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 Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In the classically unbroken phase, 3d $O(N)$ symmetric $\phi^4$ vector modelsadmit two equivalent descriptions connected by a strong-weak duality closelyrelated to the one found by Chang and Magruder long ago. We determine the exactanalytic renormalization dependence of the critical couplings in the weak andstrong branches as a function of the renormalization scheme (parametrized by$\kappa$) and for any $N$. It is shown that for $\kappa=\kappa_*$ the two fixedpoints merge and then, for $\kappa<\kappa_*$, they move into the complex planein complex conjugate pairs, making the phase transition no longer visible fromthe classically unbroken phase. Similar considerations apply in 2d for the$N=1$ $\phi^4$ theory, where the role of classically broken and unbroken phasesis inverted. We verify all these considerations by computing the perturbativeseries of the 3d $O(N)$ models for the vacuum energy and for the mass gap up toorder eight, and Borel resumming the series. In particular, we providenumerical evidence for the self-duality and verify that in renormalizationschemes where the critical couplings are complex the theory is gapped. As aby-product of our analysis, we show how the non-perturbative mass gap at large$N$ in 2d can be seen as the analytic continuation of the perturbative one inthe classically unbroken phase.

Self-Dualities and Renormalization Dependence of the Phase Diagram in 3d $O(N)$ Vector Models