Phases of supersymmetric O(N) theories

Heilmann, Marianne; Litim, Daniel F.; Synatschke-Czerwonka, Franziska; Wipf, Andreas

doi:10.48550/arxiv.1208.5389

Cited by 4 publications

(13 citation statements)

References 33 publications

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“…In 3d settings, asymptotic safety is known to arise in models with scalars, or fermions, or both. In suitable large-N limits, exact results at weak coupling are available from the renormalisation group [14][15][16][17], including models with supersymmetry or spontaneously broken scale invariance [18][19][20]. Lattice results are available for non-linear sigma models [21].…”

Section: Introductionmentioning

confidence: 99%

UV conformal window for asymptotic safety

et al. 2018

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Interacting fixed points in four-dimensional gauge theories coupled to matter are investigated using perturbation theory up to three loop order. It is shown how fixed points, scaling exponents, and anomalous dimensions are obtained as a systematic power series in a small parameter. The underlying ordering principle is explained and contrasted with conventional perturbation theory and Weyl consistency conditions. We then determine the conformal window with asymptotic safety from the complete nextto-next-to-leading order in perturbation theory. Limits for the conformal window arise due to fixed point mergers, the onset of strong coupling, or vacuum instability. A consistent picture is uncovered by comparing various levels of approximation. The theory remains perturbative in the entire conformal window, with vacuum stability dictating the tightest constraints. We also speculate about a secondary conformal window at strong coupling and estimate its lower limit. Implications for model building and cosmology are indicated.

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Section: Introductionmentioning

confidence: 99%

UV conformal window for asymptotic safety

et al. 2018

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“…The numerical values of the parameters g cr and g 6,cr can be used in (33) to obtain an approximate form of the local potential solutions. Then a decreasing anomalous dimension in Tab.…”

Section: E the Tri-ising Class In D =mentioning

confidence: 99%

“…These two methods treat the boundary conditions for the deformations of a critical potential in different ways; thus, they are complementary for the approach as will be shown by applying them to the known Ising example. Finally, we systematically apply the scaling solution approach to the supersymmetric N = 1 Wess-Zumino model in both two [29,30] and three dimensions [31][32][33], for which we compute various critical exponents for its universality classes. We also study the supersymmetric model on fractional dimensions introducing a novel analytic continuation.…”

Section: Introductionmentioning

confidence: 99%

Scaling and superscaling solutions from the functional renormalization group

2015

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We study the renormalization group flow of Z2-invariant supersymmetric and non-supersymmetric scalar models in the local potential approximation using functional renormalization group methods. We focus our attention on the fixed points of the renormalization group flow of these models, which emerge as scaling solutions. In two dimensions these solutions are interpreted as the minimal (supersymmetric) models of conformal field theory, while in three dimensions they are manifestations of the Wilson-Fisher universality class and its supersymmetric counterpart. We also study the analytically continued flow in fractal dimensions between 2 and 4 and determine the critical dimensions for which irrelevant operators become relevant and change the universality class of the scaling solution. We include novel analytic and numerical investigations of the properties that determine the occurrence of the scaling solutions within the method. For each solution we offer new techniques to compute the spectrum of the deformations and obtain the corresponding critical exponents.

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“…It has also been conjectured that asymptotic safety may exist at strong coupling [17][18][19], In 3d, the interest in fixed points of relativistic quantum fields is motivated by thermal and quantum phase transitions of spin liquids and quantum magnets, superconductors, topological insulators, and models for new materials such as graphene. These can often be described by scalar, fermionic, and Yukawa models, and gauged or supersymmetric versions thereof [20][21][22][23][24][25][26][27][28][29][30][31][32]. Some of the recent interest in 3d models is further fuelled by a conjecture for novel types of dualities [33,34], much in the spirit of Seiberg duality, or particle-vortex duality [35] between O(2) magnets and the abelian-Higgs model for superconductivity [36,37].…”

Section: Introductionmentioning

confidence: 99%

“…Secondly, the model is known to display a variety of low-and high-energy fixed points, first and second order phase transitions, and the spontaneous breaking of (scale) symmetry. Previous work has covered aspects of symmetry breaking and 1/N corrections [41][42][43][44][45], stability of the ground state and UV fixed points [41,42,[45][46][47][48][49], and extensions with supersymmetry or Chern-Simons interactions [23,24,[50][51][52][53].…”

Section: Introductionmentioning

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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Phases of supersymmetric O(N) theories

Cited by 4 publications

References 33 publications

UV conformal window for asymptotic safety

UV conformal window for asymptotic safety

Scaling and superscaling solutions from the functional renormalization group

Asymptotic safety of scalar field theories

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