UV/EFT Correspondence

Updated 1 January 2026

UV/EFT Correspondence is a framework connecting high-energy ultraviolet physics of heavy states with infrared effective field theories through analytic, diagrammatic, and geometric methods.
It employs dispersion relations, algorithmic matching prescriptions, and diagrammatic techniques to extract Wilson coefficients and structure low-energy operator expansions.
The approach underpins phenomenological analyses in collider, gravitational, and cosmological contexts by providing model-independent constraints and robust positivity bounds.

The UV/EFT correspondence is a set of principles and technical methodologies that link the ultraviolet (UV) physics of heavy massive states to the infrared (IR) predictions and structures of effective field theory (EFT), often using analyticity, unitarity, and symmetry to constrain or compute the EFT data accessible at low energies. Key developments range from algorithmic matching prescriptions for EFT Wilson coefficients, dispersion-based positivity and geometric bounds, and explicit diagrammatic and amplitude-based techniques relating UV completions to the towers of higher-dimensional operators in the EFT. These tools have enabled systematic exploration and interpretation of collider, gravitational, and cosmological data via model-independent parameterizations.

1. Analytic Structure and Dispersion Methods for UV/EFT Matching

The correspondence exploits the analytic properties of the UV theory's scattering amplitudes under complex momentum dilations to directly compute EFT Wilson coefficients (Angelis et al., 2023). Given any $n$ -point UV amplitude $A_n(p_1,\dots,p_n)$ , one introduces a complex scaling $p_i\to\sqrt{z}\,p_i$ so that all Mandelstam invariants scale as $s_I\to z\,s_I$ . The amplitude $A_n(z)$ is analytic except for simple poles (heavy propagators), branch cuts (UV loop thresholds), and potential singularities at $z=0,\infty$ .

A one-variable Cauchy integral

$A_n(0)=\frac{1}{2\pi i}\oint_{|z|=\epsilon}\frac{dz}{z}A_n(z)$

with contour deformed to include all singularities, expresses the low-energy limit as a sum over residues (tree-level propagators) and discontinuities (loop-level cuts): \begin{align*} A_n^{\rm EFT}(0)&=\sum_{\text{poles}} \mathrm{Res}{z=z_i}\frac{A_n(z)}{z}+\int{\text{cuts}} \frac{dz}{2\pi i}\frac{\mathrm{Disc}\, A_n(z)}{z}-\mathrm{Res}_{z=\infty}\frac{A_n(z)}{z} \end{align*} This approach—originally applied to scalar models—systematically generates the local EFT contact terms at tree and loop level, matching the 1/M-expansion without any explicit IR subtractions in dimensional regularization. All matching information is contained in the UV amplitude's analytic structure: tree-level poles correspond to integrating out heavy states, and loop cuts to unitarity cuts reconstructing loop-induced Wilson coefficients. No separate calculation on the EFT side is required (Angelis et al., 2023).

2. Functional, Diagrammatic, and Algorithmic Strategies

Algorithmic approaches to the correspondence include both functional and diagrammatic matching. In one-loop functional matching, the effective action is computed via supertraces over quadratic fluctuations of the heavy and light fields, organizing the result via the covariant derivative expansion (CDE) (Cohen et al., 2020, Cohen et al., 2020). Enumerating all closed loops of heavy propagators with interaction insertions yields the full tower of EFT operators, with the resulting Wilson coefficients manifestly expressed as functions of UV masses and couplings.

The diagrammatic approach systematizes the selection of heavy field quantum numbers and minimal topologies necessary to generate specific EFT operators, particularly in the SMEFT context (Bakshi et al., 2021). By categorizing SMEFT operators into schematic classes and exhaustively listing renormalizable, gauge-invariant vertices, one reads off directly the possible representations required of any UV resonance generating a given operator. This method naturally separates minimal from non-minimal completions and informs model construction.

Automated packages such as STrEAM implement symbolic evaluation of supertraces for arbitrary UV models and masses, and match2fit connects tree- and one-loop matching outputs with global fits to experimental data (Cohen et al., 2020, Hoeve et al., 2023). These tools facilitate large-scale scans of UV parameter space and make the correspondence practical for phenomenology.

