Scientists / Open questions

Edward Witten

String theory; quantum field theory; mathematical physics

1990 Fields Medal

83 questions

Completing the heterotic/F-theory bundle-moduli dictionary: a global model for the $\mathcal{W}_{E_8}$ geometry and unconditional intermediate-Jacobian identification
Quantum consistency of three-dimensional conformal gravity as an SO(3,2) Chern-Simons gauge theory: admissible levels, global gauge sectors, and finiteness
Completing the quantization of Chern-Simons gauge theory with complex gauge group: a fully defined unitary TQFT, the associated two-dimensional conformal field theory, and the Hilbert space of $2+1$ -dimensional gravity with positive cosmological constant
D-brane charges in non-torsion Neveu-Schwarz H-flux: the physical classification of conserved Ramond-Ramond charge
Quantum Higgs vacua and the conformal field theory of the Higgs branch in two-dimensional (4,4) supersymmetric NS5-brane gauge theories
Timelike Tube Theorem Beyond Real-Analytic Spacetimes: Unique Continuation for the Klein-Gordon Equation with Smooth Real Coefficients
Completing the topological-field-theory encoding of discrete flux in the AdS/CFT correspondence: modular weights, the topology-general Chern-Simons invariant, bulk fillings, quantization phases, and the six-dimensional conformal-block Hilbert space
Quantum consistency and superconformality of the Gaiotto–Witten three-dimensional $\mathcal{N}=4$ Chern–Simons–matter theories, and completion of their supergroup classification
Sufficiency and necessity of the Silverstein–Witten off-shell conformal-invariance criteria for two-dimensional (0,2) supersymmetric Lagrangian models
Non-abelian quantum field theories on an algebraic curve: explicit multiplicative Ward identities and uniqueness of the expectation-value functional
A rigorous, a priori construction of finite-level quantum Chern–Simons theory from the three-dimensional path integral
Cutoff removal and truncation-order dependence in background-independent open string field theory from local world-sheet boundary interactions
First-principles completion of the mock-modular holomorphic anomaly of Vafa-Witten theory: ultraviolet normalization, auxiliary-term ambiguities, and extensions to other topologies, twists, and ranks
Instanton-generated multi-fermion F-terms in supersymmetric QCD: the general SU( $N_c$ ) instanton evaluation, their cohomological classification, and criteria for which N=1 theories admit them
A (3+1)-dimensional analog of Witten's (2+1)-dimensional mechanism: unbroken vacuum supersymmetry, a naturally vanishing cosmological constant, and non-degenerate boson and fermion masses
Global structure and physical content of the Longo-Witten deformed boundary quantum field theory nets: relation to Lechner's factorizing-scattering models, minimal regularity, covariance, and global classification
Exact Ricci-flat metrics, normalized Yukawa couplings, CP structure, and vacuum selection in Calabi–Yau superstring compactification: the surviving open core of the Strominger–Witten (1985) program
Microscopic foundations of the Omega-deformation brane picture: exact cigar-tip couplings, higher-rank coisotropic A-branes, and the Hilbert-space structures of the gauge/Liouville correspondence
The unbroken-phase program of "Space-Time and Topological Orbifolds": combining chiral topological sigma-model sectors, the mass-shell condition, and complex saddles with independent left/right moduli
Unresolved issues in worldsheet-instanton-generated multi-fermion F-terms of heterotic (0,2) compactifications (Beasley–Witten)
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)
Extending Witten's rigorous QCD inter-flavor meson mass inequality beyond the pseudoscalar channel and to annihilation-affected flavor-singlet sectors
Exact string-theoretic fate of the two-dimensional Lorentzian black hole: is the logarithmic tachyon divergence at the $uv=1$ singularity a genuine instability of the exact $\mathrm{SL}(2,\mathbb{R})_k/\mathrm{U}(1)$ coset conformal field theory?
Large-N theta-dependence of the vacuum energy of four-dimensional pure SU(N) Yang-Mills theory: multibranched structure, the cusp at theta = pi, and the domain-wall/decay structure in the genuine asymptotically free theory

Back to open problems

Completing the heterotic/F-theory bundle-moduli dictionary: a global model for the WE8\mathcal{W}_{E_8}WE8​​ geometry and unconditional intermediate-Jacobian identification

Quantum consistency of three-dimensional conformal gravity as an SO(3,2) Chern-Simons gauge theory: admissible levels, global gauge sectors, and finiteness

Completing the quantization of Chern-Simons gauge theory with complex gauge group: a fully defined unitary TQFT, the associated two-dimensional conformal field theory, and the Hilbert space of 2+12+12+1-dimensional gravity with positive cosmological constant

