Dual conformal properties of six-dimensional maximal super Yang-Mills amplitudes

Dennen, Tristan; Huang, Yu-tin

doi:10.1007/jhep01(2011)140

Cited by 62 publications

(87 citation statements)

References 60 publications

(120 reference statements)

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“…We note that the inversion defined in eqs. (4.35) to (4.41) differs from the one presented in [4] by some signs which are necessary in order to yield the desired inversion of the amplitudes. The proof of eq.…”

Section: Jhep01(2015)098mentioning

confidence: 93%

“…Indeed, compact arbitrary multiplicity amplitudes for particular subclasses of Coulomb branch amplitudes have been obtained in [9] by making use of modern on-shell techniques. The massive 4d N = 4 SYM amplitudes are invariant under a dual conformal symmetry which is inherited from the 6d N = (1, 1) SYM theory as shown in [4]. Moreover, this symmetry remains intact also at loop-level if one restricts the loop-momentum integrations to a four-dimensional subspace.…”

Section: Jhep01(2015)098mentioning

confidence: 96%

“…Although a part of the symmetries of tree-level N = (1, 1) SYM theory amplitudes appear in the literature, e. g. in [4,37], a complete list of all generators and their algebra is missing. This section aims to close this gap.…”

Section: Superpoincaré Symmetrymentioning

confidence: 99%

“…Beautifully there is an additional non-trivial symmetry of the superamplitudes [4]. Similar to N = 4 SYM theory in four dimensions, the N = (1, 1) SYM theory in six dimensions has a treelevel dual conformal symmetry.…”

Section: Enhanced Dual Conformal Symmetrymentioning

confidence: 99%

“…Next to their constitutional maximally extended super-Poincaré symmetries they all enjoy a hidden dual conformal symmetry -at least at the tree-level [1][2][3][4][5]. The four dimensional N = 4 super Yang-Mills (SYM) theory is distinguished in this series as it also has superconformal symmetry in the standard sense.…”

Section: Introductionmentioning

confidence: 99%

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From six to four and more: massless and massive maximal super Yang-Mills amplitudes in 6d and 4d and their hidden symmetries

Plefka

Schuster

Verschinin

2015

J. High Energ. Phys.

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A self-consistent exposition of the theory of tree-level superamplitudes of the 4d N = 4 and 6d N = (1, 1) maximally supersymmetric Yang-Mills theories is provided. In 4d we work in non-chiral superspace and construct the superconformal and dual superconformal symmetry generators of the N = 4 SYM theory using the non-chiral BCFW recursion to prove the latter. In 6d we provide a complete derivation of the standard and hidden symmetries of the tree-level superamplitudes of N = (1, 1) SYM theory, again using the BCFW recursion to prove the dual conformal symmetry. Furthermore, we demonstrate that compact analytical formulae for tree-superamplitudes in N = (1, 1) SYM can be obtained from a numerical implementation of the supersymmetric BCFW recursion relation. We derive compact manifestly dual conformal representations of the five-and six-point superamplitudes as well as arbitrary multiplicity formulae valid for certain classes of superamplitudes related to ultra-helicity-violating massive amplitudes in 4d. We study massive tree superamplitudes on the Coulomb branch of the N = 4 SYM theory from dimensional reduction of the massless superamplitudes of the six-dimensional N = (1, 1) SYM theory. We exploit this correspondence to construct the super-Poincaré and enhanced dual conformal symmetries of massive tree superamplitudes in N = 4 SYM theory which are shown to close into a finite dimensional algebra of Yangian type. Finally, we address the fascinating possibility of uplifting massless 4d superamplitudes to 6d massless superamplitudes proposed by Huang. We confirm the uplift for multiplicities up to eight but show that finding the uplift is highly non-trivial and in fact not of a practical use for multiplicities larger than five.

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Section: Jhep01(2015)098mentioning

confidence: 93%

Section: Jhep01(2015)098mentioning

confidence: 96%

Section: Superpoincaré Symmetrymentioning

confidence: 99%

Section: Enhanced Dual Conformal Symmetrymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

From six to four and more: massless and massive maximal super Yang-Mills amplitudes in 6d and 4d and their hidden symmetries

Plefka

Schuster

Verschinin

2015

J. High Energ. Phys.

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Implications of Hidden $$\mathscr {N}=(0,1)$$ Super-Symmetry in $$\mathscr {N}=(1,1),\,6D$$ SYM Theory

Ivanov¹

2018

Springer Proceedings in Mathematics &Amp; Statistics

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Amplitudes of 3d Yang Mills theory

Lipstein

Mason²

2013

J. High Energ. Phys.

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This paper studies various properties of amplitudes in 3d super Yang Mills theory. First we explain how to obtain the amplitudes of 3d super Yang Mills theories from 4d super Yang Mills theories and obtain their helicity structure. Next, we use a 3d BFCW recursion relation to show that the tree amplitudes and loop integrands of maximal 3d super Yang Mills have dual conformal covariance (although not invariance, so that the amplitudes themselves are not dual conformal). Finally, we argue that the one-loop amplitudes of maximal 3d super Yang-Mills can be reduced to scalar box diagrams and evaluate these diagrams using dimensional regularization. We find that the one-loop MHV amplitudes vanish and the one-loop non-MHV amplitudes are finite.

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Dual conformal properties of six-dimensional maximal super Yang-Mills amplitudes

Cited by 62 publications

References 60 publications

From six to four and more: massless and massive maximal super Yang-Mills amplitudes in 6d and 4d and their hidden symmetries

From six to four and more: massless and massive maximal super Yang-Mills amplitudes in 6d and 4d and their hidden symmetries

Implications of Hidden $$\mathscr {N}=(0,1)$$ Super-Symmetry in $$\mathscr {N}=(1,1),\,6D$$ SYM Theory

Amplitudes of 3d Yang Mills theory

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