Ising model close to $d=2$

TL;DR

This paper investigates the behavior of the critical Ising model near two dimensions using advanced conformal bootstrap techniques, revealing complex singularities and the necessity of infinitely many new states as the dimension varies.

Contribution

It introduces novel numerical and analytical bootstrap methods in Lorentzian signature to analyze the $d=2+psilon$ Ising model, uncovering singular corrections and the emergence of infinitely many states.

Findings

Leading corrections are more singular than psilon

Infinite new states are required due to conformal symmetry dependence

Bootstrap methods can extend to non-unitary and boundary CFTs

Abstract

The $d=2$ critical Ising model is described by an exactly solvable Conformal Field Theory (CFT). The deformation to $d=2+\epsilon$ is a relatively simple system at strong coupling outside of even dimensions. Using novel numerical and analytical conformal bootstrap methods in Lorentzian signature, we show that the leading corrections to the Ising data are more singular than $\epsilon$. There must be infinitely many new states due to the $d$-dependence of conformal symmetry. The linear independence of conformal blocks is central to this bootstrap approach, which can be extended to more rigorous studies of non-positive systems, such as non-unitary, defect/boundary and thermal CFTs.