Journal
JOURNAL OF HIGH ENERGY PHYSICS
Volume -, Issue 4, Pages -Publisher
SPRINGER
DOI: 10.1007/JHEP04(2020)142
Keywords
Field Theories in Lower Dimensions; Integrable Field Theories; Nonperturbative Effects; Scattering Amplitudes
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Funding
- DOE [DE-SC0007884, DE-SC0019202]
- Keck Foundation
- Simons Foundation (Simons Collaboration on the Non-perturbative Bootstrap)
- INFN
- Government of Canada through NSERC
- Province of Ontario through MRI
- Simons Foundation [488661]
- FAPESP [2016/01343-7, 2017/03303-1]
- Fundacao de Amparo a Pesquisa do Estado de Sao Paulo (FAPESP) [16/01343-7] Funding Source: FAPESP
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We consider the scattering matrices of massive quantum field theories with no bound states and a global O(N) symmetry in two spacetime dimensions. In particular we explore the space of two-to-two S-matrices of particles of mass m transforming in the vector representation as restricted by the general conditions of unitarity, crossing, analyticity and O(N) symmetry. We found a rich structure in that space by using convex maximization and in particular its convex dual minimization problem. At the boundary of the allowed space special geometric points such as vertices were found to correspond to integrable models. The dual convex minimization problem provides a novel and useful approach to the problem allowing, for example, to prove that generically the S-matrices so obtained saturate unitarity and, in some cases, that they are at vertices of the allowed space.
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