Related papers: Note on explicit construction of conformal generat…
Recently introduced ''fuzzy sphere'' method has enabled accurate numerical regularizations of certain three-dimensional (3D) conformal field theories (CFTs). The regularization is provided by the non-commutative geometry of the lowest…
We investigate the conformal algebra on the fuzzy sphere, and in particular the generators of translations and special conformal transformations which are emergent symmetries in the infinite IR but are broken along the RG flow. We show how…
Free theories are landmarks in the landscape of quantum field theories: their exact solvability serves as a pillar for perturbative constructions of interacting theories. Fuzzy sphere regularization, which combines quantum Hall physics with…
Fuzzy sphere models conjecturally realize 3d CFTs in small systems of spinful fermions, but why they work so well is still not fully understood. Their Hamiltonians are built from electron density operators projected to the lowest Landau…
The fuzzy-sphere regularisation is a powerful tool to study conformal field theories (CFT) in three spacetime dimensions. In this paper, we extend its scope to CFTs with local fermionic operators. We realise the free-Majorana-fermion CFT on…
We use the $K$ special conformal generator in the Fuzzy sphere setup of the Ising CFT to determine primary states. For $\Delta \lesssim 8$, we recover the known primaries and find several new ones, including in the parity-odd sector. We…
Boundaries not only are fundamental elements in nearly all realistic physical systems, but also greatly enrich the structure of quantum field theories. In this paper, we demonstrate that conformal field theory (CFT) with a boundary, known…
The fuzzy sphere method has enjoyed great success in the study of (2+1)-dimensional unitary conformal field theories (CFTs) by regularizing them as quantum Hall transitions on the sphere. Here, we extend this approach to the Yang-Lee…
Defects in conformal field theory (CFT) are of significant theoretical and experimental importance. The presence of defects theoretically enriches the structure of the CFT, but at the same time, it makes it more challenging to study,…
The three-dimensional cubic conformal field theory governs the critical behaviour of Heisenberg magnets with cubic anisotropy. Studying this theory non-perturbatively is challenging, because its most easily accessible observables are…
The $F$-function, the three-dimensional counterpart of the central charge in the 2D conformal field theory, measures the effective number of degrees of freedom in 3D quantum field theory, and it is monotonically decreasing under the…
We consider the transverse field Ising model in $(2+1)$D, putting 12 spins at the vertices of the regular icosahedron. The model is tiny by the exact diagonalization standards, and breaks rotation invariance. Yet we show that it allows a…
A fuzzy circle and a fuzzy 3-sphere are constructed as subspaces of fuzzy complex projective spaces, of complex dimension one and three, by modifying the Laplacians on the latter so as to give unwanted states large eigenvalues. This leaves…
In conformal field theory (CFT), the four-point correlator is a fundamental object that encodes CFT properties, constrains CFT structures, and connects to the gravitational scattering amplitude in holography theory. However, the four-point…
We extend the recently introduced fuzzy sphere technique for the 3d Ising CFT to the case of boundary CFT (BCFT) using the fuzzy hemisphere. This allows to study conformal boundary conditions, and we investigate the three boundary…
Numerical studies of phase transitions in statistical and quantum lattice models provide crucial insights into the corresponding Conformal Field Theories (CFTs). In higher dimensions, comparing finite-volume numerical results to…
Non-commutative geometry naturally emerges in low energy physics of Landau models as a consequence of level projection. In this work, we proactively utilize the level projection as an effective tool to generate fuzzy geometry. The level…
We study at zero temperature a microscopic quantum spin-1 model on the fuzzy sphere that realizes the $O(2)$ Wilson-Fisher conformal field theory (CFT) in $(2+1)$-dimensional spacetime at a quantum critical point. Here, we use the…
Supersymmetric conformal field theories (SCFTs) form a unique subset of quantum field theories which provide powerful insights into strongly coupled critical phenomena. Here, we present a microscopic and non-perturbative realization of the…
The $3D$ Ising transition, the most celebrated and unsolved critical phenomenon in nature, has long been conjectured to have emergent conformal symmetry, similar to the case of the $2D$ Ising transition. Yet, the emergence of conformal…