Integrability and Maximally Helicity Violating Diagrams in N = 4 Supersymmetric Yang-Mills Theory

127

215

Abstract:We show how to use on-shell unitarity methods to calculate renormalisation group coefficients such as beta functions and anomalous dimensions. The central objects are the form factors of composite operators. Their discontinuities can be calculated via phasespace integrals and are related to corresponding anomalous dimensions. In particular, we find that the dilatation operator, which measures the anomalous dimensions, is given by minus the phase of the S-matrix divided by π. We illustrate our method using several examples from Yang-Mills theory, perturbative QCD and Yukawa theory at one-loop level and beyond.

Section: Length-changing Effects and Towards Higher Loops: Yukawa Theorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Renormalization group coefficients and the S-matrix

Caron-Huot¹,

Wilhelm²

2016

127

215

“…Complementary approaches based on two-point functions were recently explored in[30][31][32] 5. We also note that the discontinuities of sub-minimal form factors at two loops were computed in[33] in complete generality.…”

mentioning

confidence: 98%

The SU(2|3) dynamic two-loop form factors

Brandhuber¹,

Kostacinska²,

Penante³

et al. 2016

We compute two-loop form factors of operators in the SU(2|3) closed subsector of N = 4 supersymmetric Yang-Mills. In particular, we focus on the non-protected, dimension-three operators Tr(X[Y, Z]) and Tr(ψψ) for which we compute the four possible two-loop form factors, and corresponding remainder functions, with external states XȲZ | and ψψ |. Interestingly, the maximally transcendental part of the two-loop remainder of XȲZ |Tr(X[Y, Z])|0 turns out to be identical to that of the corresponding known quantity for the half-BPS operator Tr(X 3 ). We also find a surprising connection between the terms subleading in transcendentality and certain a priori unrelated remainder densities introduced in the study of the spin chain Hamiltonian in the SU(2) sector. Next, we use our calculation to resolve the mixing, recovering anomalous dimensions and eigenstates of the dilatation operator in the SU(2|3) sector at two loops. We also speculate on potential connections between our calculations in N = 4 super Yang-Mills and Higgs + multi-gluon amplitudes in QCD in an effective Lagrangian approach.

“…7 Other previous works discussing composite operators within the twistor framework are the proof of the correlator/amplitude duality for the Konishi multiplet [15,28] and the recent papers [29,30] where the N = 4 one-loop dilatation operator in the SO(6) sector is rederived. In either case the realisation of the operators is necessarily different from our approach because they are not connected to the Lagrangian by supersymmetry, which we use extensively.…”

Section: Jhep06(2015)198mentioning

confidence: 99%

Correlation functions of the chiral stress-tensor multiplet in N = 4 $$ \mathcal{N}=4 $$ SYM

Chicherin

Doobary

Eden

et al. 2015

We give a new method for computing the correlation functions of the chiral part of the stress-tensor supermultiplet that relies on the reformulation of N = 4 SYM in twistor space. It yields the correlation functions in the Born approximation as a sum of Feynman diagrams on twistor space that involve only propagators and no integration vertices. We use this unusual feature of the twistor Feynman rules to compute the correlation functions in terms of simple building blocks which we identify as a new class of N = 4 off-shell superconformal invariants. Making use of the duality between correlation functions and planar scattering amplitudes, we demonstrate that these invariants represent an off-shell generalisation of the on-shell invariants defining tree-level scattering amplitudes in N = 4 SYM.