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

We solve the two-point function of the lowest dimensional scalar operator in the critical φ 4 theory on 4 − ǫ dimensional real projective space in three different methods. The first is to use the conventional perturbation theory, and the second is to impose the crosscap bootstrap equation, and the third is to solve the Schwinger-Dyson equation under the assumption of conformal invariance. We find that the three methods lead to mutually consistent results but each has its own advantage.