Till Bargheer

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)

New relations for three-dimensional supersymmetric scattering amplitudes.

symmetry on tree-level scattering amplitudes in

Long-range deformations for integrable spin chains

\mathcal{N}=6

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

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.

Exact Superconformal and Yangian Symmetry of Scattering Amplitudes

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 provide evidence for a duality between color and kinematics in three-dimensional supersymmetric Chern-Simons matter theories. We show that the six-point amplitude in the maximally supersymmetric N=8 theory can be arranged so that the kinematic factors satisfy the fundamental identity of three-algebras. We further show that the four- and six-point N=8 amplitudes can be squared into the amplitudes of N=16 three-dimensional supergravity, thus providing evidence for a hidden three-algebra structure in the dynamics of the supergravity.

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

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.

Computing three-point functions for short operators

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.

Quantum Stability for the Heisenberg Ferromagnet

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’.