On a Phase with Spontaneously Broken Scale Invariance in Three Dimensional O(N) Models

Matsubara, Yoshimi; Suzuki, Tsuneo; Yamamoto, Hisashi; Yotsuyanagi, Ichiro

doi:10.1143/ptp.78.760

Cited by 4 publications

(5 citation statements)

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“…The O(N ) symmetric Wess-Zumino model with a microscopic (Φ 2 ) 2 superpotential is determined by only two renormalized parameters and critical and tricritical theories are the same. Its phase structure has attracted some attention in the past [6][7][8][9][10][11][12][13]. In the limit of infinitely many superfields, four different phases have been observed [6,7], including peculiar degenerate O(N ) symmetric phases with several mass scales.…”

Section: Introductionmentioning

confidence: 99%

“…The supersymmetric O(N ) model has also been discussed in the 1/N expansion [11], where the authors found a non-trivial UV fixed-point and a stable dilaton phase. At next-to-leading order the dilaton acquires a mass of order 1/N showing that a phase with spontaneously broken scale invariance only exists in the limit of infinitely many superfields [13].…”

Section: Introductionmentioning

confidence: 99%

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Phases of supersymmetric O(N) theories

Heilmann,

Litim,

Synatschke-Czerwonka

et al. 2012

Preprint

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We perform a global renormalization group study of O(N ) symmetric Wess-Zumino theories and their phases in three euclidean dimensions. At infinite N the theory is solved exactly. The phases and phase transitions are worked out for finite and infinite short-distance cutoffs. A distinctive new feature arises at strong coupling, where the effective superfield potential becomes multi-valued, signalled by divergences in the fermion-boson interaction. Our findings resolve the long-standing puzzle about the occurrence of degenerate O(N ) symmetric phases. At finite N , we find a strongly-coupled fixed point in the local potential approximation and explain its impact on the phase transition. We also examine the possibility for a supersymmetric Bardeen-Moshe-Bander phenomenon, and relate our findings with the spontaneous breaking of supersymmetry in other models.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Phases of supersymmetric O(N) theories

Heilmann,

Litim,

Synatschke-Czerwonka

et al. 2012

Preprint

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show abstract

“…In addition, there exists a supersymmetric analogue of the Bardeen-Moshe-Bander phenomenon [7]. The fate of this phenomenon at finite N remains yet to be resolved [45][46][47].…”

Section: Introductionmentioning

confidence: 99%

Critical behavior of supersymmetricO(N)models in the large-Nlimit

et al. 2011

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We derive a supersymmetric renormalization group (RG) equation for the scale-dependent superpotential of the supersymmetric OðNÞ model in three dimensions. For a supersymmetric optimized regulator function, we solve the RG equation for the superpotential exactly in the large-N limit. The fixed-point solutions are classified by an exactly marginal coupling. In the weakly coupled regime there exists a unique fixed-point solution, for intermediate couplings we find two separate fixed-point solutions and in the strong coupling regime no globally defined fixed-point potentials exist. We determine the exact critical exponents both for the superpotential and the associated scalar potential. Finally, we relate the hightemperature limit of the four-dimensional theory to the Wilson-Fisher fixed point of the purely scalar theory.

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“…We now turn to the specific value of the parameter c = c crit , (52), where the fixed point (47) displays the spontaneous breaking of scale invariance, also known as the Bardeen-Moshe-Bander phenomenon [38,42,49,54,55,110]. Most notably, the breaking of scale symmetry entails the generation of a light "dilaton" or "scalon" [111] in the spectrum.…”

Section: Bardeen-moshe-bander Fixed Pointmentioning

confidence: 99%

“…To obtain (110) we have made use of the identity ρ(d − 2 + 4u * ) − 1 = 2u * (1 − u * )/u * , which holds true for any non-trivial fixed point solution of ( 9) in the large-N limit. The eigenperturbations obey the eigenvalue equation ∂ t δu = θδu where θ denotes the corresponding eigenvalue.…”

Section: B Interacting Fixed Pointsmentioning

confidence: 99%

Asymptotic safety of scalar field theories

Trott

2018

Phys. Rev. D

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We study 3d O(N ) symmetric scalar field theories using Polchinski's renormalisation group. In the infinite N limit the model is solved exactly including at strong coupling. At short distances the theory is described by a line of asymptotically safe ultraviolet fixed points bounded by asymptotic freedom at weak, and the Bardeen-Moshe-Bander phenomenon at strong sextic coupling. The Wilson-Fisher fixed point arises as an isolated low-energy fixed point. Further results include the conformal window for asymptotic safety, convergence-limiting poles in the complex field plane, and the phase diagram with regions of first and second order phase transitions. We substantiate a duality between Polchinski's and Wetterich's versions of the functional renormalisation group, also showing that that eigenperturbations are identical at any fixed point. At a critical sextic coupling, the duality is worked out in detail to explain the spontaneous breaking of scale symmetry responsible for the generation of a light dilaton. Implications for asymptotic safety in other theories are indicated. Contents

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On a Phase with Spontaneously Broken Scale Invariance in Three Dimensional O(N) Models

Cited by 4 publications

References 0 publications

Phases of supersymmetric O(N) theories

Phases of supersymmetric O(N) theories

Critical behavior of supersymmetricO(N)models in the large-Nlimit

Asymptotic safety of scalar field theories

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