Frontier Questions

What remains unresolved in quantum field theory, and what would count as an answer? These pages explain a specific open question, compare established results and competing proposals, and identify the calculation, observation, or proof needed to make progress.

Evidence cutoff. The assessments below include sources available through 11 August 2026. Each page states the scope and assumptions behind its conclusions.

Questions by subject

Scattering, amplitudes, and precision EFT

• Infrared-complete scattering observables asks which inclusive, dressed, memory-sector, or detector-level quantities remain finite and operational in theories with massless gauge fields.
• The domain of color–kinematics duality and double copy separates demonstrated tree-level relations from loop, classical, curved-background, and nonperturbative conjectures.
• SMEFT validity and truncation in global fits asks when power counting, event scales, correlations, and a remainder model make a truncated inference trustworthy.
• Electroweak vacuum stability distinguishes the conditional Standard Model metastability calculation from claims about cosmology or ultraviolet completion.

Gauge theory and finite-density matter

• Confinement with dynamical matter asks what replaces a Wilson-loop area law when fundamental matter screens center charge.
• Controlled regimes of finite-density QCD maps the low-density, small-chemical-potential, and asymptotic regimes against the uncontrolled intermediate-density gap.
• The four-dimensional Yang–Mills mass gap separates continuum-extrapolated numerical evidence from the open theorem-level existence-and-gap problem.
• The QCD critical point assesses whether lattice singularity searches and heavy-ion fluctuation measurements establish or exclude an endpoint.

Conformal theories, dualities, and reconstruction

• Reconstructing non-Lagrangian QFTs asks when geometry, anomalies, protected sectors, defects, and bootstrap data uniquely determine a full theory.
• Non-supersymmetric dualities in three dimensions distinguishes exact anomaly, phase, and topological checks from conjectural equality of interacting fixed points.
• From crossing solutions to actual CFTs asks what existence and reconstruction input must supplement crossing, unitarity, and numerical islands.
• Certification in the numerical conformal bootstrap distinguishes reproducible solver output from an end-to-end certificate that also controls conformal-block approximations.

Real-time dynamics, quantum matter, and information

• Real-time continuum dynamics from regulated computations compares the observable classes accessible to finite volume, analytic continuation, tensor networks, truncation, and quantum simulation.
• The predictive domain of hydrodynamic attractors asks when an attractor improves on ordinary hydrodynamics for a specified moment, norm, and flow.
• The order of deconfined quantum critical transitions tests continuous fixed-point, walking, and weak-first-order accounts of Néel–VBS and related transitions.
• What Planckian dissipation means separates an observable-specific scaling pattern from a universal relaxation bound or microscopic mechanism.
• Operational entanglement in continuum QFT identifies which algebraic and separated-region quantities remain finite and operational when sharp-region entropy does not.
• Complexity in continuum QFT asks whether task, reference, gate set, cost, tolerance, and regulator can yield a non-arbitrary interacting continuum quantity.

Curved spacetime, black holes, and holography

• Robustness and backreaction in Hawking radiation separates robust low-energy mode conversion from a self-consistent four-dimensional evaporation history.
• Hypotheses of the generalized second law identifies the horizon-algebra, renormalization, coupling, and gravitational assumptions under which monotonicity is proved.
• Islands and unitary black-hole evaporation asks what a Page curve establishes beyond its semiclassical replica, factorization, and microscopic-completion assumptions.
• Bulk reconstruction beyond semiclassical code subspaces asks for finite-$N$, finite-coupling error control across changing geometries and state sets.

Mathematical definition and construction

• Interacting constructive QFT in four dimensions compares scalar triviality theorems and gauge-theory partial constructions with the full cutoff-free existence standard.
• Equivalence of axiomatic QFT frameworks maps the exact hypotheses for OS/Wightman, field/net, locally covariant, perturbative, and factorization-algebra comparisons.

Choosing an approach

Use Research Methods to compare techniques and their limitations, and Evidence Briefs to examine specific source comparisons. The field guides place these questions within broader research programs. Each question page links to the background and methods relevant to its scope.