Yongwei Guo

We investigate the ϕ 2 n deformations of the O ( N ) -symmetric (generalized) free theories with a flat boundary, where n ≥ 2 is an integer. The generalized free theories refer to the □ k free scalar theories with a higher derivative kinetic term, which is related to the multicritical generalizations of the Lifshitz type. We assume that the (generalized) free theories and the deformed theories have boundary conformal symmetry and O ( N ) global symmetry. The leading anomalous dimensions of some boundary operators are derived from the bulk multiplet recombination and analyticity constraints. We find that the ε 1 / 2 expansion in the ϕ 6 -tricritical version of the special transition extends to other multicritical cases with larger odd integer n , and most of the higher derivative cases involve a noninteger power expansion in ε . Using the analytic bootstrap, we further verify that the multiplet-recombination results are consistent with boundary crossing symmetry.

We investigate ϕ 2 n + 1 deformations of the generalized free theory in the ε expansion, where the canonical kinetic term is generalized to a higher-derivative version. For n = 1 , we use the conformal multiplet recombination method to determine the leading anomalous dimensions of the fundamental scalar operator ϕ and the bilinear composite operators J . Then, we extend the n = 1 analysis to the Potts model with S N + 1 symmetry and its higher-derivative generalization, in which ϕ is promoted to an N -component field. We further examine the Chew-Frautschi plots and their N dependence. However, for each integer n > 1 , the leading anomalous dimensions of ϕ and J are not fully determined and contain one unconstrained constant, which in the canonical cases can be fixed by the results from the diagrammatic method. In all cases, we verify that the multiplet-recombination results are consistent with crossing symmetry using the analytic bootstrap methods.