Confining solitons in the Higgs phase of ℂP N −1 model: self-consistent exact solutions in large-N limit

Nitta, Muneto; Yoshii, Ryosuke

doi:10.1007/jhep08(2018)007

Cited by 9 publications

(14 citation statements)

References 111 publications

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“…, leading precisely to the M 2 log l 2 M 2 term appearing in (22). These results have interesting physical implications for the Casimir effect and will be presented elsewhere [63].…”

Section: Logarithmic Contributions and The Mittag-leffler Represmentioning

confidence: 57%

“…Another point worth noticing is the independence of the coefficients of all powers of M 2 in the expansion from the size of the interval (with the exception of the logarithms). While this can be explicitly observed from formula (22) for the M 4 and M 6 coefficients, a proof that extends to all coefficients is worked out very easily from formula (20) and from the scaling of the coefficientsα ð0Þ k . This is a reminder of the large-N volume independence for the CP N−1 model (see [64]).…”

Section: Discussionmentioning

confidence: 99%

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Remarks on the large-NCPN−1model

Flachi

2020

Phys. Rev. D

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In this paper we consider the CP N−1 model confined to an interval of finite size at finite temperature and chemical potential. We obtain, in the large-N approximation, a mixed-gradient expansion of the one-loop effective action of the order parameter associated with the effective mass of the quantum fluctuations. This expansion gives an expression for the thermodynamic potential density as a functional of the order parameter, generalizing previous calculations to arbitrarily large order and to the case of finite chemical potential and allows one to discuss some generic features of the ground state of the model. The technique used here relies on analytic regularization and provides an efficient scheme to extract the coefficients of the expansion. Once a solution for the ground state is known these coefficients can be used to deduce some generic properties of the ground state as a function of external conditions. We also show that there can be no transition to a massless phase for any value of the external conditions considered and clarify a seemingly important point regarding the regularization of the effective action connected to the appearance of logarithmic divergences and to the Mermin-Wagner-Hoenberg-Coleman theorem.

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“…, leading precisely to the M 2 log l 2 M 2 term appearing in (22). These results have interesting physical implications for the Casimir effect and will be presented elsewhere [63].…”

Section: Logarithmic Contributions and The Mittag-leffler Represmentioning

confidence: 57%

Section: Discussionmentioning

confidence: 99%

Remarks on the large-NCPN−1model

Flachi

2020

Phys. Rev. D

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“…where the center of the soliton x 0 is taken at 0, satisfies the generalized gap equations (3.15) -(3.17). (More general solutions have subsequently been studied in [43].) In Gorsky et.…”

Section: Absence Of Soliton-like Solutionsmentioning

confidence: 99%

Large-N ℂℙN −1 sigma model on a Euclidean torus: uniqueness and stability of the vacuum

Bolognesi

Gudnason

Konishi

et al. 2019

J. High Energ. Phys.

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In this paper we examine analytically the large-N gap equation and its solution for the 2D CP N −1 sigma model defined on a Euclidean spacetime torus of arbitrary shape and size (L, β), β being the inverse temperature. It is shown that the system has a unique homogeneous phase, with the CP N −1 fields n i acquiring a dynamically generated mass λ ≥ Λ 2 (analogous to the mass gap of SU (N ) Yang-Mills theory in 4D), for any β and L. We comment on several related topics discussed in the recent literature. One concerns the possibility, which we will exclude, of a "Higgs-like" -or deconfinement -phase at small L and at zero temperature. Another topic involves "soliton-like" (inhomogeneous) solutions of the generalized gap equation. In both cases, a proper treatment of the zero modes is essential. A related question concerns a possible instability of the standard CP N −1 vacuum on R 2 , which is shown not to occur. The CP N −1 model with twisted boundary conditions is also analyzed. The θ dependence, and different limits involving N , β and L are briefly discussed.

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“…In Ref. [64], a confining soliton in the Higgs phase was obtained, in which a confinement phase is localized in the soliton core. This solution can be twisted as well.…”

Section: Summary and Discussionmentioning

confidence: 99%