Three-loop renormalization of the SU(N) non-abelian Thirring model

Bennett, J.F.; Gracey, J.A.

doi:10.1016/s0550-3213(99)00570-2

Cited by 20 publications

(69 citation statements)

References 66 publications

(172 reference statements)

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“…5 can generate extra terms with new algebraic structures like γ i γ j γ k ⊗ γ i γ j γ k and so on. In d = d c − δ dimensions they have to be treated as independent new interactions reflecting the fact that within dimensional regularization this theory is not multiplicatively renormalizable [39]. For the Dirac fermions this problem shows up to orders higher than one-loop and can be solved, for example, using a cutoff in strictly 2D so that the extra interactions do not arise.…”

Section: Scaling Dimensionsmentioning

confidence: 99%

Effect of disorder on 2D topological merging transition from a Dirac semi-metal to a normal insulator

Carpentier¹,

Fedorenko²,

Orignac³

2013

EPL

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-We study the influence of disorder on the topological transition from a twodimensional Dirac semi-metal to an insulating state. This transition is described as a continuous merging of two Dirac points leading to a semi-Dirac spectrum at the critical point. The latter is characterized by a dispersion relation linear in one direction and quadratic in the orthogonal one. Using the self-consistent Born approximation and renormalization group we calculate the density of states above, below and in the vicinity of the transition in the presence of different types of disorder. Beyond the expected disorder smearing of the transition we find an intermediate disordered semi-Dirac phase. On one side this phase is separated from the insulating state by a continuous transition while on the other side it evolves through a crossover to the disordered Dirac phase.

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Section: Scaling Dimensionsmentioning

confidence: 99%

Effect of disorder on 2D topological merging transition from a Dirac semi-metal to a normal insulator

Carpentier¹,

Fedorenko²,

Orignac³

2013

EPL

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“…(The usual convention corresponds to c F = 1/2 with k = 1.) A three-loop computation was performed in [9]. From the result (18) we see that the βeta function is identically zero if C adj = 0.…”

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confidence: 99%

Beta Function for Anisotropic Current Interactions in 2D

Gerganov¹,

LeClair²,

Moriconi³

2001

Phys. Rev. Lett.

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By making use of current-algebra Ward identities we study renormalization of general anisotropic current-current interactions in 2D. We obtain a set of algebraic conditions that ensure the renormalizability of the theory to all orders. In a certain minimal prescription we compute the βeta function to all orders.Left-right current-current interactions in 2D arise in many physical systems, for example in the KosterlitzThouless transitions and in the study of free electrons in random potentials. The chiral Gross-Neveu model is the simplest example which is symmetry preserving (isotropic) [1]. Because such interactions are marginal in 2D, the couplings are dimensionless and there is usually no small parameter to expand in order to explore strong coupling.In this work we determine the βeta function to all orders in a certain minimal prescription. This should be sufficient for the study of fixed points. The primary tool that allows us to isolate the log divergences at arbitrary order are the Ward identities for the currents. Kutasov performed a similar computation in the simpler isotropic case (i.e. non-abelian Thirring model, which is equivalent to the chiral Gross-Neveu model) but argued his result was the leading order in 1/k where k is the level of the current algebra [4]. We believe our result to be exact.We do not expect that there is anything dramatically new to learn for the isotropic case. The behavior of models like the Gross-Neveu model is very well understood. This is in contrast to the anisotropic, i.e. symmetry breaking perturbations where one can expect richer phenomena. In the anisotropic case not all perturbations are in fact renormalizable. We find three renormalizability conditions that ensure the theory is renormalizable to all orders. Given these conditions are satisfied, we find a compact expression for the summation of all orders in perturbation theory.We know of no reason to expect additional nonperturbative corrections to the βeta function due for instance to instantons. Our result should be a useful tool for exploring strong coupling physics for the many models in this class. In this Letter we only report the main result and defer applications to future publications.Consider a conformal field theory with Lie algebra symmetry realized in the standard way [2,3]. It possesses left and right conserved currents, J a (z),J a (z), where z = x + iy,z = x − iy, satisfying the operator product expansion (OPE)and similarly forJ a (z). η ab in the above equation is a metric (Killing form) and k is the level. We include the case of Lie superalgebras with applications to disordered systems in mind. Here each current J a has a grade [a] = 0 or 1, and the tensors satisfy:For superalgebras, η ab is generally not diagonalizable, but we have η ab η bc = δ c a . The conformal field theory can be perturbed by marginal operators which are bilinear in the currents. The most general action iswhere S cft is the conformal field theory with the currentalgebra symmetry, and d A aā are certain tensors that define the mod...

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“…The β and γ-functions have been calculated (in the M S-scheme) up to three loops by Luperini and Rossi [10] and Gracey and Bennett [11], [12], [13]:…”

Section: Numerical Resultsmentioning

confidence: 99%

Dynamical mass generation by source inversion: Calculating the mass gap of the Gross-Neveu model

Acoleyen

Verschelde

2002

Phys. Rev. D

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We probe the U(N) Gross-Neveu model with a source-term JΨΨ. We find an expression for the renormalization scheme and scale invariant source J, as a function of the generated mass gap. The expansion of this function is organized in such a way that all scheme and scale dependence is reduced to one single parameter d. We get a non-perturbative mass gap as the solution of J = 0. In one loop we find that any physical choice for d gives good results for high values of N. In two loops we can determine d self-consistently by the principle of minimal sensitivity and find remarkably accurate results for N > 2.

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Three-loop renormalization of the SU(N) non-abelian Thirring model

Cited by 20 publications

References 66 publications

Effect of disorder on 2D topological merging transition from a Dirac semi-metal to a normal insulator

Effect of disorder on 2D topological merging transition from a Dirac semi-metal to a normal insulator

Beta Function for Anisotropic Current Interactions in 2D

Dynamical mass generation by source inversion: Calculating the mass gap of the Gross-Neveu model

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