Bootstrapping pions at large N

Abstract

We revisit from a modern bootstrap perspective the longstanding problem of solving QCD in the large N limit. We derive universal bounds on the effective field theory of massless pions by imposing the full set of positivity constraints that follow from 2 → 2 scattering. Some features of our exclusion plots have intriguing connections with hadronic phenomenology. The exclusion boundary exhibits a sharp kink, raising the tantalizing scenario that large N QCD may sit at this kink. We critically examine this possibility, developing in the process a partial analytic understanding of the geometry of the bounds.

Flattening of the EFT-hedron: supersymmetric positivity bounds and the search for string theory

“…The A IST -amplitude tends to show up as an allowed solution in S-matrix bootstrap analyses [3,7]. However, it has an unsuppressed infinite tower of higher spin states, all with the same mass, so it is not expected to arise from a physical theory even though it is not explicitly forbidden by our assumptions.…”

“…they involve two different pairs of conjugate scalars, not just one. 7 We thank Enrico Hermann for suggesting this example.…”

“…IBM [20]. SDPB has previously been used for positivity bounds, see for example [3,4,7,9], but to our knowledge this is the first time CPLEX is used in the context of the S-matrix bootstrap. The main purpose of using both methods is to have non-trivial checks on, and comparisons of, the numerical results.…”

“…Consider one-loop contributions from BPS states on the Coulomb branch as an example of a UV completion [32][33][34]. 7 We start with N = 4 SYM with a SU(N ′ ) gauge group and go onto the Coulomb branch such that the gauge symmetry is broken to SU(N ) × SU(N ′′ ) with N ′ = N + N ′′ . We restrict the external states to be massless states transforming in the adjoint of the SU(N ) sector.…”

“…These basic high-energy assumptions facilitate a dispersive representation of the Wilson coefficients which implies that they must lie in a convex region sometimes called the "EFT-hedron" [2]. The allowed region of Wilson coefficients has been explored recently for theories of massless particles, including for scalars [2][3][4], massless pions [5][6][7][8][9][10], photons [11][12][13][14][15], and gravitons [16,17].…”