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.
Highlights
One can define a quantum field theory (QFT) non-perturbatively as a renormalization group (RG) flow from the UV to the IR fixed point
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 conformal field theories (CFTs) associated to a QFT with a given mass spectrum of stable particles
In this paper we have extended the S-matrix bootstrap program to include states created by local operators
Summary
One can define a quantum field theory (QFT) non-perturbatively as a renormalization group (RG) flow from the UV to the IR fixed point. In these cases, one has to resort to numerical methods (like lattice field theory, Hamiltonian truncation, tensor networks, etc) that require a UV cutoff and a costly extrapolation to the continuum limit. We can write the central charge c of the UV CFT as an integral over the spectral density of the trace of the stress tensor This allows to address the following question: what is the minimal central charge of a UV CFT that can give rise to a massive QFT with a given set of masses and couplings of stable particles?. We derive various auxiliary results in appendices A, B and C
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
