Scientists / Open questions

Edward Witten

String theory; quantum field theory; mathematical physics

1990 Fields Medal

83 questions

Exact status of the $\beta\leftrightarrow 2\pi\theta/\beta$ duality and isolation of the nonplanar winding sector in noncommutative field theory at finite temperature
Fate of the instanton gas in QCD: quantum disappearance, refinement, or replacement, and the microscopic origin of topological fluctuations in the 1/N expansion
Partially massless fields: nonlinear gauge-invariant completion and viability as interacting physical states
S-duality action on general half-BPS boundary conditions of $\mathcal{N}=4$ super Yang–Mills theory
The inverse twistor transform for ten-dimensional supergravity: what data on the twistor space of supersymmetric light-like lines characterize a supergravity background?
Rigorous construction of the two-dimensional supersymmetric nonlinear sigma model: the loop-space Hamiltonian $H_s$ and the $1/s$ expansion
Scope of mirror symmetry as a gauge symmetry: the Giveon-Witten Calabi-Yau conjecture and the classification of self-mirror N=2 group models
Mn-induced localized states, suppression of the self-activated centre, and the deep hole traps for electroluminescent memory in ZnS:Mn
Witten's two-loop radiative right-handed-neutrino mass in minimal SO(10) grand unification: quantitative viability under unification, flavor, and cosmological constraints
The anomaly-induced R-current mass in the cascading conifold gauge theory: field-theory origin and corrections beyond leading order in the cascade parameter
Asymptotic freedom and the exponentially small confinement scale in the D4-brane string dual of pure Yang-Mills (the small-'t Hooft coupling regime of Witten's 1998 model)
Order of the cosmological QCD confinement transition, stability of strange quark matter, and survival of quark-nugget relics: the open questions of Witten's 'Cosmic separation of phases'
Subleading and α′ corrections to Maldacena–Strominger–Witten black hole entropy: the ground-state momentum shift and the exact entropy of wrapped-M5-brane black strings
Complete fixed-point structure and global renormalization-group flow of the non-abelian Thirring model (the current-current-deformed Wess-Zumino-Witten theory)
Rigorous convergence of the zig-zag (Born-Oppenheimer) expansion underlying the Kachru-Witten computation of massless spectra of Landau-Ginzburg orbifolds
Criteria for conformal invariance of (0,2) heterotic worldsheet theories beyond linear sigma model realizations
Rigorous realization of Witten's sigma-model interpretation of elliptic genera: the loop-space Dirac operator, its fixed-point theorem, and geometric elliptic cohomology
Setting the quantum integrand of M-theory on non-orientable (pin+) spacetimes and general evaluation of the global phases of the effective action
Realizing Witten's 3D supersymmetric string-vacuum scenario: stable three-dimensional vacua, the $\lambda\to\infty$ strong-coupling uplift, and a non-supersymmetric four-dimensional world with zero cosmological constant
Half-integer charge sectors, bundle-moduli components, and untested dualities in M-theory on $(S^1)^5/\mathbb{Z}_2$
Complete classification of non-perturbative global gauge anomalies in four-dimensional chiral gauge theories for arbitrary compact gauge groups and fermion representations
Von Neumann type of the observer algebra and the tracial status of the Hartle-Hawking no-boundary state in background-independent quantum gravity
Exactly marginal ground-ring deformations of the two-dimensional (c=1) string
Extending Witten's direct gauge-theory eigenbrane analysis for 't Hooft operators beyond minuscule weights and regular-semisimple points

Back to open problems

Exact status of the β↔2πθ/β\beta\leftrightarrow 2\pi\theta/\betaβ↔2πθ/β duality and isolation of the nonplanar winding sector in noncommutative field theory at finite temperature

Fate of the instanton gas in QCD: quantum disappearance, refinement, or replacement, and the microscopic origin of topological fluctuations in the 1/N expansion

Partially massless fields: nonlinear gauge-invariant completion and viability as interacting physical states

S-duality action on general half-BPS boundary conditions of N=4\mathcal{N}=4N=4 super Yang–Mills theory

The inverse twistor transform for ten-dimensional supergravity: what data on the twistor space of supersymmetric light-like lines characterize a supergravity background?

