Description
The study of conformal field theories (CFTs) in 2+1 dimensions represents a significant challenge in theoretical physics due to their strong coupling nature and the lack of exact solutions.
In this talk, I will present recent advancements in numerical simulations of these CFTs using tensor network methods combined with the fuzzy sphere regularization technique.
This approach provides a powerful framework for non-perturbative studies of 2+1D CFTs, enabling (a somewhat) precise extraction of conformal data.
The fuzzy sphere regularization involves constructing quantum systems on a spherical geometry with a non-commutative structure, which serves as an ultraviolet regulator while maintaining the full SO(3) rotational symmetry of the sphere.
This construction is based on the well-known Integer quantum Hall physics and the physics of quantum Hall ferromagnets. After a brief introduction of tensor networks, I will discuss the strength and limitations of this method through the examples of the Ising and O(N) CFTs.
I will also discus its generalization to non-unitary CFTs, such as the Yang-Lee CFT or to boundary CFTs (BCFTs) using a fuzzy hemisphere.
