منابع مشابه
Integral Lattices in Tqft
We find explicit bases for naturally defined lattices over a ring of algebraic integers in the SO(3)-TQFT-modules of surfaces at roots of unity of odd prime order. Some applications relating quantum invariants to classical 3-manifold topology are given.
متن کاملHow perverse is TQFT?
In this talk we will introduce Jones polynomial and Khovanov's homology of a knot. These topological invariants are (conjecturally) related to perverse sheaves on Grassmannians. We will try to understand how, and how understanding that might lead to new developments in Topological Quantum Field Theory.
متن کاملIntegral Tqft for a One-holed Torus
We give new explicit formulas for the representations of the mapping class group of a genus one surface with one boundary component which arise from Integral TQFT. Our formulas allow one to compute the h-adic expansion of the TQFT-matrix associated to a mapping class in a straightforward way. Truncating the h-adic expansion gives an approximation of the representation by representations into fi...
متن کاملToeplitz operators in TQFT via skein theory
Topological quantum field theory associates to a punctured surface Σ, a level r and colors c in {1, . . . , r− 1} at the marked points a finite dimensional hermitian space Vr(Σ, c). Curves γ on Σ act as Hermitian operator T γ r on these spaces. In the case of the punctured torus and the 4 times punctured sphere, we prove that the matrix elements of T γ r have an asymptotic expansion in powers o...
متن کاملCoupling a QFT to a TQFT and Duality
We consider coupling an ordinary quantum field theory with an infinite number of degrees of freedom to a topological field theory. On R the new theory differs from the original one by the spectrum of operators. Sometimes the local operators are the same but there are different line operators, surface operators, etc. The effects of the added topological degrees of freedom are more dramatic when ...
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ژورنال
عنوان ژورنال: Journal of Geometry and Physics
سال: 2018
ISSN: 0393-0440
DOI: 10.1016/j.geomphys.2017.07.002