Scientists / Open questions

David J. Gross

Particle physics; quantum field theory; string theory

2004 Nobel Prize in Physics

22 questions

Exact conductivity of the disordered lowest Landau level: extending the Brézin–Gross–Itzykson supersymmetric solution from the density of states to transport
Virasoro-type constraints and the closed-form genus expansion for real symmetric matrix models in an external field: the unoriented analog of the Kontsevich model
Controlled nonperturbative treatment of dynamical symmetry breaking in asymptotically free field theories: the unresolved remainder of the Gross-Neveu program
Controlled large-p asymptotics of the Ising p-spin spin glass: finite-p corrections to the exactly solved random-energy limit and the fate of its finite-dimensional fluctuation theory
Completing the low-energy theorem for graviton scattering: spin- $\tfrac12$ targets, the quantum status of the $O(p^{2s})$ Born-exactness pattern, and the superconvergence sum rule
Negative transmitted energy flux and the interference energy balance for uniformly heterogeneous waves at absorbing interfaces: finite-beam realizability and experimental verification
Completing the cSYK line of CFTs and its rigid AdS $_2$ dual: subleading $1/N$ finiteness, bulk quartic couplings, and rigorous integral prescriptions
Onset of the asymptotic regime and logarithmic scaling-violation corrections for nucleon elastic form factors via Bloom-Gilman duality in asymptotically free theories
Completing the screening picture of adjoint matter: the all-rank string tension law of 1+1-dimensional adjoint QCD and confinement versus screening in 2+1-dimensional N=1 supersymmetric Yang-Mills
Infrared fate of asymptotically free gauge theories: Yang–Mills existence, mass gap, and confinement of colored states
Nonperturbative completion of ultrahigh-energy string/gravitational scattering: the unitary S-matrix for black-hole formation and evaporation at impact parameters near the gravitational radius, and the microscopic origin of entropy suppression
Fate of classical string backgrounds under the leading α′ correction: non-Kähler Ricci-flat compactifications, gravitational collapse, and the all-orders structure of the higher-curvature corrections (open core of the Gross–Witten 1986 problem)
Non-singlet sectors, vortices, and the non-perturbative completion of the $c=1$ string compactified on a circle
First-principles extraction of the light-quark mass ratio from the isospin-violating decay η′→3π
All-orders large-spin asymptotics of the twist-two anomalous-dimension matrix in Abelian vector-gluon theory and the residual fixed-point loophole in the Callan-Gross no-go theorem for Bjorken scaling
The high-energy symmetry of string theory: construct the symmetry behind Gross's genus-independent $\alpha'\to\infty$ linear relations and determine the $\alpha'\to\infty$ S-matrix
Exact analytic solution of two-dimensional noncommutative Yang-Mills theory on the noncommutative plane
Nonperturbative completion of the double-scaled one-matrix model for two-dimensional quantum gravity: selecting and constructing the physical solution of the string equation
Varying-dilaton extension of the heterotic $A=\bar\omega$ equivalence at quartic order in the string effective action
The classical bulk dual of the SYK model beyond cubic order: quartic and higher couplings, locality, the dilaton sector, and the organizing principle
Engineering realization of the RFOFO ring-based muon ionization cooling channel: realistic fields, window engineering, injection/extraction, bunch-train compatibility, and achievable performance
Off-constraint structure of Wilson-loop minimal surfaces in AdS/CFT: determining $G(z)$ and the prefactor $\Delta$ to test the loop equation for cusped and self-intersecting loops

Back to open problems

Exact conductivity of the disordered lowest Landau level: extending the Brézin–Gross–Itzykson supersymmetric solution from the density of states to transport

Virasoro-type constraints and the closed-form genus expansion for real symmetric matrix models in an external field: the unoriented analog of the Kontsevich model

Controlled nonperturbative treatment of dynamical symmetry breaking in asymptotically free field theories: the unresolved remainder of the Gross-Neveu program

