S-matrix bootstrap for effective field theories: massless pions

Self Cite

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.

Section: Introductionmentioning

confidence: 99%

Dual EFT bootstrap: QCD flux tubes

Miró

Guerrieri

2021

Self Cite

“…Transforming this expansion term-by term to the original coordinates x i we find the convergent expansion (with convergence understood in the same sense as in the previous section 30 )…”

Section: Os Reflection Positivitymentioning

confidence: 90%

Distributions in CFT. Part II. Minkowski space

Kravchuk

Qiao

Rychkov

2021

CFTs in Euclidean signature satisfy well-accepted rules, such as the convergent Euclidean OPE. It is nowadays common to assume that CFT correlators exist and have various properties also in Lorentzian signature. Some of these properties may represent extra assumptions, and it is an open question if they hold for familiar statistical-physics CFTs such as the critical 3d Ising model. Here we consider Wightman 4-point functions of scalar primaries in Lorentzian signature. We derive a minimal set of their properties solely from the Euclidean unitary CFT axioms, without using extra assumptions. We establish all Wightman axioms (temperedness, spectral property, local commutativity, clustering), Lorentzian conformal invariance, and distributional convergence of the s-channel Lorentzian OPE. This is done constructively, by analytically continuing the 4-point functions using the s-channel OPE expansion in the radial cross-ratios ρ, $$ \overline{\rho} $$ ρ ¯ . We prove a key fact that |ρ|, $$ \left|\overline{\rho}\right| $$ ρ ¯ < 1 inside the forward tube, and set bounds on how fast |ρ|, $$ \left|\overline{\rho}\right| $$ ρ ¯ may tend to 1 when approaching the Minkowski space.We also provide a guide to the axiomatic QFT literature for the modern CFT audience. We review the Wightman and Osterwalder-Schrader (OS) axioms for Lorentzian and Euclidean QFTs, and the celebrated OS theorem connecting them. We also review a classic result of Mack about the distributional OPE convergence. Some of the classic arguments turn out useful in our setup. Others fall short of our needs due to Lorentzian assumptions (Mack) or unverifiable Euclidean assumptions (OS theorem).

“…Although we do not assume any particular identity for the particles or form of the interaction, it is useful to describe this process in the language of pion scattering because it is a very well-studied example. This type of system has already been studied with the S-matrix bootstrap in [5,16,17,21,22]. In this paper we concentrate on the formulation of the dual problem.…”

Section: Physical Problem As a Primal Problem In Conic Optimizationmentioning

confidence: 99%

“…For the 3 + 1 dimensional case considered here, besides the previously mentioned references, the most relevant ones are [16,17] where the S-matrix bootstrap is applied to pion dynamics as originally envisioned [1,2]. Various other ideas have been discussed in the context of the S-matrix bootstrap and similar methods applied to gapped theories [18][19][20][21][22][23][24][25][26][27][28][29][30][31].…”

Section: Introductionmentioning

confidence: 99%

S-matrix bootstrap in 3+1 dimensions: regularization and dual convex problem

Kruczenski

2021

The S-matrix bootstrap maps out the space of S-matrices allowed by analyticity, crossing, unitarity, and other constraints. For the 2 → 2 scattering matrix S2→2 such space is an infinite dimensional convex space whose boundary can be determined by maximizing linear functionals. On the boundary interesting theories can be found, many times at vertices of the space. Here we consider 3 + 1 dimensional theories and focus on the equivalent dual convex minimization problem that provides strict upper bounds for the regularized primal problem and has interesting practical and physical advantages over the primal problem. Its variables are dual partial waves kℓ(s) that are free variables, namely they do not have to obey any crossing, unitarity or other constraints. Nevertheless they are directly related to the partial waves fℓ(s), for which all crossing, unitarity and symmetry properties result from the minimization. Numerically, it requires only a few dual partial waves, much as one wants to possibly match experimental results. We consider the case of scalar fields which is related to pion physics.