9,059 research outputs found
Conformal nets I: coordinate-free nets
We describe a coordinate-free perspective on conformal nets, as functors from
intervals to von Neumann algebras. We discuss an operation of fusion of
intervals and observe that a conformal net takes a fused interval to the fiber
product of von Neumann algebras. Though coordinate-free nets do not a priori
have vacuum sectors, we show that there is a vacuum sector canonically
associated to any circle equipped with a conformal structure. This is the first
in a series of papers constructing a 3-category of conformal nets, defects,
sectors, and intertwiners.Comment: Updated to published versio
Conformal nets II: conformal blocks
Conformal nets provide a mathematical formalism for conformal field theory.
Associated to a conformal net with finite index, we give a construction of the
`bundle of conformal blocks', a representation of the mapping class groupoid of
closed topological surfaces into the category of finite-dimensional projective
Hilbert spaces. We also construct infinite-dimensional spaces of conformal
blocks for topological surfaces with smooth boundary. We prove that the
conformal blocks satisfy a factorization formula for gluing surfaces along
circles, and an analogous formula for gluing surfaces along intervals. We use
this interval factorization property to give a new proof of the modularity of
the category of representations of a conformal net.Comment: Updated to published versio
NLO Corrections to the kernel of the BKP-equations
We present results for the NLO kernel of the BKP equations for composite
states of three reggeized gluons in the Odderon channel, both in QCD and in N=4
SYM. The NLO kernel consists of the NLO BFKL kernel in the color octet
representation and the connected kernel, computed in the tree
approximation.Comment: 28 pages, 7 figure
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