Controlled large-p asymptotics of the Ising p-spin spin glass: finite-p corrections to the exactly solved random-energy limit and the fate of its finite-dimensional fluctuation theory

Completing the low-energy theorem for graviton scattering: spin-12\tfrac1221​ targets, the quantum status of the O(p2s)O(p^{2s})O(p2s) Born-exactness pattern, and the superconvergence sum rule

Negative transmitted energy flux and the interference energy balance for uniformly heterogeneous waves at absorbing interfaces: finite-beam realizability and experimental verification

Completing the cSYK line of CFTs and its rigid AdS2_22​ dual: subleading 1/N1/N1/N finiteness, bulk quartic couplings, and rigorous integral prescriptions

Onset of the asymptotic regime and logarithmic scaling-violation corrections for nucleon elastic form factors via Bloom-Gilman duality in asymptotically free theories

Completing the screening picture of adjoint matter: the all-rank string tension law of 1+1-dimensional adjoint QCD and confinement versus screening in 2+1-dimensional N=1 supersymmetric Yang-Mills

Infrared fate of asymptotically free gauge theories: Yang–Mills existence, mass gap, and confinement of colored states

Nonperturbative completion of ultrahigh-energy string/gravitational scattering: the unitary S-matrix for black-hole formation and evaporation at impact parameters near the gravitational radius, and the microscopic origin of entropy suppression

Fate of classical string backgrounds under the leading α′ correction: non-Kähler Ricci-flat compactifications, gravitational collapse, and the all-orders structure of the higher-curvature corrections (open core of the Gross–Witten 1986 problem)

Non-singlet sectors, vortices, and the non-perturbative completion of the c=1c=1c=1 string compactified on a circle

First-principles extraction of the light-quark mass ratio from the isospin-violating decay η′→3π

All-orders large-spin asymptotics of the twist-two anomalous-dimension matrix in Abelian vector-gluon theory and the residual fixed-point loophole in the Callan-Gross no-go theorem for Bjorken scaling

The high-energy symmetry of string theory: construct the symmetry behind Gross's genus-independent α′→∞\alpha'\to\inftyα′→∞ linear relations and determine the α′→∞\alpha'\to\inftyα′→∞ S-matrix

Exact analytic solution of two-dimensional noncommutative Yang-Mills theory on the noncommutative plane

Nonperturbative completion of the double-scaled one-matrix model for two-dimensional quantum gravity: selecting and constructing the physical solution of the string equation

Varying-dilaton extension of the heterotic A=ωˉA=\bar\omegaA=ωˉ equivalence at quartic order in the string effective action

The classical bulk dual of the SYK model beyond cubic order: quartic and higher couplings, locality, the dilaton sector, and the organizing principle

Engineering realization of the RFOFO ring-based muon ionization cooling channel: realistic fields, window engineering, injection/extraction, bunch-train compatibility, and achievable performance

Off-constraint structure of Wilson-loop minimal surfaces in AdS/CFT: determining G(z)G(z)G(z) and the prefactor Δ\DeltaΔ to test the loop equation for cusped and self-intersecting loops

Completing the low-energy theorem for graviton scattering: spin- $\tfrac12$ targets, the quantum status of the $O(p^{2s})$ Born-exactness pattern, and the superconvergence sum rule

Completing the cSYK line of CFTs and its rigid AdS $_2$ dual: subleading $1/N$ finiteness, bulk quartic couplings, and rigorous integral prescriptions

Non-singlet sectors, vortices, and the non-perturbative completion of the $c=1$ string compactified on a circle

The high-energy symmetry of string theory: construct the symmetry behind Gross's genus-independent $\alpha'\to\infty$ linear relations and determine the $\alpha'\to\infty$ S-matrix

Varying-dilaton extension of the heterotic $A=\bar\omega$ equivalence at quartic order in the string effective action

Off-constraint structure of Wilson-loop minimal surfaces in AdS/CFT: determining $G(z)$ and the prefactor $\Delta$ to test the loop equation for cusped and self-intersecting loops