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Extremal Effective Field Theories
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Effective field theories (EFT) parameterize the long-distance effects of short-distance dynamics whose details may or may not be known. It is known that EFT coefficients must obey certain positivity constraints if causality and unitarity are satisfied at all scales. We explore those constraints from the perspective of 2 to 2 scattering amplitudes of a light real scalar field, using semi-definite programming to carve out the space of allowed EFT coefficients for a given mass threshold M. We point out that all EFT parameters are bounded both below and above, effectively showing that dimensional analysis scaling is a consequence of causality. This includes the coefficients of four- and six-derivative interactions. We present simple extremal amplitudes which realize, or "rule in", kinks in coefficient space and whose convex hull span a large fraction of the allowed space.
Forward citations
Cited by 23 Pith papers
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The open string Veneziano amplitude emerges as the unique tree-level completion of N=4 super Yang-Mills when supersymmetry, factorization, and positivity are imposed.
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A covariant Higgs mechanism turns the partially massless graviton into a fully massive spin-2 field by condensing a fractonic matter field with dipole symmetry.
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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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Supersymmetry, Supergravity and the Consistency of On-Shell Massive Superamplitudes
Consistent scattering amplitudes force a massless spin-3/2 particle to be the gravitino of a supergravity theory, and constrain massive BPS vector couplings to form a Lie algebra.
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Analytic Boundaries of Infinite-Spin-Tower Amplitudes from Hidden Zero
The exact analytic boundary of unitary infinite-spin-tower amplitudes is derived and shown to be maximal unless energy poles accumulate.
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Unitary Dual-Resonance S-matrices
Smearing Veneziano blocks over continuous Regge slopes yields local, analytic, crossing-symmetric S-matrices with full partial-wave unitarity and controllable second-sheet resonances.
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Gravitational Effective Theories with Maximal Supersymmetry and a Peculiar Parity
Peculiar parity plus N=8 SUSY, tree-level factorization, and finitely many states at the mass gap uniquely select the Virasoro–Shapiro amplitude among weakly-coupled UV completions of N=8 supergravity.
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Bootstrapping black holes at low impact parameter
After subtracting the eikonal carrier, the residual SDR spectrum in six dimensions organizes into a cap-saturated low-impact band, an empty gap, and Regge-like ridges whose weak-coupling edge is the G_N=0 baseline.
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Propagator positivity bounds for cosmological correlators
An infinite tower of two-sided positivity bounds constrains the EFT coefficients of heavy fields on de Sitter, ruling out correlators with no unitary/causal UV completion.
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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 tricritical Ising CFT and conformal bootstrap
First conformal-bootstrap islands for the tricritical Ising CFT in d=2.5 and d=2.75, consistent with Padé interpolations between the 3−ε expansion and the exact 2d minimal model.
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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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Running EFT-hedron with null constraints at loop level
One-loop massless corrections modify the null constraints of shift-symmetric scalar EFTs, and IR-finite combinations of them reproduce tree-level bounds in the weak-coupling limit while deforming bounds in five and si...
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Towards the HEFT-hedron: the complete set of positivity constraints at NLO
Complete positivity constraints from causality and unitarity are derived for the 15 NLO HEFT operators contributing to longitudinal gauge-Higgs scattering, shrinking the allowed space to about 5 percent.
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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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Bootstrapping $\mathcal{N} = 4$ sYM correlators using Integrability and Localization
Two-sided bounds on the Konishi OPE coefficient in planar N=4 sYM are derived at finite 't Hooft coupling by adding localization constraints to an integrability-based dispersive bootstrap.
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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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Light scalars in light of UV/IR mixing: classicalization via synergy between Vainshtein and chameleon screenings
Classicalizing k-essence scalars need m << Λ* and, when potentials or fermion couplings are present, a chameleon-like screening layer to keep Vainshtein screening and classicalon stability intact.
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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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