D-brane charges in non-torsion Neveu-Schwarz H-flux: the physical classification of conserved Ramond-Ramond charge

Quantum Higgs vacua and the conformal field theory of the Higgs branch in two-dimensional (4,4) supersymmetric NS5-brane gauge theories

Timelike Tube Theorem Beyond Real-Analytic Spacetimes: Unique Continuation for the Klein-Gordon Equation with Smooth Real Coefficients

Completing the topological-field-theory encoding of discrete flux in the AdS/CFT correspondence: modular weights, the topology-general Chern-Simons invariant, bulk fillings, quantization phases, and the six-dimensional conformal-block Hilbert space

Quantum consistency and superconformality of the Gaiotto–Witten three-dimensional N=4\mathcal{N}=4N=4 Chern–Simons–matter theories, and completion of their supergroup classification

Sufficiency and necessity of the Silverstein–Witten off-shell conformal-invariance criteria for two-dimensional (0,2) supersymmetric Lagrangian models

Non-abelian quantum field theories on an algebraic curve: explicit multiplicative Ward identities and uniqueness of the expectation-value functional

A rigorous, a priori construction of finite-level quantum Chern–Simons theory from the three-dimensional path integral

Cutoff removal and truncation-order dependence in background-independent open string field theory from local world-sheet boundary interactions

First-principles completion of the mock-modular holomorphic anomaly of Vafa-Witten theory: ultraviolet normalization, auxiliary-term ambiguities, and extensions to other topologies, twists, and ranks

Instanton-generated multi-fermion F-terms in supersymmetric QCD: the general SU(NcN_cNc​) instanton evaluation, their cohomological classification, and criteria for which N=1 theories admit them

A (3+1)-dimensional analog of Witten's (2+1)-dimensional mechanism: unbroken vacuum supersymmetry, a naturally vanishing cosmological constant, and non-degenerate boson and fermion masses

Global structure and physical content of the Longo-Witten deformed boundary quantum field theory nets: relation to Lechner's factorizing-scattering models, minimal regularity, covariance, and global classification

Exact Ricci-flat metrics, normalized Yukawa couplings, CP structure, and vacuum selection in Calabi–Yau superstring compactification: the surviving open core of the Strominger–Witten (1985) program

Microscopic foundations of the Omega-deformation brane picture: exact cigar-tip couplings, higher-rank coisotropic A-branes, and the Hilbert-space structures of the gauge/Liouville correspondence

The unbroken-phase program of "Space-Time and Topological Orbifolds": combining chiral topological sigma-model sectors, the mass-shell condition, and complex saddles with independent left/right moduli

Unresolved issues in worldsheet-instanton-generated multi-fermion F-terms of heterotic (0,2) compactifications (Beasley–Witten)

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)

Extending Witten's rigorous QCD inter-flavor meson mass inequality beyond the pseudoscalar channel and to annihilation-affected flavor-singlet sectors

Exact string-theoretic fate of the two-dimensional Lorentzian black hole: is the logarithmic tachyon divergence at the uv=1uv=1uv=1 singularity a genuine instability of the exact SL(2,R)k/U(1)\mathrm{SL}(2,\mathbb{R})_k/\mathrm{U}(1)SL(2,R)k​/U(1) coset conformal field theory?

Large-N theta-dependence of the vacuum energy of four-dimensional pure SU(N) Yang-Mills theory: multibranched structure, the cusp at theta = pi, and the domain-wall/decay structure in the genuine asymptotically free theory

Completing the heterotic/F-theory bundle-moduli dictionary: a global model for the $\mathcal{W}_{E_8}$ geometry and unconditional intermediate-Jacobian identification

Completing the quantization of Chern-Simons gauge theory with complex gauge group: a fully defined unitary TQFT, the associated two-dimensional conformal field theory, and the Hilbert space of $2+1$ -dimensional gravity with positive cosmological constant

Quantum consistency and superconformality of the Gaiotto–Witten three-dimensional $\mathcal{N}=4$ Chern–Simons–matter theories, and completion of their supergroup classification

Instanton-generated multi-fermion F-terms in supersymmetric QCD: the general SU( $N_c$ ) instanton evaluation, their cohomological classification, and criteria for which N=1 theories admit them

Exact string-theoretic fate of the two-dimensional Lorentzian black hole: is the logarithmic tachyon divergence at the $uv=1$ singularity a genuine instability of the exact $\mathrm{SL}(2,\mathbb{R})_k/\mathrm{U}(1)$ coset conformal field theory?