<p>We introduce the notion of jets, states of collinear flux-tube excitations. We argue for the analyticity, crossing, and unitarity of the multiparticle scattering of these jets and, through the S-matrix bootstrap, place bounds on a set of finite-energy multiparticle sum rules. Such bounds define a matrioska with a smaller and smaller allowed regions as we impose more constraints. The Yang-Mills flux tube, as well as other interesting flux-tube theories recently studied through lattice simulations, lie inside a tiny island hundreds of times smaller than the most general space of allowed theories.</p>

Canada

Italy

Andrea Guerrieri

Alexandre Homrich

Brazil

Pedro Vieira

Multiparticle Flux-Tube S-matrix Bootstrap

We study the space of 2 → 2 scattering amplitudes of neutral Goldstone bosons in four space-time dimensions. We establish universal bounds on the first two non-universal Wilson coefficients of the low energy Effective Field Theory (EFT) for such particles. We reconstruct the analytic, crossing-symmetric, and unitary amplitudes saturating our bounds, and we study their physical content. We uncover non-perturbative Regge trajectories by continuing our numerical amplitudes to complex spins. We then explore the consequence of additional constraints arising when we impose the knowledge about the EFT up to the cut-off scale. In the process, we improve on some aspects of the numerical S-matrix bootstrap technology for massless particles.

Francesca Acanfora

CERN

Switzerland

Kelian Häring

Denis Karateev

Bounds on scattering of neutral Goldstones

The worldsheet axion plays a crucial role in the dynamics of the Yang-Mills confining flux tubes. According to the lattice measurements, its mass is of order the string tension and its coupling is close to a certain critical value. Using the S-matrix Bootstrap, we construct non-perturbative 2 → 2 branon scattering amplitudes which also feature a weakly coupled axion resonance with these properties. We study the extremal bootstrap amplitudes in detail and show that the axion plays a dominant role in their UV completion in two distinct regimes, in one of which it cannot be considered a parametrically light particle. We conjecture that the actual flux tube amplitudes exhibit a similar behavior.

Israel

Adwait Gaikwad

Victor Gorbenko

QCD worldsheet axion from the bootstrap

We use the S-matrix bootstrap to carve out the space of unitary, analytic, crossing symmetric and supersymmetric graviton scattering amplitudes in nine, ten and eleven dimensions. We extend and improve the numerical methods of our previous work in ten dimensions. A key new tool employed here is unitarity in the celestial sphere. In all dimensions, we find that the minimal allowed value of the Wilson coefficient α, controlling the leading correction to maximal supergravity, is very close but not equal to the minimal value realized in Superstring theory or M-theory. This small difference may be related to inelastic effects that are not well described by our numerical extremal amplitudes. Although α has a unique value in M-theory, we found no evidence of an upper bound on α in 11D.

Harish Murali

Joao Penedones

Where is M-theory in the space of scattering amplitudes?

The main objective of this work is to isolate Effective Field Theory scattering amplitudes in the space of non-perturbative two-to-two amplitudes, using the S-matrix Bootstrap. We do so by introducing the notion of Effective Field Theory cutoff in the S-matrix Bootstrap approach. We introduce a number of novel numerical techniques and improvements both for the primal and the linearized dual approach. We perform a detailed comparison of the full unitarity bounds with those obtained using positivity and linearized unitarity. Moreover, we discuss the notion of Spin-Zero and UV dominance along the boundary of the allowed amplitude space by introducing suitable observables. Finally, we show that this construction also leads to novel bounds on operators of dimension less than or equal to six.

Joan Miró

Mehmet Gümüş

Bridging positivity and S-matrix bootstrap bounds

We consider a dual <math><mi>S</mi></math>-matrix bootstrap approach in <math><mrow><mi>d</mi><mo>≥</mo><mn>3</mn></mrow></math> space-time dimensions which relies solely on the rigorously proven analyticity, crossing, and unitarity properties of the scattering amplitudes. As a proof of principle, we provide rigorous upper and lower numerical bounds on the quartic coupling for the scattering of identical scalar particles in four dimensions.

Amit Sever

Rigorous Bounds on the Analytic <math><mrow><mi>S</mi></mrow></math> Matrix

We develop a bootstrap approach to Effective Field Theories (EFTs) based on the concept of duality in optimisation theory. As a first application, we consider the fascinating set of EFTs for confining flux tubes. The outcome of our analysis are optimal bounds on the scattering amplitude of Goldstone excitations of the flux tube, which in turn translate into bounds on the Wilson coefficients of the EFT action. Finally, we comment on how our approach compares to EFT positivity bounds.

Dual EFT bootstrap: QCD flux tubes

We use the <math><mrow><mi>S</mi></mrow></math>-matrix bootstrap to carve out the space of unitary, crossing symmetric and supersymmetric graviton scattering amplitudes in ten dimensions. We focus on the leading Wilson coefficient <math><mi>α</mi></math> controlling the leading correction to maximal supergravity. The negative region <math><mi>α</mi><mo>&lt;</mo><mn>0</mn></math> is excluded by a simple dual argument based on linearized unitarity (the desert). A whole semi-infinite region <math><mi>α</mi><mo>≳</mo><mn>0.14</mn></math> is allowed by the primal bootstrap (the garden). A finite intermediate region is excluded by nonperturbative unitarity (the swamp). Remarkably, string theory seems to cover all (or at least almost all) the garden from very large positive <math><mi>α</mi></math>—at weak coupling—to the swamp boundary—at strong coupling.

João Penedones

Where Is String Theory in the Space of Scattering Amplitudes?

We use the numerical S-matrix bootstrap method to obtain bounds on the two leading Wilson coefficients (or low energy constants) of the chiral lagrangian controlling the low-energy dynamics of massless pions. This provides a proof of concept that the numerical S-matrix bootstrap can be used to derive non-perturbative bounds on massless EFTs in more than two spacetime dimensions.

S-matrix bootstrap for effective field theories: massless pions

Using duality in optimization theory we formulate a dual approach to the S-matrix bootstrap that provides rigorous bounds to 2D QFT observables as a consequence of unitarity, crossing symmetry and analyticity of the scattering matrix. We then explain how to optimize such bounds numerically, and prove that they provide the same bounds obtained from the usual primal formulation of the S-matrix Bootstrap, at least once convergence is attained from both perspectives. These techniques are then applied to the study of a gapped system with two stable particles of different masses, which serves as a toy model for bootstrapping popular physical systems.