4,034 research outputs found
A note on a canonical dynamical r-matrix
It is well known that a classical dynamical -matrix can be associated with
every finite-dimensional self-dual Lie algebra \G by the definition
, where \omega\in \G and is the
holomorphic function given by for
z\in \C\setminus 2\pi i \Z^*. We present a new, direct proof of the statement
that this canonical -matrix satisfies the modified classical dynamical
Yang-Baxter equation on \G.Comment: 17 pages, LaTeX2
D-branes in the WZW model
It is stated in the literature that D-branes in the WZW-model associated with
the gluing condition J = - \bar{J} along the boundary correspond to branes
filling out the whole group volume. We show instead that the end-points of open
strings are rather bound to stay on `integer' conjugacy classes. In the case of
SU(2) level k WZW model we obtain k-1 two dimensional Euclidean D-branes and
two D particles sitting at the points e and -e.Comment: 2 pages, LaTe
The embedding structure and the shift operator of the U(1) lattice current algebra
The structure of block-spin embeddings of the U(1) lattice current algebra is
described. For an odd number of lattice sites, the inner realizations of the
shift automorphism areclassified. We present a particular inner shift operator
which admits a factorization involving quantum dilogarithms analogous to the
results of Faddeev and Volkov.Comment: 14 pages, Plain TeX; typos and a terminological mishap corrected;
version to appear in Lett.Math.Phy
Various versions of analytic QCD and skeleton-motivated evaluation of observables
We present skeleton-motivated evaluation of QCD observables. The approach can
be applied in analytic versions of QCD in certain classes of renormalization
schemes. We present two versions of analytic QCD which can be regarded as
low-energy modifications of the ``minimal'' analytic QCD and which reproduce
the measured value of the semihadronic tau decay ratio r{tau}. Further, we
describe an approach of calculating the higher order analytic couplings Ak
(k=2,3,...) on the basis of logarithmic derivatives of the analytic coupling
A1(Q^2). This approach can be easily applied in any version of analytic QCD. We
adjust the free parameters of the afore-mentioned two analytic models in such a
way that the skeleton-motivated evaluation reproduces the correct known values
of r{tau} and of the Bjorken polarized sum rule (BjPSR) db(Q^2) at a given
point (e.g., at Q^2=2 GeV^2). We then evaluate the low-energy behavior of the
Adler function dv(Q^2) and the BjPSR db(Q^2) in the afore-mentioned evaluation
approach, in the three analytic versions of QCD. We compare with the results
obtained in the ``minimal'' analytic QCD and with the evaluation approach of
Milton et al. and Shirkov.Comment: 30 pages, 14 eps-figures; v3: parameters of the analytic QCD models
M1 and M2 were refined, the numerical results modified accordingly, new
paragraph at the end of Sec.II and at the end of Sec.III, discussion of
Figs.4 extended, references added; version to appear in PR
Representation Theory of Lattice Current Algebras
Lattice current algebras were introduced as a regularization of the left- and
right moving degrees of freedom in the WZNW model. They provide examples of
lattice theories with a local quantum symmetry U_q(\sg). Their representation
theory is studied in detail. In particular, we construct all irreducible
representations along with a lattice analogue of the fusion product for
representations of the lattice current algebra. It is shown that for an
arbitrary number of lattice sites, the representation categories of the lattice
current algebras agree with their continuum counterparts.Comment: 35 pages, LaTeX file, the revised version of the paper, to be
published in Commun. Math. Phys. , the definition of the fusion product for
lattice current algebras is correcte
Realistic theory of electromagnetically-induced transparency and slow light in a hot vapor of atoms undergoing collisions
We present a realistic theoretical treatment of a three-level
system in a hot atomic vapor interacting with a coupling and a probe field of
arbitrary strengths, leading to electromagnetically-induced transparency and
slow light under the two-photon resonance condition. We take into account all
the relevant decoherence processes including col5Blisions. Velocity-changing
collisions (VCCs) are modeled in the strong collision limit effectively, which
helps in achieving optical pumping by the coupling beam across the entire
Doppler profile. The steady-state expressions for the atomic density-matrix
elements are numerically evaluated to yield the experimentally measured
response characteristics. The predictions, taking into account a dynamic rate
of influx of atoms in the two lower levels of the , are in excellent
agreement with the reported experimental results for He*. The role played
by the VCC parameter is seen to be distinct from that by the transit time or
Raman coherence decay rate
Decomposable representations and Lagrangian submanifolds of moduli spaces associated to surface groups
In this paper, we construct a Lagrangian submanifold of the moduli space
associated to the fundamental group of a punctured Riemann surface (the space
of representations of this fundamental group into a compact connected Lie
group). This Lagrangian submanifold is obtained as the fixed-point set of an
anti-symplectic involution defined on the moduli space. The notion of
decomposable representation provides a geometric interpretation of this
Lagrangian submanifold
2D Conformal Field Theories and Holography
It is known that the chiral part of any 2d conformal field theory defines a
3d topological quantum field theory: quantum states of this TQFT are the CFT
conformal blocks. The main aim of this paper is to show that a similar CFT/TQFT
relation exists also for the full CFT. The 3d topological theory that arises is
a certain ``square'' of the chiral TQFT. Such topological theories were studied
by Turaev and Viro; they are related to 3d gravity. We establish an
operator/state correspondence in which operators in the chiral TQFT correspond
to states in the Turaev-Viro theory. We use this correspondence to interpret
CFT correlation functions as particular quantum states of the Turaev-Viro
theory. We compute the components of these states in the basis in the
Turaev-Viro Hilbert space given by colored 3-valent graphs. The formula we
obtain is a generalization of the Verlinde formula. The later is obtained from
our expression for a zero colored graph. Our results give an interesting
``holographic'' perspective on conformal field theories in 2 dimensions.Comment: 29+1 pages, many figure
On dynamical adjoint functor
We give an explicit formula relating the dynamical adjoint functor and
dynamical twist over nonalbelian base to the invariant pairing on parabolic
Verma modules. As an illustration, we give explicit - and
-invariant star product on projective spaces
- âŠ