clifford algebras and plays
important roles.Comment: 17pages. to be published in Mathematical Physics, Analysis and
Geometr
D6-branes and torsion
The D6-brane spectrum of type IIA vacua based on twisted tori and RR
background fluxes is analyzed. In particular, we compute the torsion factors of
the (co)homology groups H_n and describe the effect that they have on D6-brane
physics. For instance, the fact that H_3 contains Z_N subgroups explains why RR
tadpole conditions are affected by geometric fluxes. In addition, the presence
of torsional (co)homology shows why some D6-brane moduli are lifted, and it
suggests how the D-brane discretum appears in type IIA flux compactifications.
Finally, we give a clear, geometrical understanding of the Freed-Witten anomaly
in the present type IIA setup, and discuss its consequences for the
construction of semi-realistic flux vacua.Comment: 35 pages, 1 figure. One reference adde
Integrability of Type II Superstrings on Ramond-Ramond Backgrounds in Various Dimensions
We consider type II superstrings on AdS backgrounds with Ramond-Ramond flux
in various dimensions. We realize the backgrounds as supercosets and analyze
explicitly two classes of models: non-critical superstrings on AdS_{2d} and
critical superstrings on AdS_p\times S^p\times CY. We work both in the
Green--Schwarz and in the pure spinor formalisms. We construct a one-parameter
family of flat currents (a Lax connection) leading to an infinite number of
conserved non-local charges, which imply the classical integrability of both
sigma-models. In the pure spinor formulation, we use the BRST symmetry to prove
the quantum integrability of the sigma-model. We discuss how classical
\kappa-symmetry implies one-loop conformal invariance. We consider the addition
of space-filling D-branes to the pure spinor formalism.Comment: LaTeX2e, 56 pages, 1 figure, JHEP style; v2: references added, typos
fixed in some equations; v3: typos fixed to match the published versio
Type II compactifications on manifolds with SU(2) x SU(2) structure
We study compactifications of type II theories on SU(2) x SU(2) structure
manifolds to six, five and four spacetime dimensions. We use the framework of
generalized geometry to describe the NS-NS sector of such compactifications and
derive the structure of their moduli spaces. We show that in contrast to SU(3)
x SU(3) structure compactifications, there is no dynamical SU(2) x SU(2)
structure interpolating between an SU(2) structure and an identity structure.
Furthermore, we formulate type II compactifications on SU(2) x SU(2) structures
in the context of exceptional generalized geometry which makes the U-duality
group manifest and naturally incorporates the scalar degrees of freedom arising
in the Ramond-Ramond sector. Via this formalism we derive the structure of the
moduli spaces as it is expected from N=4 supergravity.Comment: 69 pages, v2 published versio
Random Matrices and Chaos in Nuclear Physics
The authors review the evidence for the applicability of random--matrix
theory to nuclear spectra. In analogy to systems with few degrees of freedom,
one speaks of chaos (more accurately: quantum chaos) in nuclei whenever
random--matrix predictions are fulfilled. An introduction into the basic
concepts of random--matrix theory is followed by a survey over the extant
experimental information on spectral fluctuations, including a discussion of
the violation of a symmetry or invariance property. Chaos in nuclear models is
discussed for the spherical shell model, for the deformed shell model, and for
the interacting boson model. Evidence for chaos also comes from random--matrix
ensembles patterned after the shell model such as the embedded two--body
ensemble, the two--body random ensemble, and the constrained ensembles. All
this evidence points to the fact that chaos is a generic property of nuclear
spectra, except for the ground--state regions of strongly deformed nuclei.Comment: 54 pages, 28 figure
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