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

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.