Abstract
We establish an all-loop conformal Yangian symmetry for the full set of planar amplitudes in the recently proposed integrable bi-scalar field theory in four dimensions. This chiral theory is a particular double scaling limit of γ-twisted weakly coupled mathcal{N}=4 SYM theory. Each amplitude with a certain order of scalar particles is given by a single fishnet Feynman graph of disc topology cut out of a regular square lattice. The Yangian can be realized by the action of a product of Lax operators with a specific sequence of inhomogeneity parameters on the boundary of the disc. Based on this observation, the Yangian generators of level one for generic bi-scalar amplitudes are explicitly constructed. Finally, we comment on the relation to the dual conformal symmetry of these scattering amplitudes.
Highlights
For their computation, a few very promising ideas have been proposed, such as the pentagon OPE of [10] for instance
The Yangian symmetry has been well established as a symmetry of tree-level scattering amplitudes, but its generalization to higher loop orders is hindered by IR singularities which, being regularized, destroy this symmetry [13, 14]
As we will show in this paper, an all-loop Yangian symmetry can be constructed for the case of scalar amplitudes within the recently proposed, by one of the authors and O
Summary
We briefly review the construction of Yangian invariants before specifying it to the case of the conformal algebra so(2, 4). The algebra given by the RTT-relation possesses a comultiplication structure This means that the matrix product of several Lax operators (each acting on its own spin chain site) respects (2.1). As was shown in [26, 27], the eigenvalue problem for an inhomogeneous monodromy constructed out of Lax operators, i.e. provides a natural way to obtain Yangian invariants |λ; inv , which live on n sites of a noncompact spin chain. Provides a natural way to obtain Yangian invariants |λ; inv , which live on n sites of a noncompact spin chain Both sides of eq (2.4) are matrices and 1 denotes the identity matrix. In this case xμi are the usual position space coordinates
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