On the large charge sector in the critical O(N) model at large N

A bstract We study operators in the rank- j totally symmetric representation of O ( N ) critical model arbitrary dimension d , limit large and charge with j/N ≡ $$ \hat{j} j ̂ fixed. The scaling dimensions this may be obtained by a semiclassical saddle point calculation. Using standard Hubbard-Stratonovich description at we solve relevant equation determine as function finding agreement all existing results various limits. In 4 < 6, observe that becomes complex above value ratio signaling an instability theory range . Finally, also derive for correlation functions involving two “heavy” one or “light” operators. particular, form “heavy-heavy-light” OPE coefficients charges