Local integrand representations of all two-loop amplitudes in planar SYM

Bourjaily, Jacob L.; Trnka, Jaroslav

doi:10.1007/jhep08(2015)119

Cited by 69 publications

(157 citation statements)

References 62 publications

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“…(2.7) which can be expressed explicitly as a single dlog form [25]. More complicated dlog integrands have been used to write explicit expressions for one-loop and two-loop planar integrands for all multiplicities [71,72]. Whenever the amplitude is built…”

Section: Jhep06(2016)098mentioning

confidence: 99%

Evidence for a nonplanar amplituhedron

Bern¹,

Herrmann

Litsey³

et al. 2016

J. High Energ. Phys.

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157

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The scattering amplitudes of planar N = 4 super-Yang-Mills exhibit a number of remarkable analytic structures, including dual conformal symmetry and logarithmic singularities of integrands. The amplituhedron is a geometric construction of the integrand that incorporates these structures. This geometric construction further implies the amplitude is fully specified by constraining it to vanish on spurious residues. By writing the amplitude in a dlog basis, we provide nontrivial evidence that these analytic properties and "zero conditions" carry over into the nonplanar sector. This suggests that the concept of the amplituhedron can be extended to the nonplanar sector of N = 4 super-Yang-Mills theory.

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Section: Jhep06(2016)098mentioning

confidence: 99%

Evidence for a nonplanar amplituhedron

Bern¹,

Herrmann

Litsey³

et al. 2016

J. High Energ. Phys.

Self Cite

157

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“…[62], has since been extended to the non-planar sector and cast into a complete set of numerators satisfying colour-kinematics duality [63]. The integrands in planar N = 4 sYM are known to all loop orders [64,65], and recent studies indicate that this simplicity may extend to the non-planar sector [66,67].…”

Section: Jhep10(2015)064mentioning

confidence: 99%

A complete two-loop, five-gluon helicity amplitude in Yang-Mills theory

Badger

Mogull

Ochirov

et al. 2015

J. High Energ. Phys.

120

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Abstract:We compute the integrand of the full-colour, two-loop, five-gluon scattering amplitude in pure Yang-Mills theory with all helicities positive, using generalized unitarity cuts. Tree-level BCJ relations, satisfied by amplitudes appearing in the cuts, allow us to deduce all the necessary non-planar information for the full-colour amplitude from known planar data. We present our result in terms of irreducible numerators, with colour factors derived from the multi-peripheral colour decomposition. Finally, the leading soft divergences are checked to reproduce the expected infrared behaviour.

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“…A particularly powerful technique in N = 4 sYM has been the use of local integrands to control infrared singularities and provide a basis of simple integrals [36][37][38]. In this work we have explored the use of these numerator functions in dimensionally-regulated amplitudes outside four-dimensional N = 4.…”

Section: Generalised Unitarity and Integrand Reductionmentioning

confidence: 99%

“…The main principle is to build an integrand representation in which infrared singularities are manifest and a basis of simple integrals can be identified. Originally developed for use in N = 4 maximally supersymmetric Yang-Mills (sYM) theory, these local integrands have been successfully used to obtain results in many high-multiplicity two-and three-loop cases [36][37][38]. Recently, we have found such a local representation for the five-and six-gluon amplitudes in Yang-Mills with all positive helicities [39].…”

Section: Introductionmentioning

confidence: 99%