Adding flavour to the S-matrix bootstrap

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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. arXiv:1909.06495v2 [hep-th]

Section: The Monolith and Slatementioning

confidence: 99%

Section: C3 the σ 2 = 0 Linementioning

confidence: 99%

Section: C3 the σ 2 = 0 Linementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

The O(N) S-matrix monolith

Córdova

Kruczenski

et al. 2020

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A study of quantum field theories in AdS at finite coupling

Carmi

Pietro

Komatsu

2019

104

191

We study the O(N ) and Gross-Neveu models at large N on AdS d+1 background.Thanks to the isometries of AdS, the observables in these theories are constrained by the SO(d, 2) conformal group even in the presence of mass deformations, as was discussed by Callan and Wilczek [1], and provide an interesting two-parameter family of quantities which interpolate between the S-matrices in flat space and the correlators in CFT with a boundary. For the actual computation, we judiciously use the spectral representation to resum loop diagrams in the bulk. After the resummation, the AdS 4-particle scattering amplitude is given in terms of a single unknown function of the spectral parameter. We then "bootstrap" the unknown function by requiring the absence of double-trace operators in the boundary OPE. Our results are at leading nontrivial order in 1 N , and include the full dependence on the quartic coupling, the mass parameters, and the AdS radius. In the bosonic O(N ) model we study both the massive phase and the symmetry-breaking phase, which exists even in AdS 2 evading Coleman's theorem, and identify the AdS analogue of a resonance in flat space. We then propose that symmetry breaking in AdS implies the existence of a conformal manifold in the boundary conformal theory. We also provide evidence for the existence of a critical point with bulk conformal symmetry, matching existing results and finding new ones for the conformal boundary conditions of the critical theories. For the Gross-Neveu model we find a bound state, which interpolates between the familiar bound state in flat space and the displacement operator at the critical point.

Thermodynamic Bethe Ansatz past turning points: the (elliptic) sinh-Gordon model

Córdova

Negro

Massolo

2022

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We analyze the Thermodynamic Bethe Ansatz (TBA) for various integrable S-matrices in the context of generalized T$$ \overline{\mathrm{T}} $$ T ¯ deformations. We focus on the sinh-Gordon model and its elliptic deformation in both its fermionic and bosonic realizations. We confirm that the determining factor for a turning point in the TBA, interpreted as a finite Hagedorn temperature, is the difference between the number of bound states and resonances in the theory. Implementing the numerical pseudo-arclength continuation method, we are able to follow the solutions to the TBA equations past the turning point all the way to the ultraviolet regime. We find that for any number k of resonances the pair of complex conjugate solutions below the turning point is such that the effective central charge is minimized. As k → ∞ the UV effective central charge goes to zero as in the elliptic sinh-Gordon model. Finally we uncover a new family of UV complete integrable theories defined by the bosonic counterparts of the S-matrices describing the Φ1,3 integrable deformation of non-unitary minimal models $$ \mathcal{M} $$ M 2,2n+3.