English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We investigate the analytic properties of the fixed charge expansion for anumber of conformal field theories in different space-time dimensions. Themodels investigated here are $O(N)$ and $QED_3$. We show that in $d=3-\epsilon$dimensions the contribution to the $O(N)$ fixed charge $Q$ conformal dimensionsobtained in the double scaling limit of large charge and vanishing $\epsilon$is non-Borel summable, doubly factorial divergent, and with order $\sqrt{Q}$optimal truncation order. By using resurgence techniques we show that thesingularities in the Borel plane are related to worldline instantons that werediscovered in the other double scaling limit of large $Q$ and $N$ of Ref. [1].In $d=4-\epsilon$ dimensions the story changes since in the same large $Q$ andsmall $\epsilon$ regime the next order corrections to the scaling dimensionslead to a convergent series. The resummed series displays a new branch cutsingularity which is relevant for the stability of the $O(N)$ large chargesector for negative $\epsilon$. Although the $QED_3$ model shares the samelarge charge behaviour of the $O(N)$ model, we discover that at leading orderin the large number of matter field expansion the large charge scalingdimensions are Borel summable, single factorial divergent, and with order $Q$optimal truncation order.

The analytic structure of the fixed charge expansion