Laberintos de la era del liberalismo económico

Vergara, Maribel de la Cruz

doi:10.32997/2382-4794-vol.8-num.8/2016/251

Cited by 1 publication

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“…Whilst being a satisfying result in its own, the discovery of the Amplituhedron is by no means sufficient to replace -or better translate -everything we knew on quantum field theories with an equivalent dictionary in the world of positive geometries. Indeed, till very recently [2,18], there was no other instance of a quantum field theory whose amplitudes could be computed in the same amplituhedral fashion as N = 4 SYM. However, we now know that this is possible for a larger class of theories, such as the bi-adjoint scalar field theory, at least at tree level.…”

Section: Introductionmentioning

confidence: 99%

Hyperbolic geometry and amplituhedra in 1+2 dimensions

Salvatori

Cacciatori

2018

J. High Energ. Phys.

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Recently, the existence of an Amplituhedron for tree level amplitudes in the biadjoint scalar field theory has been proved by Arkhani-Hamed et al. We argue that hyperbolic geometry constitutes a natural framework to address the study of positive geometries in moduli spaces of Riemann surfaces, and thus to try to extend this achievement beyond tree level. In this paper we begin an exploration of these ideas starting from the simplest example of hyperbolic geometry, the hyperbolic plane. The hyperboloid model naturally guides us to re-discover the moduli space Associahedron, and a new version of its kinematical avatar. As a by-product we obtain a solution to the scattering equations which can be interpreted as a special case of the two well known solutions in terms of spinor-helicity formalism. The construction is done in 1 + 2 dimensions and this makes harder to understand how to extract the amplitude from the dlog of the space time Associahedron. Nevertheless, we continue the investigation accommodating a loop momentum in the picture. By doing this we are led to another polytope called Halohedron, which was already known to mathematicians. We argue that the Halohedron fulfils many criteria that make it plausible to be understood as a 1-loop Amplituhedron for the cubic theory. Furthermore, the hyperboloid model again allows to understand that a kinematical version of the Halohedron exists and is related to the one living in moduli space by a simple generalisation of the tree level map. arXiv:1803.05809v1 [hep-th]

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Section: Introductionmentioning

confidence: 99%