The a-function in six dimensions

Gracey, J.A.; Jack, I.; Poole, C.

doi:10.1007/jhep01(2016)174

Cited by 18 publications

(28 citation statements)

References 65 publications

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“…As we have observed already in four dimensions [10,32] and six dimensions [33], and indeed at lower orders in three dimensions [21,22], the a-function coefficients are determined completely (within a given renormalisation scheme) up to the arbitrariness parametrised by the coefficientã.…”

Section: Consistency Conditions For Four-loop Anomalous Dimensionsupporting

confidence: 65%

a -function for N=2 supersymmetric gauge theories in three dimensions

et al. 2017

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Recently, the existence of a candidate a-function for renormalisable theories in three dimensions was demonstrated for a general theory at leading order and for a scalar-fermion theory at next-to-leading order. Here we extend this work by constructing the a-function at next-to-leading order for an N = 2 supersymmetric Chern-Simons theory. This increase in precision for the a-function necessitated the evaluation of the underlying renormalization-group functions at four loops.

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Section: Consistency Conditions For Four-loop Anomalous Dimensionsupporting

confidence: 65%

a -function for N=2 supersymmetric gauge theories in three dimensions

et al. 2017

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“…If the kinetic terms of the theory possess a global symmetry, then β I in (1.1) is replaced by a generalized function B I , which begins to differ at three loops [5], and is related to the possible existence of theories with limit cycles [20]. While the effects of this shift have been included for the simple case of six-dimensional φ 3 theory [21] and the more complicated four-dimensional scalar-fermion theory [5], equivalent analyses for general gauge theories have not yet reached the point where considering this shift is necessary [6]. All quantities in Osborn's equation are given as functions of the couplings and group structures of the theory.…”

Section: The Long Versionmentioning

confidence: 99%

“…This is perhaps not surprising, as it has already been shown that the first off-diagonal contributions to T IJ in a general theory occur at three loops [6]. When deriving constraints on the β(B)-functions, imposing symmetry on T IJ would correspond to identifying the coefficients of each pair of tensors related by the interchange of open indices I and J, and setting them equal-in six-dimensional φ 3 theory at sufficiently high loop order, it has been shown that this does indeed force an additional CC, which (rather amazingly) turn out to be satisfied by the MS coefficients, and renormalizationscheme independent [21]. Effectively, we conjecture that it is always possible to choose local counter terms such that T IJ is symmetric, and that an analogous construction can be made in the extension to all even dimensions.…”

Section: Imposing Symmetry On T Ijmentioning

confidence: 99%

Constraints on 3- and 4-loop β-functions in a general four-dimensional Quantum Field Theory

Poole

Thomsen

2019

J. High Energ. Phys.

137

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The β-functions of marginal couplings are known to be closely related to the Afunction through Osborn's equation, derived using the local renormalization group. It is possible to derive strong constraints on the β-functions by parametrizing the terms in Osborn's equation as polynomials in the couplings, then eliminating unknowñ A and T IJ coefficients. In this paper we extend this program to completely general gauge theories with arbitrarily many Abelian and non-Abelian factors. We detail the computational strategy used to extract consistency conditions on β-functions, and discuss our automation of the procedure. Finally, we implement the procedure up to 4-, 3-, and 2-loops for the gauge, Yukawa and quartic couplings respectively, corresponding to the present forefront of general β-function computations. We find an extensive collection of highly non-trivial constraints, and argue that they constitute an useful supplement to traditional perturbative computations; as a corollary, we present the complete 3-loop gauge β-function of a general QFT in the MS scheme, including kinetic mixing. 1 cpoole@cp3.sdu.dk 2 aethomsen@cp3.sdu.dk arXiv:1906.04625v3 [hep-th]

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“…The beta-functions and anomalous dimensions for such a general sextic coupling were calculated in [37,38]; see also [39,40] for earlier results on the O(n) invariant sextic theory. The diagram topology contributing to the leading two-loop beta function is shown in figure 12.…”

Section: Renormalized Perturbation Theorymentioning

confidence: 99%

Prismatic large N models for bosonic tensors

et al. 2018

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We study the O(N ) 3 symmetric quantum field theory of a bosonic tensor φ abc with sextic interactions. Its large N limit is dominated by a positive-definite operator, whose index structure has the topology of a prism. We present a large N solution of the model using Schwinger-Dyson equations to sum the leading diagrams, finding that for 2.81 < d < 3 and for d < 1.68 the spectrum of bilinear operators has no complex scaling dimensions. We also develop perturbation theory in 3 − dimensions including eight O(N ) 3 invariant operators necessary for the renormalizability. For sufficiently large N , we find a "prismatic" fixed point of the renormalization group, where all eight coupling constants are real. The large N limit of the resulting expansions of various operator dimensions agrees with the Schwinger-Dyson equations. Furthermore, the expansion allows us to calculate the 1/N corrections to operator dimensions. The prismatic fixed point in 3 − dimensions survives down to N ≈ 53.65, where it merges with another fixed point and becomes complex. We also discuss the d = 1 model where our approach gives a slightly negative scaling dimension for φ, while the spectrum of bilinear operators is free of complex dimensions.

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The a-function in six dimensions

Cited by 18 publications

References 65 publications

a -function for N=2 supersymmetric gauge theories in three dimensions

a -function for N=2 supersymmetric gauge theories in three dimensions

Constraints on 3- and 4-loop β-functions in a general four-dimensional Quantum Field Theory

Prismatic large N models for bosonic tensors

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