3. Geometric and Amplitude-Based UV/EFT Dictionaries

The UV/EFT correspondence is also illuminated by geometric perspectives and amplitude-based dictionaries. The second derivatives of forward EFT amplitudes form a convex cone in Wilson coefficient space, whose extremal rays directly encode irreducible UV multiplets (Zhang et al., 2020). Each extremal ray corresponds to a physical scenario in which all UV particles live in one irreducible representation, and the complete set of facet inequalities (beyond simple positivity) generically yields stronger bounds on operator coefficients.

Amplitude-based techniques, as in the j-basis/UV correspondence, classify all possible UV completions of a given operator by constructing local partial-wave amplitudes labeled by spin and gauge quantum numbers in a chosen channel (Li et al., 2022). Each j-basis block arises only from a heavy state with matching quantum numbers. By diagonalizing Casimir operators, one systematically lists all possible UV origins at tree level for SMEFT operators up to dimension 8.

4. Physical Interpretation: RG Flows, Symmetries, and Universality

In nonrelativistic finite-range theories, hidden symmetries of the S-matrix (such as momentum-scale inversion p→1/(a^2p)) become geometric symmetries of the EFT renormalization-group flow, manifesting as reflections or inversions in coupling space (Beane et al., 2021). UV/IR symmetry breaking in the scattering amplitude forces unique constraints on RG flows and tie effective-range and higher-derivative operators to the leading-order coupling. This equivalence realizes a concrete UV/EFT correspondence between full scattering operator symmetries and the geometric structure of EFT RG trajectories.

5. Positivity Constraints and Phenomenological Impact

Analyticity and unitarity enforce dispersion relation bounds on EFT Wilson coefficients—positivity, convexity, and geometric inequalities—which are calculable from the UV amplitude's discontinuities (Melville, 31 Dec 2025, Zhang et al., 2020, Chen et al., 2024). For example, twice-subtracted fixed-t dispersion relations yield inequalities such as $c_{20}\ge 0$ , with $c_{20}$ the coefficient of the $(\partial\phi)^4$ operator. Implementing such bounds universally constrains dark-energy, gravitational, and gauge-EFT parameter spaces: most naïvely acceptable phenomenological regions may be inconsistent with any causal, unitary UV completion.

In gravitational EFTs, the signs and magnitudes of marginal mode corrections in extremal black-hole horizons are directly related to the UV values of EFT four-derivative Wilson coefficients and must respect not only flat-space amplitude positivity but also stronger near-horizon constraints associated with the tower of marginal perturbations (Chen et al., 2024).

6. Bottom-Up and Top-Down Model Building: SMEFT Dictionaries

The correspondence underpins both bottom-up mappings (enumerating possible UV completions for observed EFT structures) and top-down pipelines (matching explicit heavy-particle models to EFT operator towers). Cross-dimension dictionaries enumerate all possible tree- and loop-level UV resonances generating dimension-5,6,7,8 SMEFT operators, prescribing a direct route from experimental data to candidate UV sectors (Li et al., 2023, Guedes et al., 2024, Li et al., 2022). Openness to both approaches enables rapid recasting of fits, reverse engineering of UV scenarios from operator patterns, and systematic checking of IR-induced constraints on new physics.

7. Classical-Quantum Correspondence and Well-Posedness

The correspondence remains valid both at quantum and classical levels: integrating out massive fields yields well-posed EFT equations for the light modes, and rigorous approximation theorems guarantee that classical solutions of the UV theory remain close to those of the truncated EFT within the admissible class (Reall et al., 2021). For generic initial data, averaged or modified EFTs reproduce the UV theory in coarse-grained observables, matching the underlying physics.

In summary, the UV/EFT correspondence comprises a multi-faceted body of principles, technical methods, and algorithmic pipelines transforming the connection between UV physics and IR EFT descriptions into a systematic field blending analytic, geometric, amplitude-based, and computational approaches, directly impacting model building, phenomenology, and the interpretation of experimental data across particle, gravitational, and cosmological domains (Angelis et al., 2023, Zhang et al., 2020, Bakshi et al., 2021, Li et al., 2022, Guedes et al., 2024, Li et al., 2023, Hoeve et al., 2023, Melville, 31 Dec 2025, Chen et al., 2024).