On-shell diagrams, Graßmannians and integrability for form factors

TY - JOUR

T1 - On-shell diagrams, Graßmannians and integrability for form factors

AU - Frassek, Rouven

AU - Meidinger, David

AU - Nandan, Dhritiman

AU - Wilhelm, Matthias

PY - 2016/1/1

Y1 - 2016/1/1

N2 - We apply on-shell and integrability methods that have been developed in the context of scattering amplitudes in N=4 (Formula Presented.) SYM theory to tree-level form factors of this theory. Focussing on the colour-ordered super form factors of the chiral part of the stress-tensor multiplet as an example, we show how to systematically construct on-shell diagrams for these form factors with the minimal form factor as further building block in addition to the three-point amplitudes. Moreover, we obtain analytic representations in terms of Graßmannian integrals in spinor helicity, twistor and momentum twistor variables. While Yangian invariance is broken by the operator insertion, we find that the form factors are eigenstates of the integrable spin-chain transfer matrix built from the monodromy matrix that yields the Yangian generators. Constructing them via the method of R operators allows to introduce deformations that preserve the integrable structure. We finally show that the integrable properties extend to minimal tree-level form factors of generic composite operators as well as certain leading singularities of their n-point loop-level form factors.

AB - We apply on-shell and integrability methods that have been developed in the context of scattering amplitudes in N=4 (Formula Presented.) SYM theory to tree-level form factors of this theory. Focussing on the colour-ordered super form factors of the chiral part of the stress-tensor multiplet as an example, we show how to systematically construct on-shell diagrams for these form factors with the minimal form factor as further building block in addition to the three-point amplitudes. Moreover, we obtain analytic representations in terms of Graßmannian integrals in spinor helicity, twistor and momentum twistor variables. While Yangian invariance is broken by the operator insertion, we find that the form factors are eigenstates of the integrable spin-chain transfer matrix built from the monodromy matrix that yields the Yangian generators. Constructing them via the method of R operators allows to introduce deformations that preserve the integrable structure. We finally show that the integrable properties extend to minimal tree-level form factors of generic composite operators as well as certain leading singularities of their n-point loop-level form factors.

KW - AdS-CFT Correspondence

KW - Integrable Field Theories

KW - Scattering Amplitudes

KW - Supersymmetric gauge theory

U2 - 10.1007/JHEP01(2016)182

DO - 10.1007/JHEP01(2016)182

M3 - Journal article

AN - SCOPUS:84957593243

SN - 1126-6708

VL - 2016

SP - 1

EP - 46

JO - Journal of High Energy Physics (Online)

JF - Journal of High Energy Physics (Online)

IS - 1

M1 - 182

ER -