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arXiv · 2206.09368

From tree- to loop-simplicity in affine Toda theories I: Landau singularities and their subleading coefficients

Patrick Dorey·Davide Polvara
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Abstract

Various features of the even order poles appearing in the S-matrices of simply-laced affine Toda field theories are analysed in some detail. In particular, the coefficients of first- and second-order singularities appearing in the Laurent expansion of the S-matrix around a general $2N^{\rm th}$ order pole are derived in a universal way using perturbation theory at one loop. We show how to cut loop diagrams contributing to the pole into particular products of tree-level graphs that depend on the on-shell geometry of the loop; in this way, we recover the coefficients of the Laurent expansion around the pole exploiting tree-level integrability properties of the theory. The analysis is independent of the particular simply-laced theory considered, and all the results agree with those obtained in the conjectured bootstrapped S-matrices of the ADE series of theories.

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Patrick Dorey, Davide Polvara. 2022-06-19. From tree- to loop-simplicity in affine Toda theories I: Landau singularities and their subleading coefficients. https://doi.org/10.1007/jhep09(2022)220

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