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Cornering Large-$N_c$ QCD with Positivity Bounds
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abstract
The simple analytic structure of meson scattering amplitudes in the large-$N_c$ limit, combined with positivity of the spectral density, provides precise predictions on low-energy observables. Building upon previous studies, we explore the allowed regions of chiral Lagrangian parameters and meson couplings to pions. We reveal a structure of kinks at all orders in the chiral expansion and develop analytical tools to show that kinks always correspond to amplitudes with a single light pole. We build (scalar- and vector-less) deformations of the Lovelace-Shapiro and Coon UV-complete amplitudes, and show that they lie close to the boundaries. Moreover, constraints from crossing-symmetry imply that meson couplings to pions become smaller as their spin increases, providing an explanation for the success of Vector Meson Dominance and holographic QCD. We study how these conclusions depend on assumptions about the high-energy behavior of amplitudes. Finally, we emphasize the complementarity between our results and Lattice computations in the exploration of large-$N_c$ QCD.
Forward citations
Cited by 14 Pith papers
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(Super)$\,$Gravity from Positivity
Positivity of scattering amplitudes forces weakly coupled EFTs of a massive spin-3/2 particle to include gravity, and for charged states a gauged photon with g=2 and WGC-saturating charge.
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Partial Waves for Multipositivity
The paper constructs kinematic charts and partial-wave expansions for four-, five-, and six-point massless planar amplitudes tailored to multipositivity bounds.
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Geometry of effective field theory positivity cones
For three particle flavors, the positivity cone C_W has exactly three families of extremal rays, one of which yields genuinely new inelastic constraints not implied by elastic bounds.
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Strings from Almost Nothing
Ultrasoft, minimally structured scattering amplitudes are forced onto the Veneziano and Virasoro-Shapiro amplitudes of string theory.
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Splitting Regions and Shrinking Islands from Higher Point Constraints
Imposing 5-point split conditions and unitarity bounds selects the string beta function as the unique 4-point amplitude, up to equal-mass infinite spin towers.
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The EFT Bootstrap at Finite $M_{PL}$
One-loop gravity effects make forward-limit positivity bounds ill-defined for massless scalar-gravity EFTs, forcing non-forward dispersion relations that shift the tree-level bounds by order-one factors.
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Bootstrapping Extremal Scalar Amplitudes With and Without Supersymmetry
The full space of allowed four-point scalar amplitudes is conjectured to be the convex hull of a single scalar amplitude and a one-parameter family of extremal theories, generatable from maximally supersymmetric amplitudes.
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Matrix moment approach to positivity bounds and UV reconstruction from IR
Positivity bounds for multi-field EFTs are formulated as matrix moment problems, yielding optimal bounds and a method to reverse engineer the UV mass, spin, and coupling spectrum from low-energy coefficients.
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Worldsheet for Generalized Veneziano Amplitudes
A chiral composite linear dilaton worldsheet action reproduces Mandelstam's generalized Veneziano amplitudes and yields new partially crossing-symmetric higher-point and closed-string amplitudes.
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The Rise of Linear Trajectories
Numerical S-matrix bootstrap shows that maximized couplings of the second and third higher-spin resonances select spectra lying on a linear Regge trajectory, anchored by the graviton in gravitational theories.
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Dark Photons and Gravitino Like Particles: Complete EFT Operator Basis
A new on-shell method using Young tableaux constructs complete EFT operator bases for massive particles of any spin, applied to dark photons and spin-3/2 gravitino-like particles up to dimension 8.
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Analytic bootstrap bounds on masses and spins in gravitational and non-gravitational scalar theories
The authors derive 'Sequential Spin and Mass Constraints' for su-symmetric and stu-symmetric four-point amplitudes, claiming any weakly-coupled spectrum must have ordered spins and bounded mass ratios.
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Bootstrapping Gravity with Crossing Symmetric Dispersion Relations
A crossing-symmetric dispersion-relation bootstrap reproduces known gravitational EFT bounds and gives new tree-level limits on the graviton coupling to a massive spin-4 state.
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Causality bounds from charged shockwaves in 5d
Causality on 5d charged shockwaves gives positivity bounds on four-derivative Einstein-Maxwell couplings, with gravity weakening the pure-field-theory bounds and near-horizon photons providing the strongest constraints.
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