Gauge Invariance at Large Charge.

Quantum field theories with global symmetries simplify considerably in the large-charge limit allowing us to compute correlators via a semiclassical expansion in the inverse powers of the conserved charges. A generalization of the approach to gauge symmetries has faced the problem of defining gauge-independent observables and, therefore, has not been developed so far. We employ the large-charge expansion to calculate the scaling dimension of the lowest-lying operators carrying U(1) charge Q in the critical Abelian Higgs model in D=4-ε dimensions to leading and next-to-leading orders in the charge and all orders in the ε expansion. Remarkably, the results match our independent diagrammatic computation of the three-loop scaling dimension of the operator ϕ^{Q}(x) in the Landau gauge. We argue that this matching is a consequence of the equivalence between the gauge-independent dressed two-point function of Dirac type with the gauge-dependent two-point function of ϕ^{Q}(x) in the Landau gauge. We, therefore, shed new light on the problem of defining gauge-independent exponents which has been controversial in the literature on critical superconductors, as well as lay the foundation for large-charge methods in gauge theories.

The analytic structure of the fixed charge expansion.

We investigate the analytic properties of the fixed charge expansion for a number of conformal field theories in different space-time dimensions. The models investigated here are O(N) and QED 3. We show that in d = 3 - ϵ dimensions the contribution to the O(N) fixed charge Q conformal dimensions obtained in the double scaling limit of large charge and vanishing ϵ is non-Borel summable, doubly factorial divergent, and with order Q optimal truncation order. By using resurgence techniques we show that the singularities in the Borel plane are related to worldline instantons that were discovered in the other double scaling limit of large Q and N of ref. [1]. In d = 4 - ϵ dimensions the story changes since in the same large Q and small E regime the next order corrections to the scaling dimensions lead to a convergent series. The resummed series displays a new branch cut singularity which is relevant for the stability of the O(N) large charge sector for negative ϵ. Although the QED 3 model shares the same large charge behaviour of the O(N) model, we discover that at leading order in the large number of matter field expansion the large charge scaling dimensions are Borel summable, single factorial divergent, and with order Q optimal truncation order.