Research Methods
Research methods earn evidential force only inside a declared domain. This directory compares what each method takes as input, what it computes, how uncertainty enters, and which cross-checks can expose a failure. It is a routing page, not a universal ranking of techniques.
Evidence cutoff. Method assessments include sources and implementations available through 11 August 2026. Software-specific performance and benchmark records can change sooner than the underlying formalism.
Match the method to the inferential task
Section titled “Match the method to the inferential task”| Method map | Best suited to | Principal limitation to inspect first |
|---|---|---|
| Multiloop amplitudes, resummation, and precision prediction | infrared-safe scattering observables with perturbative scale separation | truncation, scale choices, nonperturbative corrections, and observable definition |
| EFT inference, power counting, and truncation | separating short-distance coefficients from controlled low-energy expansions | validity range, basis assumptions, coefficient priors, and correlated truncation error |
| Functional equations and functional renormalization group | continuum nonperturbative propagators, vertices, and phase structure | closure and regulator dependence after hierarchy truncation |
| Euclidean lattice fields and continuum extrapolation | equilibrium and Euclidean observables with a controlled regulator | continuum, volume, mass, sampling, and real-time reconstruction errors |
| Hamiltonian truncation, tensor networks, and quantum simulation | spectra and dynamics where Hilbert-space structure can be exploited | truncation, entanglement growth, device noise, and continuum matching |
| Analytic and numerical conformal bootstrap | consequences of symmetry, unitarity, and crossing for CFT data | finite derivative/spin truncations and assumptions used to isolate a solution |
| Semiclassics, resurgence, and transseries | weak-coupling saddles, nonperturbative sectors, and large-order structure | saddle completeness, Stokes data, and continuation to the target regime |
| Schwinger–Keldysh, kinetic theory, and hydrodynamics | real-time response and controlled long-wavelength evolution | closure, quasiparticle or gradient assumptions, and initialization |
| Replica, modular, and operator-algebra methods | entanglement, relative entropy, and localization questions | analytic continuation, domain issues, and regulator-sensitive factorization |
| Holographic reconstruction and gravitational path integrals | large-, strongly coupled sectors with a semiclassical bulk regime | dictionary assumptions, saddle selection, and corrections beyond the code subspace |
Read across methods, not just down one column
Section titled “Read across methods, not just down one column”A strong comparison fixes a common observable before comparing answers. Methods that nominally address “the same problem” may instead compute a Euclidean proxy, an asymptotic coefficient, a finite-volume spectrum, or a coarse-grained constitutive parameter. Those quantities should not be merged until the map between them is explicit.
For each method, separate at least four error classes:
- input uncertainty: measured parameters, ensembles, initial states, priors, or matching coefficients;
- controlled approximation: perturbative order, lattice spacing, volume, derivative order, bond dimension, or bootstrap truncation;
- structural assumption: unitarity, locality, quasiparticles, saddle dominance, a gap, a code subspace, or a closure ansatz;
- implementation error: solver tolerance, autocorrelation, conditioning, code defects, or insufficient numerical precision.
Agreement is most discriminating when the methods do not share the assumption under test. For example, two lattice analyses with different actions may still share scale-setting inputs; two bootstrap studies may use the same block tables and gap assumptions; two phenomenological fits may inherit the same experimental covariance. The individual maps make those dependencies explicit.
What a benchmark can and cannot show
Section titled “What a benchmark can and cannot show”A benchmark should have an independently known or overdetermined answer, exercise the claimed hard step, and be held out from tuning when possible. Reproducing a benchmark supports the computational chain in that regime. It does not by itself validate extrapolation to stronger coupling, longer times, larger volumes, or a different observable class.
Use the frontier dossiers to see which discriminants matter for a scientific question and the evidence briefs to inspect concrete source comparisons. The field guides show how these methods combine within research programs.