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

Abstract

Recently it was shown that the scaling dimension of the operator ${\varphi }^n$ in $\lambda ({\varphi }^{\ast }\varphi {)}^2$ theory may be computed semi-classically at the Wilson-Fisher fixed point in $d=4-\epsilon$, for generic values of $\lambda n$ and this was verified to two loop order in perturbation theory at leading and sub-leading $n$. 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 sub-leading order. Here we extend this verification to four loops in $O(N)$ theory, once again at leading and sub-leading order. We also investigate the strong-coupling regime.

16 pages. 6 Figures. Typos corrected; references and an acknowledgement added. Some minor errors corrected in a figure and equations

References in corpus (6)

• Selected Topics in the Large Quantum Number Expansion
• Naturalness and Dimensional Transmutation in Classically Scale-Invariant Gravity
• Feynman diagrams and the large charge expansion in $3-\epsilon$ dimensions
• Charging the $O(N)$ model
• Charging the Walking U(N)$\times$U(N) Higgs Theory as a Complex CFT
• Anomalous dimensions for ${\varphi }^n$ in scale invariant $d=3$ theory

Cited by in corpus (14)

• Resurgence of the large-charge expansion
• More on the Weak Gravity Conjecture via Convexity of Charged Operators
• Untangling scaling dimensions of fixed charge operators in Higgs Theories
• More on the cubic versus quartic interaction equivalence in the $O(N)$ model
• Nonrelativistic CFTs at Large Charge: Casimir Energy and Logarithmic Enhancements
• Following the flow for large N and large charge
• Anomalous dimensions at large charge for $U(N)\times U(N)$ theory in three and four dimensions
• Six-loop anomalous dimension of the ${\varphi }^Q$ operator in the $O(N)$ symmetric model
• The analytic structure of the fixed charge expansion
• Gauge Invariance at Large Charge
• On the exponentially small corrections to $\mathcal{N}=2$ superconformal correlators at large R-charge
• On Convexity of Charged Operators in CFTs and the Weak Gravity Conjecture
• Boundary Conformal Field Theory at Large Charge
• Convexity, large charge and the large-N phase diagram of the ${\phi }^4$ theory