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A note on the S-matrix bootstrap for the 2d O(N) bosonic model · Around

2018

A note on the S-matrix bootstrap for the 2d O(N) bosonic model

He, Yifei, Irrgang, Andrew, Kruczenski, Martin

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In this work we apply the S-matrix bootstrap maximization program to the 2d bosonic O(N) integrable model which has N species of scalar particles of mass m and no bound states.

Since in previous studies theories were defined by maximizing the coupling between particles and their bound states, the main problem appears to be to find what other functional can be used to define this model.
Instead, we argue that the defining property of this integrable model is that it resides at a vertex of the convex space determined by the unitarity and crossing constraints.
Thus, the integrable model can be found by maximizing any linear functional whose gradient points in the general direction of the vertex, namely within a cone determined by the normals to the faces intersecting at the vertex.

Built on

L. Castillejo, R. H. Dalitz and F. J. Dyson, “Low’s scattering equation for the charged and neutral scalar theories,” Phys. Rev. 101
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R. J. Eden, P. V. Landshoff, D. I. Olive, J. C. Polkinghorne, “The Analytic S-Matrix”, Cambridge University Press, 1966, G. F. Chew, “The Analytic S Matrix: A Basis for Nuclear Democracy”, W. A. Benjamin, 1966
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A.M. Polyakov, Phys. Lett.. B 59
1975
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Similar

A. B. Zamolodchikov and A. B. Zamolodchikov, “Relativistic factorized S-matrix in two-dimensions having O ⁡ ( N ) O(N) isotopic symmetry,” Nucl. Phys. B133
1979
Cited alongside, same era.
Michael Grant and Stephen Boyd, “CVX: Matlab software for disciplined convex programming”, version 2.0 beta. http://cvxr.com/cvx , September 2013, Michael Grant and Stephen Boyd, “Graph implementations for nonsmooth convex programs”, Recent Advances in Learning and Control (a tribute to M. Vidyasagar), V. Blondel, S. Boyd, and H. Kimura, editors, pages 95-110, Lecture Notes in Control and Information Sciences, Springer, 2008. http://stanford.edu/~boyd/graph_dcp.html
2008
Cited alongside, same era.
N. I. Muskhelishvili, “Singular Integral Equations: Boundary Problems of Function Theory and Their Application to Mathematical Physics”, Dover Publications Inc., 2008
2008
Cited alongside, same era.
M. F. Paulos, J. Penedones, J. Toledo, B. C. van Rees and P. Vieira, “The S-matrix Bootstrap III: Higher Dimensional Amplitudes,” arXiv:1708.06765 [hep-th]
Original
Cited in the paper.
N. Doroud and J. E. Miró, “S-matrix bootstrap for resonances,” arXiv:1804.04376 [hep-th]
Original
Cited in the paper.
L. Córdova and P. Vieira, “Adding flavour to the S-matrix bootstrap,” arXiv:1805.11143 [hep-th]
Original
Cited in the paper.
M. F. Paulos and Z. Zheng, “Bounding scattering of charged particles in 1+1 dimensions,” arXiv:1805.11429 [hep-th]
Original
Cited in the paper.

Then

M. F. Paulos, J. Penedones, J. Toledo, B. C. van Rees and P. Vieira, “The S-matrix bootstrap. Part I: QFT in AdS,” JHEP 1711
Original
2017
Later among the works it cites.
M. F. Paulos, J. Penedones, J. Toledo, B. C. van Rees and P. Vieira, “The S-matrix bootstrap II: two dimensional amplitudes,” JHEP 1711
Original
2017
Later among the works it cites.

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