On the amplitudes in $ \mathcal{N}=\left( {1,1} \right) $ D = 6 SYM

Bork, L. V.; Kazakov, D. I.; Vlasenko, D. E.

doi:10.1007/jhep11(2013)065

Cited by 11 publications

(5 citation statements)

References 49 publications

(44 reference statements)

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“…It is instructive to compare our results on the one-loop low-energy effective action in 6D, N = (1, 1) SYM theory with the recent activity on calculating the one-loop on-shell amplitudes in the same theory [49][50][51][52][53]. The four-point amplitude nicely matches with the JHEP09(2018)039 F 4 component term in the superfield effective action (4.19) and, as a function of the inverse square of v.e.v.…”

Section: Discussionmentioning

confidence: 89%

“…However, we emphasize that unlike the amplitudes, the result for the effective action in our paper was derived in a manifest superfield form. The four-point amplitude in [51][52][53] does not allow to directly restore this effective action. The point is that the effective action (4.17) contains the hypermultiplet superfield whose scalar component serves as a natural infrared regulator.…”

Section: Discussionmentioning

confidence: 99%

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Leading low-energy effective action in 6D, $$ \mathcal{N}=\left(1,1\right) $$ SYM theory

Buchbinder

Ivanov²,

Мерзликин

2018

J. High Energ. Phys.

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We elaborate on the low-energy effective action of 6D, N = (1, 1) supersymmetric Yang-Mills (SYM) theory in the N = (1, 0) harmonic superspace formulation. The theory is described in terms of analytic N = (1, 0) gauge superfield V ++ and analytic ω-hypermultiplet, both in the adjoint representation of gauge group. The effective action is defined in the framework of the background superfield method ensuring the manifest gauge invariance along with manifest N = (1, 0) supersymmetry. We calculate leading contribution to the one-loop effective action using the on-shell background superfields corresponding to the option when gauge group SU(N) is broken to SU(N −1)×Υ(1) ⊂ SU(N). In the bosonic sector the effective action involves the structure ∼ F 4 X 2 , where F 4 is a monomial of the fourth degree in an abelian field strength F M N and X stands for the scalar fields from the ω-hypermultiplet. It is manifestly demonstrated that the expectation values of the hypermultiplet scalar fields play the role of a natural infrared cutoff.

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Section: Discussionmentioning

confidence: 89%

Section: Discussionmentioning

confidence: 99%

Leading low-energy effective action in 6D, $$ \mathcal{N}=\left(1,1\right) $$ SYM theory

Buchbinder

Ivanov²,

Мерзликин

2018

J. High Energ. Phys.

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“…It is a well-known feature, and we tried to avoid it using mainly diagonal approximations. With 15 terms of PT the (6,6), (6,7) and (7,7) approximants are almost identical and give a smooth function.…”

Section: The General Casementioning

confidence: 93%

“…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].…”

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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“…The aim of this paper, which is a continuation of our previous papers [30][31][32][33], is to investigate the amplitudes and their UV properties in maximally supersymmetric gauge theories in various dimensions. Namely, we evaluate the leading UV divergences in the four-point amplitude on shell in a number of loops and investigate their properties in all loops.…”

Section: Jhep11(2015)059mentioning

confidence: 98%

Divergences in maximal supersymmetric Yang-Mills theories in diverse dimensions

Bork

Kazakov

Kompaniets

et al. 2015

J. High Energ. Phys.

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Abstract:The main aim of this paper is to study the scattering amplitudes in gauge field theories with maximal supersymmetry in dimensions D = 6, 8 and 10. We perform a systematic study of the leading ultraviolet divergences using the spinor helicity and on-shell momentum superspace framework. In D = 6 the first divergences start at 3 loops and we calculate them up to 5 loops, in D = 8, 10 the first divergences start at 1 loop and we calculate them up to 4 loops. The leading divergences in a given order are the polynomials of Mandelstam variables. To be on the safe side, we check our analytical calculations by numerical ones applying the alpha-representation and the dedicated routines. Then we derive an analog of the RG equations for the leading pole that allows us to get the recursive relations and construct the generating procedure to obtain the polynomials at any order of perturbation theory (PT). At last, we make an attempt to sum the PT series and derive the differential equation for the infinite sum. This equation possesses a fixed point which might be stable or unstable depending on the kinematics. Some consequences of these fixed points are discussed.

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On the amplitudes in $ \mathcal{N}=\left( {1,1} \right) $ D = 6 SYM

Cited by 11 publications

References 49 publications

Leading low-energy effective action in 6D, $$ \mathcal{N}=\left(1,1\right) $$ SYM theory

Leading low-energy effective action in 6D, $$ \mathcal{N}=\left(1,1\right) $$ SYM theory

High Energy Behavior in Maximally Supersymmetric Gauge Theories in Various Dimensions

Divergences in maximal supersymmetric Yang-Mills theories in diverse dimensions

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