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The ODE/IM Correspondence
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This article reviews a recently-discovered link between integrable quantum field theories and certain ordinary differential equations in the complex domain. Along the way, aspects of PT-symmetric quantum mechanics are discussed, and some elementary features of the six-vertex model and the Bethe ansatz are explained.
Forward citations
Cited by 11 Pith papers
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q-Opers, QQ-Systems, and Bethe Ansatz
Introduces (G,q)-opers and Miura (G,q)-opers, then establishes their bijection with Bethe Ansatz solutions, yielding a qDE/IM correspondence that uses Langlands dual for non-simply-laced cases via the QQ-system.
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Time-Dependent Integrability from Gauge Theory, I
Spacetime-dependent 4d Chern-Simons theory generates time-dependent integrable field theories whose allowed time dependence coincides with one-loop RG flow while preserving Lax integrability.
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The ODE/IM Correspondence between $C(2)^{(2)}$-type Linear Problems and 2d $\mathcal{N}=1$ SCFT
WKB periods of the fully diagonalized C(2)^{(2)} Lax operator coincide with NS-sector local IoM eigenvalues of N=1 SCFT up to sixth order under a fixed parameter dictionary.
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Exact WKB in all sectors II: Potentials with non-degenerate saddles
For generic one-dimensional potentials, the exact spectrum decomposes into as many trans-series sectors as there are distinct local-minimum energy levels, with continuous transitions across barrier tops and discontinu...
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Generalizing quantum dimensions: Symmetry-based classification of local pseudo-Hermitian systems and the corresponding domain walls
Generalized quantum dimensions from SymTFTs classify massless and massive RG flows in pseudo-Hermitian systems and relate coset constructions to domain walls.
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On W-algebras and ODE/IM correspondence
The eigenvalues of quantum KdV-type charges in Virasoro, W3, and W4 algebras are computed from Bethe roots via WKB periods of Catalan curves, verified against direct CFT diagonalization.
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Path integral analysis of Schr\"odinger-type eigenvalue problems in the complex plane: Establishing the relation between instantons and resonant states
Path integrals on complex contours that terminate in prescribed Stokes sectors yield spectral formulas for resonant energies, explaining why the instanton bounce calculation and real-time decay rates agree.
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Integrable Spherical Brane Model at Large $N$
Large-N saddle-point calculation confirms the Lukyanov-Zamolodchikov conjecture for boundary free energy in the spherical brane model to O(1/N) and connects it to the RG running of the coupling g.
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Template masks for 4D-STEM
A template-to-mask correlation imaging method for 4D-STEM is claimed in the abstract, but the supplied full text is an unrelated hep-th paper, leaving the claim unverifiable.
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An Introduction to String Newton-Cartan Holography and Integrability
String Newton-Cartan holography, the non-relativistic limit of the AdS/CFT correspondence, is organized and reviewed around five consistency conditions, with its classical solutions, spectrum, and integrability structure.
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Spectral Networks: Bridging higher-rank Teichm\"uller theory and BPS states
A comprehensive introduction to spectral networks that develops higher-rank Teichmüller theory in parallel with class S gauge theory and BPS spectra.
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