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.

Self-Dualities and Renormalization Dependence of the Phase Diagram in 3d $O(N)$ Vector Models / Sberveglieri, Giacomo; Serone, Marco; Spada, Gabriele. - In: JOURNAL OF HIGH ENERGY PHYSICS. - ISSN 1029-8479. - 2021:(2021), pp. 1-37. [10.1007/JHEP02(2021)098]

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

Giacomo Sberveglieri;Marco Serone;Gabriele Spada
2021

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.
2021
1
37
98
https://doi.org/10.1007/JHEP02(2021)098
http://arxiv.org/abs/2010.09737v3
Sberveglieri, Giacomo; Serone, Marco; Spada, Gabriele
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.11767/128531
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