Solving the Conformal Bootstrap: Four-Fermion Interactions at 2<d<4

Abstract

We formulate the conformal bootstrap approach to four--fermion theory at its strong coupling fixed point in dimensions $2<d<4$. We present a solution of the bootstrap equations in the five--vertex approximation. We show that the bootstrap approach gives a particularly simple way to obtain next to leading order corrections to critical exponents in the large $N$ expansion and present the values of the anomalous dimensions of the fermion field $\psi$ and the composite $\bar\psi\psi$ to order $1/N^2$.