др Игор Прлина

09. марта 2022.

У оквиру семинара Групе за гравитацију, честице и поља Института за физику у Београду, у петак, 11. марта 2022. године у 11 часова путем BigBlueButton платформе, др Игор Прлина (Браун универзитет), одржаће предавање:

Landau Singularities in Planar Massless Theories


In this work we present our contribution to the method of using Landau singularities for probing scattering amplitudes in planar massless quantum field theories. We start by proposing a simple geometric algorithm for determining the complete set of branch points of amplitudes in planar N = 4 super-Yang-Mills theory directly from the amplituhedron, without resorting to any particular representation in terms of local Feynman integrals. This represents a step towards translating integrands directly into integrals. In particular, the algorithm provides information about the symbol alphabets of general amplitudes. First we illustrate the algorithm applied to the one-and two-loop MHV amplitudes. Then we demonstrate how to use the reformulation of amplituhedra in terms of ‘sign flips’ in order to streamline the application of this algorithm to amplitudes of any helicity. In this way we recover the known branch points of all one loop amplitudes, and we find an ’emergent positivity’ on boundaries of amplituhedra. Lastly, we look beyond planar N = 4 super-Yang-Mills theory, and analyze Landau singularities of general massless planar theories. In massless quantum field theories the Landau equations are invariant under graph operations familiar from the theory of electrical circuits. Using a theorem on the Y-∆ reducibility of planar circuits we prove that the set of first-type Landau singularities of an n-particle scattering amplitude in any massless planar theory, in any spacetime dimension D, at any finite loop order in perturbation theory, is a subset of those of a certain n-particle ⌊(n−2)^2/4⌋-loop „ziggurat“ graph. We determine this singularity locus explicitly for D = 4 and n = 6 and find that it corresponds precisely to the vanishing of the symbol letters familiar from the hexagon bootstrap in SYM theory. Further implications for SYM theory are discussed.

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