Convergence of derivative expansion in supersymmetric functional RG flows

Heilmann, Marianne; Hellwig, Tobias; Knorr, Benjamin; Ansorg, Marcus; Wipf, Andreas

doi:10.1007/jhep02(2015)109

Cited by 25 publications

(26 citation statements)

References 35 publications

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“…Our approach is particularly suited for global aspects and also resolves asymptotic behaviour in a controlled way. Recently, it has been used to globally resolve the supersymmetric analogue of the Wilson-Fisher fixed point [57].…”

Section: Introductionmentioning

confidence: 99%

Global solutions of functional fixed point equations via pseudospectral methods

Borchardt

Knorr

2015

Phys. Rev. D

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We apply pseudo-spectral methods to construct global solutions of functional renormalisation group equations in field space to high accuracy. For this, we introduce a basis to resolve both finite as well as asymptotic regions of effective potentials. Our approach is benchmarked using the critical behaviour of the scalar O(1) model, providing results for the global fixed point potential as well as leading critical exponents and their respective global eigenfunctions. We provide new results for (1) multi-critical O(1) models in fractional dimensions, (2) the three-dimensional Gross-Neveu model at both small and large N , and (3) the scalar-tensor model, also in three dimensions.

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Section: Introductionmentioning

confidence: 99%

Global solutions of functional fixed point equations via pseudospectral methods

Borchardt

Knorr

2015

Phys. Rev. D

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“…A supersymmetric version of this model has been investigated in Ref. 68 in next-to-next-to-leading order. Due to the higher symmetry, there only 4 independent functions had to be considered.…”

Section: The Modelmentioning

confidence: 99%

Ising and Gross-Neveu model in next-to-leading order

Knorr

2016

Phys. Rev. B

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We study scalar and chiral fermionic models in next-to-leading order with the help of the functional renormalisation group. Their critical behaviour is of special interest in condensed matter systems, in particular graphene. To derive the beta functions, we make extensive use of computer algebra. The resulting flow equations were solved with pseudo-spectral methods to guarantee high accuracy. New estimates on critical quantities for both the Ising and the Gross-Neveu model are provided. For the Ising model, the estimates agree with earlier renormalisation group studies of the same level of approximation. By contrast, the approximation for the Gross-Neveu model retains many more operators than all earlier studies. For two Dirac fermions, the results agree with both lattice and large-N f calculations, but for a single flavour, different methods disagree quantitatively, and further studies are necessary.

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“…The critical point can also be understood as the N = 1 supersymmetric generalization of the well-known Wilson-Fisher fixed point. The non-perturbative renormalization group flow of the superpotential W (ϕ) has been studied in [54,55] for the three dimensional case, and it has been generalized in [51] to the whole range 2 ≤ d < 4. The latter work contains leading order of the universal contributions to the flow close to the upper critical dimension d = 4 − , which agrees with the RG flow presented in [21] and which we shall use in our work.…”

Section: Jhep12(2017)132mentioning

confidence: 99%

“…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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Convergence of derivative expansion in supersymmetric functional RG flows

Cited by 25 publications

References 35 publications

Global solutions of functional fixed point equations via pseudospectral methods

Global solutions of functional fixed point equations via pseudospectral methods

Ising and Gross-Neveu model in next-to-leading order

A functional perspective on emergent supersymmetry

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