Flux Tube S-matrix Bootstrap

Abstract

We bootstrap the S-matrix of massless particles in unitary, relativistic two dimensional quantum field theories. We find that the low energy expansion of such S-matrices is strongly constrained by the existence of a UV completion. In the context of flux tube physics, this allows us to constrain several terms in the S-matrix low energy expansion or -- equivalently -- on Wilson coefficients of several irrelevant operators showing up in the flux tube effective action. These bounds have direct implications for other physical quantities; for instance, they allow us to further bound the ground state energy as well as the level splitting of degenerate energy levels of large flux tubes. We find that the S-matrices living at the boundary of the allowed space exhibit an intricate pattern of resonances with one sharper resonance whose quantum numbers, mass and width are precisely those of the world-sheet axion proposed in [1,2]. The general method proposed here should be extendable to massless S-matrices in higher dimensions and should lead to new quantitative bounds on irrelevant operators in theories of Goldstones and also in gauge and gravity theories.

arXiv comment7 + 10 pages, 13 figures; v2: Axionic String Ansatz appendix added. New SP bound added. Typos fixed, references added

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• Distributions in CFT II. Minkowski Space
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• QFT, EFT and GFT
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• Classical Integrability of the Zigzag Model
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• Numerical determination of the width and shape of the effective string using Stochastic Normalizing Flows
• $T\bar{T}$ deformation of classical Liouville field theory
• Confining strings in three-dimensional gauge theories beyond the Nambu--Gotō approximation
• Real-Time Scattering in Ising Field Theory using Matrix Product States
• Bootstrapping 2d ${\varphi }^4$ Theory with Hamiltonian Truncation Data
• Ising string beyond Nambu-Goto
• From conformal correlators to analytic S-matrices: CFT${}_1$/QFT${}_2$
• A Celestial Route to AdS Bulk Locality
• Strings from Almost Nothing
• 3D Yang-Mills Glueballs vs Closed Effective Strings
• The finite temperature ground state energy of the confining string in three-dimensional U(1) gauge theory
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• Saturating unitarity bounds at U-duality symmetric points