Phase diagram and fixed-point structure of two-dimensional<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="script">N</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:math>Wess-Zumino models

Synatschke, Franziska; Gies, Holger; Wipf, Andreas

doi:10.1103/physrevd.80.085007

Cited by 35 publications

(48 citation statements)

References 24 publications

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“…To find a manifestly supersymmetric flow equation in the off-shell formulation we extend our earlier results on the one-and two-dimensional Wess-Zumino models [13,15] to three dimensions. Since there are no Majorana fermions in three-dimensional Euclidean space we begin with a Minkowski spacetime formulation of the Wetterich equation [37,38]:…”

Section: Flow Equation At Zero Temperaturementioning

confidence: 78%

“…The present study builds on our earlier results on twodimensional supersymmetric field theories at zero temperature [13,14] as well as on supersymmetric quantum mechanics, where we have constructed a manifestly supersymmetric functional RG flow, see [15]. The twodimensional models possess an infinite series of fixed points described by two-dimensional super-conformal theories.…”

Section: Introductionmentioning

confidence: 76%

“…Contrary to the model in two dimensions [13], the regulator function (18) regularizes the flow even if we allow for running wave function renormalizations. For the superpotential W k we then obtain the simple flow equation…”

Section: A Local Potential Approximationmentioning

confidence: 99%

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N=1Wess-Zumino model ind=3at zero and finite temperature

2010

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Supersymmetric renormalization group (RG) flow equations for the effective superpotential of the three-dimensional Wess-Zumino model are derived at zero and non-zero temperature. This model with fermions and bosons interacting via a Yukawa term possesses a supersymmetric analogue of the Wilson-Fisher fixed-point. At zero temperature we determine the phase-transition line in coupling-constant space separating the supersymmetric from the nonsupersymmetric phase. At finite temperature we encounter dimensional reduction from 3 to 2 dimensions in the infrared regime. We determine the finite-temperature phase diagram for the restoration of the global 2-symmetry and show that for temperatures above the 2 phase-transition the pressure obeys the Stefan-Boltzmann law of a gas of massless bosons in 2 + 1 dimensions.

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Section: Flow Equation At Zero Temperaturementioning

confidence: 78%

Section: Introductionmentioning

confidence: 76%

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N=1Wess-Zumino model ind=3at zero and finite temperature

2010

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“…Here we implicitly assume that a supersymmetric action flows into another supersymmetric action, a fact which is confirmed by direct observation when using MS methods [21], but that can be proven explicitly using functional RG methods and choosing a supersymmetric cutoff [51][52][53][54][55].…”

Section: Jhep12(2017)132mentioning

confidence: 98%

“…These non-perturbative RG functions have been computed using the functional RG methods formulated in terms of a flow equation for the 1PI effective action [44]. Using a manifestly off-shell supersymmetric regularization [52,53], the functional RG equations for the present model have been derived and analyzed in [54,55] and were extended to arbitrary dimension 2 < d ≤ 4 in [51]. These methods allow for the construction of an RG which is manifestly off-shell supersymmetric at any scale and in any dimension as long as the supersymmetry imposed on the level of the action.…”

Section: Jhep12(2017)132mentioning

confidence: 99%

A functional perspective on emergent supersymmetry

Gies

Hellwig

Wipf

et al. 2017

J. High Energ. Phys.

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Abstract:We investigate the emergence of N = 1 supersymmetry in the long-range behavior of three-dimensional parity-symmetric Yukawa systems. We discuss a renormalization approach that manifestly preserves supersymmetry whenever such symmetry is realized, and use it to prove that supersymmetry-breaking operators are irrelevant, thus proving that such operators are suppressed in the infrared. All our findings are illustrated with the aid of the -expansion and a functional variant of perturbation theory, but we provide numerical estimates of critical exponents that are based on the non-perturbative functional renormalization group.

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On Gauge Fixing Aspects of the Infrared Behavior of Yang-Mills Green Functions

Huber¹

2012

Springer Theses

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The infrared behavior of propagators and vertices is derived for the maximally Abelian gauge and the Gribov-Zwanziger action relying on functional equations. The derivation and analysis of Dyson-Schwinger equations increase considerably in complexity when going beyond the standard Landau gauge fixing and the available tools have to be improved. For the derivation of the equations a computer program (DoDSE ) was developed in order to handle the plethora of terms. The process of determining possible infrared solutions is abstracted to obtain further insight into the structure of the so-called infrared scaling solutions. It is found that a few simple steps suffice to determine possible infrared scaling relations directly from the action. This makes also complicated actions easily accessible.For the maximally Abelian gauge an infrared enhanced diagonal gluon propagator is found, while the off-diagonal degrees of freedom are infrared suppressed. This is in agreement with the idea of Abelian infrared dominance. Furthermore, it is proven that SU (2) and higher SU (N ) have the same infrared behavior, although the corresponding actions differ. Under a suitable truncation the Dyson-Schwinger equations are solved in the deep infrared to obtain values for the exponents of the power laws. The maximally Abelian gauge constitutes the first instance where a consistent scaling solution was found besides the Landau gauge.Restricting the integration in field configuration space to the Gribov region of the Landau gauge with the Gribov-Zwanziger action leads to two solutions qualitatively equivalent to the one obtained with the standard Faddeev-Popov gauge fixing. In both cases the gluon propagator is infrared suppressed and the infrared enhanced ghost propagator For further investigations of Yang-Mills theory the possibility to derive Dyson-Schwinger equations with the computer will prove useful. The presented method for determining possible infrared scaling solutions will also alleviate their analyses.

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Phase diagram and fixed-point structure of two-dimensionalN=1Wess-Zumino models

Cited by 35 publications

References 24 publications

N=1Wess-Zumino model ind=3at zero and finite temperature

N=1Wess-Zumino model ind=3at zero and finite temperature

A functional perspective on emergent supersymmetry

On Gauge Fixing Aspects of the Infrared Behavior of Yang-Mills Green Functions

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