# Construction of Modular Functors from Modular Tensor Categories

@article{Andersen2016ConstructionOM, title={Construction of Modular Functors from Modular Tensor Categories}, author={J{\o}rgen Ellegaard Andersen and William Elbaek Petersen}, journal={arXiv: Quantum Algebra}, year={2016} }

In this paper we follow the constructions of Turaev's book [Tu] closely, but with small modifications, to construct of a modular functor, in the sense of Kevin Walker, from any modular tensor category. We further show that this modular functor has duality and if the modular tensor category category is Hermitian or unitary, then the resulting modular functor is also Hermitian or unitary respectively.

## 2 Citations

### Geometric quantisation, the Hitchin-Witten connection and quantum operators in complex Chern-Simons theory

- Mathematics
- 2018

The present thesis is the result of my three-year PhD studies at the Centre for Quantum Geometry of Moduli Spaces under the supervision of Jørgen Ellegaard Andersen. The main focus is on Chern-Simons…

### Modular functors, cohomological field theories, and topological recursion

- MathematicsProceedings of Symposia in Pure Mathematics
- 2018

Given a topological modular functor $\mathcal{V}$ in the sense of Walker \cite{Walker}, we construct vector bundles over $\bar{\mathcal{M}}_{g,n}$, whose Chern classes define semi-simple…

## References

SHOWING 1-10 OF 34 REFERENCES

### GEOMETRIC CONSTRUCTION OF MODULAR FUNCTORS FROM CONFORMAL FIELD THEORY

- Mathematics
- 2007

We give a geometric construct of a modular functor for any simple Lie-algebra and any level by twisting the constructions in [16, 19] by a certain fractional power of the abelian theory first…

### Modular functors are determined by their genus zero data

- Mathematics
- 2006

We prove in this paper that the genus zero data of a modular functor determines the modular functor. We do this by establishing that the S-matrix in genus one with one point labeled arbitrarily can…

### CONSTRUCTING TQFTS FROM MODULAR FUNCTORS

- Mathematics
- 2001

We prove in this paper that any 2 dimensional modular functor satisfying that S1,1≠0 induces a family of 2+1 dimensionally topological quantum field theories. We do this for two kinds of modular…

### Flat connections and geometric quantization

- Mathematics
- 1990

Using the space of holomorphic symmetric tensors on the moduli space of stable bundles over a Riemann surface we construct a projectively flat connection on a vector bundle over Teichmüller space.…

### Hitchin’s connection in metaplectic quantization

- Mathematics
- 2012

We give a differential geometric construction of a connection, which we call the Hitchin connection, in the bundle of quantum Hilbert spaces arising from metaplectically corrected geometric…

### ABELIAN CONFORMAL FIELD THEORY AND DETERMINANT BUNDLES

- Mathematics
- 2003

Following [10], we study a so-called bc-ghost system of zero conformal dimension from the viewpoint of [14, 16]. We show that the ghost vacua construction results in holomorphic line bundles with…

### Quantum Invariants of Knots and 3-Manifolds

- Physics
- 1994

This monograph, now in its second revised edition, provides a systematic treatment of topological quantum field theories in three dimensions, inspired by the discovery of the Jones polynomial of…

### On Hitchin’s connection

- Mathematics
- 1997

The aim of this paper is to give an explicit expression for Hitchin's connection in the case of rank 2 bundles with trivial determinant over curves of genus 2. We recall the definition of this…

### Quantum field theory and the Jones polynomial

- Mathematics
- 1989

It is shown that 2+1 dimensional quantum Yang-Mills theory, with an action consisting purely of the Chern-Simons term, is exactly soluble and gives a natural framework for understanding the Jones…