Conformal scalar field theory from Ising tricriticality on the fuzzy sphere

TL;DR

This paper demonstrates how a bilayer quantum Hall system on the fuzzy sphere can realize a free scalar conformal field theory, expanding the types of theories accessible via this regularization method.

Contribution

It introduces a new approach to simulate free theories on the fuzzy sphere by engineering an Ising tricritical point in a bilayer quantum Hall system.

Findings

Matching energy spectrum with Gaussian fixed point

Operator structure consistent with free scalar CFT

Nonperturbative evidence for free theory emergence

Abstract

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 state-operator correspondence, has recently been proposed as a promising framework for simulating three-dimensional conformal field theories (CFTs), but so far it has not provided access to free theories. We overcome this limitation by designing a bilayer quantum Hall system that hosts an Ising tricritical point -- a nontrivial fixed point where first-order and second-order transitions meet -- which flows to the conformally coupled scalar theory in the infrared. The critical energy spectrum and operator structure match those at the Gaussian fixed point, providing nonperturbative evidence for the emergence of a free scalar CFT. Our results expand the landscape of CFTs realizable on the fuzzy sphere and demonstrate that even free bosonic theories -- previously inaccessible -- can emerge from interacting electrons in this framework.