Leading and subleading UV divergences in scattering amplitudes for<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>D</mml:mi><mml:mo>=</mml:mo><mml:mn>8</mml:mn></mml:mrow></mml:math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi mathvariant="script">N</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math>SYM theory in all loops

Kazakov, D. I.; Vlasenko, D. E.

doi:10.1103/physrevd.95.045006

Cited by 17 publications

(30 citation statements)

References 24 publications

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“…These relations are known as pole equations (within dimensional regularization) in renormalizable theories [18] and can be expressed in the form of the renormalization group. This holds true for any local theory, though can be trickier to execute technically, as we have shown in [9,10]. We recall the main steps of this procedure below.…”

Section: On-shell Momentum Superspacementioning

confidence: 98%

“…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%

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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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Section: On-shell Momentum Superspacementioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

High Energy Behavior in Maximally Supersymmetric Gauge Theories in Various Dimensions

et al. 2019

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“…The same is true for subleading, subsubleading, etc. poles as well (see [9]), but one should take into account the diagrams with two, three, etc. loops, respectively, just like it takes place in renormalizable theories.…”

Section: Bogoliubov R-operation and Local Counter Termsmentioning

confidence: 99%

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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“…One can continue this procedure for the subleading divergences where now both the one loop and the two loop genuine contributions to the simple pole have to be taken as initial conditions [4]. The relations are too cumbersome to write them down here but work perfectly well as the ones for the leading poles.…”

Section: D=8 Sym Theory In Spinor Helicity Formalismmentioning

confidence: 99%

“…When using dimensional regularization these relations are nothing more than the 't Hoofts pole equations [2], which relate the higher order poles in with the lower order ones. In a recent set of papers [3,4] we demonstrated how these generalized pole equations could be written in the case of D=6, 8 and 10 dimensional super Yang-Mills theories, which are non-renormalizable by power counting.…”

Section: Introductionmentioning

confidence: 99%

Kinematically dependent renormalization

Kazakov

2018

Physics Letters B

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We suggest a renewed view on non-renormalizable interactions treated perturbatively within a kinematically dependent renormalization procedure. It is based on the usual BPHZ R-operation which is equally applicable to any local QFT independently whether it is renormalizable or not. The key point is that the renormalization constant becomes the function of kinematical variables acting as an operator on the amplitude. The procedure is demonstrated by the example of D=8 supersymmetric gauge theory considered within the spinor helicity formalism.

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Leading and subleading UV divergences in scattering amplitudes forD=8N=1SYM theory in all loops

Cited by 17 publications

References 24 publications

High Energy Behavior in Maximally Supersymmetric Gauge Theories in Various Dimensions

High Energy Behavior in Maximally Supersymmetric Gauge Theories in Various Dimensions

RG equations and high energy behaviour in non-renormalizable theories

Kinematically dependent renormalization

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