810,160 research outputs found
The Jones polynomial of ribbon links
For every n-component ribbon link L we prove that the Jones polynomial V(L)
is divisible by the polynomial V(O^n) of the trivial link. This integrality
property allows us to define a generalized determinant det V(L) :=
[V(L)/V(O^n)]_(t=-1), for which we derive congruences reminiscent of the Arf
invariant: every ribbon link L = (K_1,...,K_n) satisfies det V(L) = det(K_1)
>... det(K_n) modulo 32, whence in particular det V(L) = 1 modulo 8.
These results motivate to study the power series expansion V(L) =
\sum_{k=0}^\infty d_k(L) h^k at t=-1, instead of t=1 as usual. We obtain a
family of link invariants d_k(L), starting with the link determinant d_0(L) =
det(L) obtained from a Seifert surface S spanning L. The invariants d_k(L) are
not of finite type with respect to crossing changes of L, but they turn out to
be of finite type with respect to band crossing changes of S. This discovery is
the starting point of a theory of surface invariants of finite type, which
promises to reconcile quantum invariants with the theory of Seifert surfaces,
or more generally ribbon surfaces.Comment: 38 pages, reformatted in G&T style; minor changes suggested by the
refere
Modular invariance for conformal full field algebras
Let V^L and V^R be simple vertex operator algebras satisfying certain natural
uniqueness-of-vacuum, complete reducibility and cofiniteness conditions and let
F be a conformal full field algebra over the tensor product of V^L and V^R. We
prove that the q_\tau-\bar{q_\tau}-traces (natural traces involving
q_\tau=e^{2\pi i\tau} and \bar{q_\tau}=\bar{e^{2\pi i\tau}}) of geometrically
modified genus-zero correlation functions for F are convergent in suitable
regions and can be extended to doubly periodic functions with periods 1 and
\tau. We obtain necessary and sufficient conditions for these functions to be
modular invariant. In the case that V^L=V^R and F is one of those constructed
by the authors in \cite{HK}, we prove that all these functions are modular
invariant.Comment: 54 page
Microscopic theory for the glass transition in a system without static correlations
We study the orientational dynamics of infinitely thin hard rods of length L,
with the centers-of-mass fixed on a simple cubic lattice with lattice constant
a.We approximate the influence of the surrounding rods onto dynamics of a pair
of rods by introducing an effective rotational diffusion constant D(l),l=L/a.
We get D(l) ~ [1-v(l)], where v(l) is given through an integral of a
time-dependent torque-torque correlator of an isolated pair of rods. A glass
transition occurs at l_c, if v(l_c)=1. We present a variational and a
numerically exact evaluation of v(l).Close to l_c the diffusion constant
decreases as D(l) ~ (l_c-l)^\gamma, with \gamma=1. Our approach predicts a
glass transition in the absence of any static correlations, in contrast to
present form of mode coupling theory.Comment: 6 pages, 3 figure
Conformal off-diagonal boundary density profiles on a semi-infinite strip
The off-diagonal profile phi(v) associated with a local operator (order
parameter or energy density) close to the boundary of a semi-infinite strip
with width L is obtained at criticality using conformal methods. It involves
the surface exponent x_phi^s and displays a simple universal behaviour which
crosses over from surface finite-size scaling when v/L is held constant to
corner finite-size scaling when v/L -> 0.Comment: 5 pages, 1 figure, IOP macros and eps
On Deformation Quantization of Poisson-Lie Groups and Moduli Spaces of Flat Connections
We give simple explicit formulas for deformation quantization of Poisson-Lie
groups and of similar Poisson manifolds which can be represented as moduli
spaces of flat connections on surfaces. The star products depend on a choice of
Drinfe\v{l}d associator and are obtained by applying certain monoidal functors
(fusion and reduction) to commutative algebras in Drinfe\v{l}d categories. From
a geometric point of view this construction can be understood as a quantization
of the quasi-Poisson structures on moduli spaces of flat connections.Comment: 11 page
Charm meson resonances in D semileptonic decays
Motivated by recent experimental results we reconsider semileptonic D to P l
nu_l and D to V l nu_l decays within a model which combines heavy quark
symmetry and properties of the chiral Lagrangian. Using limits of soft
collinear effective theory and heavy quark effective theory we parametrize the
semileptonic form factors. We include excited charm meson states in our
Lagrangians and determine their impact on the charm meson semileptonic form
factors. Then we calculate branching ratios for all D to P l nu_l and D to V l
nu_l decays.Comment: 7 pages, 2 figures, Prepared for QCD@Work 2005 International Workshop
on Quantum Chromodynamics: Theory and Experiment, Conversano (Bari, Italy),
16-20 June 200
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