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Extremal Effective Field Theories
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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 29 Pith papers
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Positivity in Massive Spin-3/2 EFTs and the Planck-Suppressed Neighbourhood of Supergravity
Massive spin-3/2 EFT contact couplings are constrained by positivity to a Planck-suppressed neighborhood of supergravity values whose volume scales as m^6/M_Pl^6 and vanishes as m approaches zero.
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String Theory from Maximal Supersymmetry
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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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 eikonal subtraction, finite-grid SDR bootstrap extremal spectra support a cap-saturated black-hole-scale band and Regge-like ridge while leaving the intervening gap mostly empty.
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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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Bootstrapping Pion Form Factors at Large $N$
Bootstrap analysis of meromorphic observables in large-N QCD yields universal and SVZ-type bounds that constrain chiral Lagrangian parameters and link hadronic data to asymptotic freedom.
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Thermal Positivity
Lorentz invariance and unitarity imply strictly positive low-temperature interaction corrections of the form T^{2D-4+4k} (k>0) to the pressure in perturbative massless boson theories.
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Analytic Bootstrap of the Veneziano Amplitude
The Veneziano amplitude is the unique solution to a dual bootstrap from dispersive sum rules interpreted as moments, unitarity, and string monodromy or splitting conditions.
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Analytic Bootstrap of the Veneziano Amplitude
The Veneziano amplitude is the unique outcome of an analytic dual bootstrap from dispersive sum rules, unitarity, and either string monodromy or splitting and hidden-zero conditions.
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Consistent Scattering Amplitudes, Yang-Mills, the Higgs Mechanism and the EFTs Beyond
S-matrix consistency forces the complete gluon amplitude structure and requires Yang-Mills Lie algebra plus Higgs mechanism for unitarised massive vector boson scattering.
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Full positivity bounds for anomalous quartic gauge couplings in SMEFT
Complete positivity bounds for the 22 aQGC coefficients in SMEFT restrict the viable parameter space to approximately 0.0313% of the naive total.
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Negative running of gravitational positivity
Non-minimal three-point interactions induce negative one-loop running of Wilson coefficients in gravitational EFTs, yet graviton loops generate positive IR contributions that dominate the bounds after smearing if the ...
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String Theory from Maximal Supersymmetry
Supersymmetry, R-symmetry, and positivity constrain planar 4d EFTs to match the open string Veneziano amplitude at tree level.
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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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Positivity with Long-Range Interactions
Defines IR-finite amplitudes M_E that preserve analyticity and unitarity to derive positivity bounds on EFTs including electromagnetism and gravity in D=4.
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Primal S-matrix bootstrap with dispersion relations
A primal S-matrix bootstrap framework parameterizes imaginary parts of partial waves, uses dispersion relations to enforce consistency, computes coupling bounds, and handles Regge behavior plus spinning states like glueballs.
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An Ultraviolet Finite Theory of Scalars
A ghost-free polynomially bounded scalar theory with momentum-dependent interactions that cancels all loop divergences to all orders, with finite one-loop self-energy and beta function computed, plus a variant with ze...
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A Dispersive Bootstrap for the Virasoro-Shapiro Amplitude
Dispersive bootstrap with unitarity, crossing and a Virasoro-inspired ansatz isolates the Virasoro-Shapiro amplitude in a small island for the gravity-pole-subtracted four-point amplitude in 10D supersymmetry.
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Where is tree-level heterotic string theory?
Bootstrap constraints on 10D half-maximal supergravity and SYM show gravitational boundaries dominated by single linear Regge trajectory amplitudes, with representation positivity tensions obstructing direct gauge-gra...
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Multipositivity Constrains the Chiral Lagrangian
Multipositivity bounds derived from planar tree-level scattering amplitudes constrain Wilson coefficients of the chiral Lagrangian from below by the chiral anomaly.
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The Equivalence Principle at High Energies Completes the Spectrum
Tree-level gravitational scattering under the equivalence principle mandates single-particle states in all irreducible representations constructible from a single seed charge, with equal interaction strengths.
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Positivity in Massive Spin-3/2 EFTs and the Planck-Suppressed Neighbourhood of Supergravity
Positivity bounds on massive spin-3/2 four-fermion operators restrict the couplings to a bounded region around supergravity values whose volume scales as m^6/M_Pl^6 and vanishes as m approaches zero.
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Sampling the Graviton Pole and Deprojecting the Swampland
A sampling-based bootstrap for graviton poles in EFTs yields non-projective bounds that fix the EFT cutoff scale relative to the Planck mass, with M/M_P ≲ 7.8 in D=5.
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Completeness from Gravitational Scattering
Symmetry plus perturbative gravitational scattering consistency requires the abelian charge lattice to be completely populated by single-particle states for SU(N) with N≥3 and SO(N) with N≥5.
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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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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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IR side of bounds on Theories with Spontaneously Broken Lorentz Symmetry
The analysis shows that analyticity bounds in Lorentz-broken theories require gapped excitations to propagate slower than gapless ones at low momenta relative to the mass gap.
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