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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7 Pith papers cite this work, alongside 278 external citations. Polarity classification is still indexing.
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abstract
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.
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Exact WKB analysis produces median-summed spectra and an algebraic equation for the exceptional point of PT-symmetry breaking in the inverted triple-well system.
Generalized quantum dimensions from SymTFTs classify massless and massive RG flows in pseudo-Hermitian systems and relate coset constructions to domain walls.
Derives TBA equations for the higher-order Mathieu equation of the SU(r+1) quantum Seiberg-Witten curve, obtains an analytic effective central charge from Y-function boundary conditions at theta to -infinity, and verifies subleading analytic plus higher-order numerical agreement with WKB expansions.
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.
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.
A comprehensive introduction to spectral networks that develops higher-rank Teichmüller theory in parallel with class S gauge theory and BPS spectra.
citing papers explorer
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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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Exact WKB analysis of inverted triple-well: resonance, PT-symmetry breaking, and resurgence
Exact WKB analysis produces median-summed spectra and an algebraic equation for the exceptional point of PT-symmetry breaking in the inverted triple-well system.
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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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TBA equations for $SU(r+1)$ quantum Seiberg-Witten curve: higher-order Mathieu equation
Derives TBA equations for the higher-order Mathieu equation of the SU(r+1) quantum Seiberg-Witten curve, obtains an analytic effective central charge from Y-function boundary conditions at theta to -infinity, and verifies subleading analytic plus higher-order numerical agreement with WKB expansions.
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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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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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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.