Florian Loebbert

Symmetries of Tree-level Scattering Amplitudes in N = 6 Superconformal Chern{Simons Theory

Constraints of the

Exacting N=4 Superconformal Symmetry

\mathfrak{o}\mathfrak{s}\mathfrak{p}(6|4)

Long-range deformations for integrable spin chains

symmetry on tree-level scattering amplitudes in

Conformal Anomaly for Amplitudes in N = 6 Superconformal Chern{Simons Theory

\mathcal{N}=6

Exact Superconformal and Yangian Symmetry of Scattering Amplitudes

superconformal Chern-Simons theory are derived. Supplemented by Feynman diagram calculations, solutions to these constraints, namely, the four- and six-point superamplitudes, are presented and shown to be invariant under Yangian symmetry. This introduces integrability into the amplitude sector of the theory.

Fixing the quantum three-point function

Tree level scattering amplitudes in N = 4 super Yang-Mills theory are al- most, but not exactly invariant under the free action of the N = 4 superconformal algebra. What causes the non-invariance is the holomorphic anomaly at poles where external par- ticles become collinear. In this paper we propose a deformation of the free superconformal representation by contributions which change the number of external legs. This modified classical representation not only makes tree amplitudes fully invariant, but it also leads to additional constraints from symmetry alone mediating between hitherto unrelated ampli- tudes. Moreover, in a constructive approach it appears to fully constrain all tree amplitudes when combined with dual superconformal alias Yangian symmetry.

Boosting nearest-neighbour to long-range integrable spin chains

We present a recursion relation for the explicit construction of integrable spin chain Hamiltonians with long-range interactions. Based on arbitrary shortrange (e.g. nearest neighbor) integrable spin chains, it allows us to construct an infinite set of conserved long-range charges. We explain the moduli space of deformation parameters by different classes of generating operators. The rapidity map and dressing phase in the long-range Bethe equations are a result of these deformations. The closed chain asymptotic Bethe equations for long-range spin chains transforming under a generic symmetry algebra are derived. Notably, our construction applies to generalizations of standard nearest neighbor chains such as alternating spin chains. We also discuss relevant properties for its application to planar D = 4, N = 4 and D = 3, N = 6 supersymmetric gauge theories. Finally, we present a map between long-range and inhomogeneous spin chains delivering more insight into the structures of these models, as well as their limitations at wrapping order.

Integrable Amplitude Deformations for N=4 Super Yang-Mills and ABJM Theory

Scattering amplitudes in three-dimensional Chern?Simons theory are shown to be non-invariant with respect to the free representation of the symmetry generators. At tree and one-loop level these ?anomalous? terms occur only for non-generic, singular configurations of the external momenta and can be used to determine the form of the amplitudes. In particular we show that the symmetries predict that the one-loop six-point amplitude is non-vanishing and confirm this by means of an explicit calculation using generalized unitarity methods. We comment on the implications of this finding for any putative Wilson loop/amplitude duality in Chern?Simons theory.

Open Perturbatively Long-Range Integrable GL(N) Spin Chains

We review recent progress in the understanding of symmetries for scattering amplitudes in N = 4 superconformal Yang–Mills theory. It is summarized how the superficial breaking of superconformal symmetry by collinear anomalies and the renormalization process can be cured at tree and loop level. This is achieved by correcting the representation of the superconformal group on amplitudes. Moreover, we comment on the Yangian symmetry of scattering amplitudes and how it inherits these correction terms from the ordinary Lie algebra symmetry. Invariants under this algebra and their relation to the Grasmannian generating function for scattering amplitudes are discussed. Finally, parallel developments in N = 6 superconformal Chern–Simons theory are summarized. This paper is an invited review for a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Scattering amplitudes in gauge theories’.

Yangian Symmetry for Fishnet Feynman Graphs

A bstractWe propose a new method for the computation of quantum three-point functions for operators in