Anomalous dimensions at large charge in d=4 O(N) theory

Abstract

Recently it was shown that the scaling dimension of the operator φ n in λ( φφ) 2 theory may be computed semiclassically at the Wilson-Fisher fixed point in d = 4 − , for generic values of λn, and this was verified to two loop order in perturbation theory at leading and subleading n. In subsequent work, this result was generalised to operators of fixed charge Q in O(N ) theory and verified up to three loops in perturbation theory at leading and subleading Q. Here we extend this verification to four loops in O(N ) theory, once again at leading and subleading Q. We also investigate the strong-coupling regime.

Spin impurities, Wilson lines and semiclassics

“…This double-scaling limit is analogous to similar ones considered in the context of the large charge expansion[104,[111][112][113][114] 25. It would also be interesting to analyze in a semiclassical expansion the fusion of two line defects[115,116],maybe along the lines of earlier studies of OPE coefficients of large charge operators[117].…”

Untangling scaling dimensions of fixed charge operators in Higgs Theories

“…This is an example of how the semiclassical expansion at fixed charge can be helpful in improving and checking perturbative results. Conversely, the diagrammatic check of the semiclassical computation has been recently further extended to the 4-loop level in [18]. Notice that for Q = 1 the relevant operator is the φ field, while for Q = 2, it is the bilinear traceless symmetric O(N) tensor φ a φ b − 1 N φ c φ c , which is of interest to many critical phenomena being responsible for crossover behaviour in the O(N) theory.…”

“…As we will see in the next section, in the perturbative regime the operator identification can be proven via group-theoretical arguments. For sake of completeness, we report here also the large A expansion of ∆ T Q [18]…”

“…In particular, much attention has been paid to the time-honoured O(N) model, first investigated for any N in 4 − dimensions in [15]. The results were recently successfully tested against ordinary perturbation theory in [18] to four loops. Later the O(N) model was investigated via the semiclassical approach at large N in various dimensions in [19,20].…”

Anomalous dimensions at large charge for $U(N)\times U(N)$ theory in three and four dimensions

“…[9], the U (1) result was compared with perturbation theory up to two loops, and in Refs. [10], [17] the check was performed for the O(N ) theory up to three and four loops respectively. Most recently, the classically scale-invariant U (N ) × U (N ) model has been investigated in Ref.…”