806 research outputs found
Paths on graphs and associated quantum groupoids
Given any simple biorientable graph it is shown that there exists a weak
{*}-Hopf algebra constructed on the vector space of graded endomorphisms of
essential paths on the graph. This construction is based on a direct sum
decomposition of the space of paths into orthogonal subspaces one of which is
the space of essential paths. Two simple examples are worked out with certain
detail, the ADE graph and the affine graph . For the first
example the weak {*}-Hopf algebra coincides with the so called double triangle
algebra. No use is made of Ocneanu's cell calculus.Comment: To appear in the proceedings of "Colloquium on Hopf Algebras, Quantum
Groups and Tensor Categories", August 31st to September 4th 2009, La Falda,
Cordoba, Argentina. Additional clarifying remarks has been include
QCD condensates and holographic Wilson loops for asymptotically AdS spaces
The minimization of the Nambu-Goto action for a surface whose contour defines
a circular Wilson loop of radius a placed at a finite value of the coordinate
orthogonal to the boundary is considered. This is done for asymptotically AdS
spaces. The condensates of even dimension through are calculated in
terms of the coefficient of in the expansion of the on-shell subtracted
Nambu-Goto action for small
The subtraction employed is such that it presents no conflict with conformal
invariance in the AdS case and need not introduce an additional infrared scale
for the case of confining geometries. It is shown that the UV value of the
condensates is universal in the sense that they only depends on the first
coefficients of the difference with the AdS case.Comment: 11 pages, 1 figur
- …