We consider 3+1 dimensional Quantum Field Theories (QFTs) coupled to the dilaton and the graviton. We show that the graviton-dilaton scattering amplitude receives a universal contribution which is helicity flipping and is proportional to ∆$\textit{c}$ − ∆$\textit{a}$ along any RG flow, where ∆$\textit{c}$ and ∆$\textit{a}$ are the differences of the UV and IR $\textit{c}$- and $\textit{a}$-trace anomalies respectively. This allows us to relate ∆$\textit{c}$ − ∆$\textit{a}$ to spinning massive states in the spectrum of the QFT. We test our predictions in two simple examples: in the theory of a massive free scalar and in the theory of a massive Dirac fermion (a more complicated example is provided in a companion paper [1]). We discuss possible applications.

Switzerland

Denis Karateev

United States

Zohar Komargodski

João Penedones

United Kingdom

Biswajit Sahoo

Trace anomalies and the graviton-dilaton amplitude

We study 2-to-2 scattering amplitudes of massless spin one particles in d = 4 space-time dimensions, like real world photons. We define a set of non-perturbative observables (Wilson coefficients) which describe these amplitudes at low energies. We use full non-linear unitarity to construct various novel numerical bounds on these observables. For completeness, we also rederive some bounds using positivity only. We discover and explain why some of these Wilson coefficients cannot be bounded.

CERN

Kelian Häring

France

Aditya Hebbar

Marco Meineri

Bounds on photon scattering

We perform Monte-Carlo measurements of two and three-point functions of charged operators in the critical O(2) model in 3 dimensions. Our results are compatible with the predictions of the large charge superfluid effective field theory. To obtain reliable measurements for large values of the charge, we improved the Worm algorithm and devised a measurement scheme which mitigates the uncertainties due to lattice and finite size effects.

Gabriel Cuomo

Portugal

J.M.Viana Lopes

José Matos

Júlio Oliveira

Numerical tests of the large charge expansion

We study two-point functions of symmetric traceless local operators in the bulk of de Sitter spacetime. We derive the Källén-Lehmann spectral decomposition for any spin and show that unitarity implies its spectral densities are nonnegative. In addition, we recover the Källén-Lehmann decomposition in Minkowski space by taking the flat space limit. Using harmonic analysis and the Wick rotation to Euclidean Anti de Sitter, we derive an inversion formula to compute the spectral densities. Using the inversion formula, we relate the analytic structure of the spectral densities to the late-time boundary operator content. We apply our technical tools to study two-point functions of composite operators in free and weakly coupled theories. In the weakly coupled case, we show how the Källén-Lehmann decomposition is useful to find the anomalous dimensions of the late-time boundary operators. We also derive the Källén-Lehmann representation of two-point functions of spinning primary operators of a Conformal Field Theory on de Sitter.

Manuel Loparco

Netherlands

Kamran Salehi Vaziri

Zimo Sun

The Källén-Lehmann representation in de Sitter spacetime

We merge together recent developments in the S-matrix bootstrap program to develop a dual setup in 2 space-time dimensions incorporating scattering amplitudes of massive particles and matrix elements of local operators. In particular, the stress energy tensor allows us to input UV constraints on IR observables in terms of the central charge c UV of the UV Conformal Field Theory. We consider two applications: (1) We establish a rigorous lower bound on c UV of a class of ℤ 2 symmetric scalar theories in the IR (including ϕ 4); (2) We target Ising Field Theory by, first, minimizing c UV for different values of the magnetic field and, secondly, by determining the allowed range of cubic coupling and one-particle form-factor for fixed c UV = 1/2 and magnetic field.

Miguel Correia

Antoine Vuignier

Injecting the UV into the bootstrap: Ising Field Theory

We study gapped 4d quantum field theories (QFTs) obtained from a relevant deformation of a UV conformal field theory (CFT). For simplicity, we assume the existence of a ℤ2 symmetry and a single ℤ2-odd stable particle and no ℤ2-even particles at low energies. Using unitarity, crossing and the assumption of maximal analyticity we compute numerically a lower bound on the value of the a-anomaly of the UV CFT as a function of various non-perturbative parameters describing the two-to-two scattering amplitude of the particle.

Jan Marucha

Bootstrapping the a-anomaly in 4d QFTs

We review unitarity and crossing constraints on scattering amplitudes for particles with spin in four dimensional quantum field theories. As an application we study two to two scattering of neutral spin 1/2 fermions in detail. Assuming Mandelstam analyticity of its scattering amplitude, we use the numerical S-matrix bootstrap method to estimate various non-perturbative bounds on quartic and cubic (Yukawa) couplings.

Spinning S-matrix bootstrap in 4d

The boundary correlation functions for a Quantum Field Theory (QFT) in an Anti-de Sitter (AdS) background can stay conformally covariant even if the bulk theory undergoes a renormalization group (RG) flow. Studying such correlation functions with the numerical conformal bootstrap leads to non-perturbative constraints that must hold along the entire flow. In this paper we carry out this analysis for the sine-Gordon RG flows in AdS2, which start with a free (compact) scalar in the UV and end with well-known massive integrable theories that saturate many S-matrix bootstrap bounds. We numerically analyze the correlation functions of both breathers and kinks and provide a detailed comparison with perturbation theory near the UV fixed point. Our bounds are often saturated to one or two orders in perturbation theory, as well as in the flat-space limit, but not necessarily in between.

António Antunes

Miguel Costa

Aaditya Salgarkar

Balt Rees

Towards bootstrapping RG flows: sine-Gordon in AdS

We study the phase diagram of 5-dimensional SU(2) Yang-Mills theory on the lattice. We consider two extensions of the fundamental plaquette Wilson action in the search for the continuous phase transition suggested by the 4 + ϵ expansion. The extensions correspond to new terms in the action: i) a unit size plaquette in the adjoint representation or ii) a two-unit sided square plaquette in the fundamental representation. We use Monte Carlo to sample the first and second derivative of the entropy near the confinement phase transition, with lattices up to 125. While we exclude the presence of a second order phase transition in the parameter space we sampled for model i), our data is not conclusive in some regions of the parameter space of model ii).

Adrien Florio

João Lopes

Searching for continuous phase transitions in 5D SU(2) lattice gauge theory

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.

Brazil

Andrea Guerrieri

Pedro Vieira

Where Is String Theory in the Space of Scattering Amplitudes?