Divergences in maximal supersymmetric Yang-Mills theories in diverse dimensions

Bork, L. V.; Kazakov, D. I.; Kompaniets, M. V.; Tolkachev, D. M.; Vlasenko, D. E.

doi:10.1007/jhep11(2015)059

Cited by 45 publications

(64 citation statements)

References 58 publications

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“…To get the desired recurrence relation, which is the starting point of our analysis, one has to write down the R-operation and analyze the one loop diagrams left after subtraction of the counter terms. In the case of the φ 4 theory one always has a bubble, while in the maximally SUSY gauge theories one has a triangle [2]. The difference is not principle, the recurrence relations look similar.…”

Section: Discussionmentioning

confidence: 99%

“…In renormalizable theories these relations are known as pole equations (within dimensional regularization) and are governed by the renormalization group [7]. The same is true, though technically is more complicated, in any local theory, as we have demonstrated in [2]- [4]. We remind here some features of this procedure.…”

Section: Bogoliubov R-operation and Local Counter Termsmentioning

confidence: 97%

“…In our previous papers [2]- [4] we chose as a playground for our analysis the planar scattering amplitudes in D=8 super Yang-Mills theory considered within the spinor helicity formalism [5]. There were some reasons for that.…”

Section: Introductionmentioning

confidence: 99%

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RG equations and high energy behaviour in non-renormalizable theories

Kazakov

2019

Physics Letters B

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We suggest a novel view on non-renormalizable interactions. It is based on the usual BPHZ R-operation which is equally applicable to any local QFT independently whether it is renormalizable or not. As a playground we take the φ 4 D theory in D dimensions for D = 4, 6, 8, 10 and consider the four-point scattering amplitude on shell. We derive the generalized RG equation and find the solution valid for any D that sums up the leading logarithms in all orders of PT in full analogy with the renormalizable case. It is found that the scattering amplitude in the φ 4 D theory possesses the Landau pole at high energy for any D. We discuss the application of the proposed procedure to other non-renormalizable theories.

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Section: Discussionmentioning

confidence: 99%

Section: Bogoliubov R-operation and Local Counter Termsmentioning

confidence: 97%

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RG equations and high energy behaviour in non-renormalizable theories

Kazakov

2019

Physics Letters B

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“…This provides an efficient tool to apply the generalized unitary method to compute on-shell scattering amplitudes in N = (1, 1), 6D SYM theory [52] (see also [53] and references therein). It would be interesting to clarify the relations between the Feynman rules in N = (1, 0) harmonic superspace and this generalized unitary method in momentum on-shell harmonic superspace.…”

Section: Jhep12(2015)085mentioning

confidence: 99%

Ultraviolet behavior of 6D supersymmetric Yang-Mills theories and harmonic superspace

Bossard¹,

Ivanov²,

Smilga³

2015

J. High Energ. Phys.

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Abstract:We revisit the issue of higher-dimensional counterterms for the N = (1, 1) supersymmetric Yang-Mills (SYM) theory in six dimensions using the off-shell N = (1, 0) and on-shell N = (1, 1) harmonic superspace approaches. The second approach is developed in full generality and used to solve, for the first time, the N = (1, 1) SYM constraints in terms of N = (1, 0) superfields. This provides a convenient tool to write explicit expressions for the candidate counterterms and other N = (1, 1) invariants and may be conducive to proving non-renormalization theorems needed to explain the absence of certain logarithmic divergences in higher-loop contributions to scattering amplitudes in N = (1, 1) SYM.

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“…In the sequence of papers [7,8,9,10], we considered the leading and subleading UV divergences of the on-shell four point scattering amplitudes for all three cases of maximally supersymmetric SYM theories, D=6 (N=2 SUSY), D=8 (N=1 SUSY) and D=10 (N=1 SUSY). We obtained the recursive relations that allow one to get leading and subleading divergences in all loops in a pure algebraic way [9,10]. Then we constructed the differential equations, which are the generalization of the RG equations for non-renormalizable theories [9,10].…”

Section: Introductionmentioning

confidence: 99%

High Energy Behavior in Maximally Supersymmetric Gauge Theories in Various Dimensions

et al. 2019

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Maximally supersymmetric field theories in various dimensions are believed to possess special properties due to extended supersymmetry. In four dimensions they are free from UV divergences but are IR divergent on shell, in higher dimensions, on the contrary, they are IR finite but UV divergent. In what follows we consider the four-point on-shell scattering amplitudes in D=6,8,10 supersymmetric Yang-Mills theory in the planar limit within the spinor-helicity and on shell supersymmetric formalism. We study the UV divergences and demonstrate how one can sum them over all orders of PT. Analyzing the R-operation, we obtain the recursive relations and derive differential equations that sum all leading, subleading, etc., divergences in all loops generalizing the standard RG formalism for the case of nonrenormalizable interactions. We then perform the renormalization procedure which differs from the ordinary one in that the renormalization constant becomes the operator depending on kinematics. Solving the obtained RG equations for particular sets of diagrams analytically and for the general case numerically, we analyze their high energy behaviour and find out that while each term of PT increases as a power of energy, the total sum behaves differently: in D=6 two partial amplitudes decrease with energy and the third one increases exponentially, while in D=8 and 10 the amplitudes possess an infinite number of periodic poles at finite energy.

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Divergences in maximal supersymmetric Yang-Mills theories in diverse dimensions

Cited by 45 publications

References 58 publications

RG equations and high energy behaviour in non-renormalizable theories

RG equations and high energy behaviour in non-renormalizable theories

Ultraviolet behavior of 6D supersymmetric Yang-Mills theories and harmonic superspace

High Energy Behavior in Maximally Supersymmetric Gauge Theories in Various Dimensions

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