Self-dualities and renormalization dependence of the phase diagram in 3d O(N) vector models

Year: 2021

Authors: Sberveglieri G., Serone M., Spada G.

Autors Affiliation: SISSA, Via Bonomea 265, I-4136 Trieste, Italy; Ist Nazl Fis Nucl, Via Bonomea 265, I-4136 Trieste, Italy; Univ PSL, Sorbonne Univ, Coll France, Lab Kastler Brossel,ENS,CNRS, 24 Rue Lhomond, F-75005 Paris, France; Univ Trento, INO CNR BEC Ctr, Via Sommar 14, I-38123 Povo, Trento, Italy; Univ Trento, Dipartimento Fis, Via Sommar 14, I-38123 Povo, Trento, Italy.

Abstract: In the classically unbroken phase, 3d O(N) symmetric phi (4) vector models admit two equivalent descriptions connected by a strong-weak duality closely related to the one found by Chang and Magruder long ago. We determine the exact analytic renormalization dependence of the critical couplings in the weak and strong branches as a function of the renormalization scheme (parametrized by kappa) and for any N. It is shown that for kappa = kappa the two fixed points merge and then, for kappa < , they move into the complex plane in complex conjugate pairs, making the phase transition no longer visible from the classically unbroken phase. Similar considerations apply in 2d for the N = 1 phi (4) theory, where the role of classically broken and unbroken phases is inverted. We verify all these considerations by computing the perturbative series of the 3d O(N) models for the vacuum energy and for the mass gap up to order eight, and Borel resumming the series. In particular, we provide numerical evidence for the self-duality and verify that in renormalization schemes where the critical couplings are complex the theory is gapped. As a by-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 in the classically unbroken phase. Journal/Review: JOURNAL OF HIGH ENERGY PHYSICS

Volume: (2)      Pages from: 98-1  to: 98-37

More Information: We thank Joan Elias-Miro and Slava Rychkov for useful comments on the draft. We also thank Nikhil Anand, Emanuel Katz, Zuhair U. Khandker and Matthew T. Walters for discussions and for having shared with us the draft of [47] before publication. GSp would like to thank Gerard P. Lepage for the support given with the vegas python module. GSb and MS are partially supported by INFN Iniziativa Specifica ST&FI.
KeyWords: Field Theories in Lower Dimensions; Conformal Field Theory; Renormalization Group
DOI: 10.1007/JHEP02(2021)098

Citations: 11
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