$\epsilon$-Expansion in Critical $\phi^3$-Theory on Real Projective Space from Conformal Field Theory

TL;DR

This paper computes the one-point function in the critical $ u$-theory on real projective space using conformal symmetry and equations of motion, confirming results with perturbation theory and bootstrap methods.

Contribution

It introduces a method combining conformal symmetry and equations of motion to solve for one-point functions in critical $ u$-theory on real projective space, advancing analytical techniques.

Findings

Results match conventional perturbation theory

Agreement with numerical conformal bootstrap

First non-trivial order in $$-expansion achieved

Abstract

We use a compatibility between the conformal symmetry and the equations of motion to solve the one-point function in the critical $\phi^3$-theory (a.k.a the critical Lee-Yang model) on the $d = 6 - \epsilon$ dimensional real projective space to the first non-trivial order in the $\epsilon$-expansion. It reproduces the conventional perturbation theory and agrees with the numerical conformal bootstrap result.