Rigorous construction of the two-dimensional supersymmetric nonlinear sigma model: the loop-space Hamiltonian HsH_sHs​ and the 1/s1/s1/s expansion

Scope of mirror symmetry as a gauge symmetry: the Giveon-Witten Calabi-Yau conjecture and the classification of self-mirror N=2 group models

Mn-induced localized states, suppression of the self-activated centre, and the deep hole traps for electroluminescent memory in ZnS:Mn

Witten's two-loop radiative right-handed-neutrino mass in minimal SO(10) grand unification: quantitative viability under unification, flavor, and cosmological constraints

The anomaly-induced R-current mass in the cascading conifold gauge theory: field-theory origin and corrections beyond leading order in the cascade parameter

Asymptotic freedom and the exponentially small confinement scale in the D4-brane string dual of pure Yang-Mills (the small-'t Hooft coupling regime of Witten's 1998 model)

Order of the cosmological QCD confinement transition, stability of strange quark matter, and survival of quark-nugget relics: the open questions of Witten's 'Cosmic separation of phases'

Subleading and α′ corrections to Maldacena–Strominger–Witten black hole entropy: the ground-state momentum shift and the exact entropy of wrapped-M5-brane black strings

Complete fixed-point structure and global renormalization-group flow of the non-abelian Thirring model (the current-current-deformed Wess-Zumino-Witten theory)

Rigorous convergence of the zig-zag (Born-Oppenheimer) expansion underlying the Kachru-Witten computation of massless spectra of Landau-Ginzburg orbifolds

Criteria for conformal invariance of (0,2) heterotic worldsheet theories beyond linear sigma model realizations

Rigorous realization of Witten's sigma-model interpretation of elliptic genera: the loop-space Dirac operator, its fixed-point theorem, and geometric elliptic cohomology

Setting the quantum integrand of M-theory on non-orientable (pin+) spacetimes and general evaluation of the global phases of the effective action

Realizing Witten's 3D supersymmetric string-vacuum scenario: stable three-dimensional vacua, the λ→∞\lambda\to\inftyλ→∞ strong-coupling uplift, and a non-supersymmetric four-dimensional world with zero cosmological constant

Half-integer charge sectors, bundle-moduli components, and untested dualities in M-theory on (S1)5/Z2(S^1)^5/\mathbb{Z}_2(S1)5/Z2​

Complete classification of non-perturbative global gauge anomalies in four-dimensional chiral gauge theories for arbitrary compact gauge groups and fermion representations

Von Neumann type of the observer algebra and the tracial status of the Hartle-Hawking no-boundary state in background-independent quantum gravity

Exactly marginal ground-ring deformations of the two-dimensional (c=1) string

Extending Witten's direct gauge-theory eigenbrane analysis for 't Hooft operators beyond minuscule weights and regular-semisimple points

Exact status of the $\beta\leftrightarrow 2\pi\theta/\beta$ duality and isolation of the nonplanar winding sector in noncommutative field theory at finite temperature

S-duality action on general half-BPS boundary conditions of $\mathcal{N}=4$ super Yang–Mills theory

Rigorous construction of the two-dimensional supersymmetric nonlinear sigma model: the loop-space Hamiltonian $H_s$ and the $1/s$ expansion

Realizing Witten's 3D supersymmetric string-vacuum scenario: stable three-dimensional vacua, the $\lambda\to\infty$ strong-coupling uplift, and a non-supersymmetric four-dimensional world with zero cosmological constant

Half-integer charge sectors, bundle-moduli components, and untested dualities in M-theory on $(S^1)^5/\mathbb{Z}_2$