Bootstrapping Massive Quantum Field Theories

Abstract

We propose a new non-perturbative method for studying UV complete unitary quantum field theories (QFTs) with a mass gap in general number of spacetime dimensions. The method relies on unitarity formulated as positive semi-definiteness of the matrix of inner products between asymptotic states (in and out) and states created by the action of local operators on the vacuum. The corresponding matrix elements involve scattering amplitudes, form factors and spectral densities of local operators. We test this method in two-dimensional QFTs by setting up a linear optimization problem that gives a lower bound on the central charge of the UV CFT associated to a QFT with a given mass spectrum of stable particles (and couplings between them). Some of our numerical bounds are saturated by known form factors in integrable theories like the sine-Gordon, E8 and O(N) models.

57 pages, 12 figures. In v3 typos corrected, references added

References in corpus (10)

• The Conformal Bootstrap: Theory, Numerical Techniques, and Applications
• Bootstrapping QCD: the Lake, the Peninsula and the Kink
• Lorentzian CFT 3-point functions in momentum space
• Flux Tube S-matrix Bootstrap
• Momentum-space conformal blocks on the light cone
• The S-matrix Bootstrap IV: Multiple Amplitudes
• Adding flavour to the S-matrix bootstrap
• The O(N) S-matrix Monolith
• A note on the S-matrix bootstrap for the 2d O(N) bosonic model
• Hadronic decays of a light Higgs-like scalar

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• Nonperturbative Bounds on Scattering of Massive Scalar Particles in $d\ge 2$
• Swampland Conditions for Higher Derivative Couplings from CFT
• EFT Asymptotics: the Growth of Operator Degeneracy
• Bootstrapping the $a$-anomaly in $4d$ QFTs
• Thermodynamic Bethe Ansatz past turning points: the (elliptic) sinh-Gordon model
• Bounds on photon scattering
• The R-matrix bootstrap for the 2d O(N) bosonic model with a boundary
• Renormalization group flows in AdS and the bootstrap program
• Towards a nonperturbative construction of the $S$-matrix
• Real-Time Scattering in Ising Field Theory using Matrix Product States
• Bootstrapping 2d ${\varphi }^4$ Theory with Hamiltonian Truncation Data
• Bootstrapping gauge theories
• Lectures in Quantum Gravity
• From conformal correlators to analytic S-matrices: CFT${}_1$/QFT${}_2$
• Strings from Almost Nothing
• RG flows in de Sitter: c-functions and sum rules
• Bootstrapping leading hadronic muon anomaly
• A Large-$N$ Expansion for Minimum Bias