The Yangian origin of the Grassmannian integral

Drummond, J. M.; Ferro, Livia

doi:10.1007/jhep12(2010)010

Cited by 83 publications

(100 citation statements)

References 89 publications

(200 reference statements)

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“…Indeed the integrand can be recursively constructed via a BCFW type recursion relation [19] (see also [20]). Ignoring regularisation, this recursive construction can be written as a sequence of Yangian invariant operations on the basic Yangian invariant functions [19] (see also [21][22][23][24] for a discussion of Yangian invariants).…”

Section: Jhep04(2011)083 1 Introductionmentioning

confidence: 99%

New differential equations for on-shell loop integrals

Drummond

Henn

Trnka

2011

J. High Energ. Phys.

155

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We present a novel type of differential equations for on-shell loop integrals. The equations are second-order and importantly, they reduce the loop level by one, so that they can be solved iteratively in the loop order. We present several infinite series of integrals satisfying such iterative differential equations. The differential operators we use are best written using momentum twistor space. The use of the latter was advocated in recent papers discussing loop integrals in N = 4 super Yang-Mills. One of our motivations is to provide a tool for deriving analytical results for scattering amplitudes in this theory. We show that the integrals needed for planar MHV amplitudes up to two loops can be thought of as deriving from a single master topology. The master integral satisfies our differential equations, and so do most of the reduced integrals. A consequence of the differential equations is that the integrals we discuss are not arbitrarily complicated transcendental functions. For two specific two-loop integrals we give the full analytic solution. The simplicity of the integrals appearing in the scattering amplitudes in planar N = 4 super Yang-Mills is strongly suggestive of a relation to the conjectured underlying integrability of the theory. We expect these differential equations to be relevant for all planar MHV and non-MHV amplitudes. We also discuss possible extensions of our method to more general classes of integrals.

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Section: Jhep04(2011)083 1 Introductionmentioning

confidence: 99%

New differential equations for on-shell loop integrals

Drummond

Henn

Trnka

2011

J. High Energ. Phys.

155

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“…Using the covariance of δ 2k|3k (C · Λ), we can trade it with an inverse O(2k) action on the matrix C. The factors dC and δ(C · C T ) are invariant under the O(2k) action, so we can do an integration by parts to make O ij act on the denominator. Following the same steps as in [10], we can show that the quartic and quadratic terms in (7) acting on A 2k cancel each other.…”

Section: Contour Integral Formula and Yangian Invariancementioning

confidence: 84%

“…We follow the methods developed in [10] for four-dimensional amplitudes. As shown in [6,4], the level one Yangian generators can be written in the bilinear form,…”

Section: Contour Integral Formula and Yangian Invariancementioning

confidence: 99%

“…The key insight we adopt from [10] is that Z C i Z Cj generates an O(2k) action on {Λ i }. Using the covariance of δ 2k|3k (C · Λ), we can trade it with an inverse O(2k) action on the matrix C. The factors dC and δ(C · C T ) are invariant under the O(2k) action, so we can do an integration by parts to make O ij act on the denominator.…”

Section: Contour Integral Formula and Yangian Invariancementioning

confidence: 99%

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Scattering Amplitudes in supersymmetric Chern–Simons theory

Lee

2011

Nuclear Physics B - Proceedings Supplements

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“…• it is claimed [65,66] that the Grassmannian integral representation for amplitudes (2.1) is the most general form of rational Yangian invariant, which makes all symmetries of the theory manifest. This further points to the integrable structure [21][22][23][24][25][26] behind amplitudes in N = 4 SYM (at least at tree level);…”

Section: Jhep12(2016)076mentioning

confidence: 99%

Grassmannians and form factors with q 2 = 0 in N $$ \mathcal{N} $$ =4 SYM theory

Bork¹,

Onishchenko²

2016

J. High Energ. Phys.

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In this paper we consider tree level form factors of operators from stress tensor operator supermultiplet with light-like operator momentum q 2 = 0. We present a conjecture for the Grassmannian integral representation both for these tree level form factors as well as for leading singularities of their loop counterparts. The presented conjecture was successfully checked by reproducing several known answers in MHV and N k−2 MHV, k ≥ 3 sectors together with appropriate soft limits. We also discuss the cancellation of spurious poles and relations between different BCFW representations for such form factors on simple examples.

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The Yangian origin of the Grassmannian integral

Cited by 83 publications

References 89 publications

New differential equations for on-shell loop integrals

New differential equations for on-shell loop integrals

Scattering Amplitudes in supersymmetric Chern–Simons theory

Grassmannians and form factors with q 2 = 0 in N $$ \mathcal{N} $$ =4 SYM theory

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