New tools to constrain EFTs and CFTs

Abstract

In this thesis, we develop new methods for the S matrix bootstrap in the context of 2-2 scattering amplitudes and four-point correlators in conformal field theories (CFTs).

For 2-2 scattering in quantum field theories, we consider manifestly three-channel crossing symmetric dispersion relation (CSDR), unlike the two-channel symmetric fixed-t dispersion relation. We give simple derivations of certain known positivity conditions for effective field theories, including the null constraints, which lead to two-sided bounds and derive a general set of new nonperturbative inequalities. We derive the analyticity domain of the CSDR analogously to the Lehmann-Martin ellipse. We present a fascinating correspondence between an area of mathematics called geometric function theory (GFT) and the scattering amplitudes focusing on the case with O(N) global symmetry. We obtain two-sided bounds on Wilson coefficients of physical Pion amplitudes via positivity and GFT.

Then we consider Bell correlations in light-by-light (LbyL) scattering at low energies. The known contributions in the Standard Model (SM) lead to Bell violation at all scattering angles except for a small transverse region, leading to a fine-tuning problem. Incorporating a light axion/axion-like particle (ALP) removes this problem and constrains the axion-coupling--axion-mass parameter space.

In the second part of the thesis, we consider CSDR for Mellin amplitudes of scalar four-point correlators in conformal field theories. This allows us to rigorously set up the nonperturbative Polyakov bootstrap for the conformal field theories in Mellin space, fixing the contact term ambiguities in previous work. Our framework allows us to connect with the conceptually rich picture of the Polyakov blocks being identified with Witten diagrams in anti-de Sitter space. We also give two-sided bounds for Wilson coefficients for effective field theories in anti-de Sitter space. The derivation of the Polyakov bootstrap allows rigorous epsilon expansion solely from bootstrap principles.