36 problems

Gukov–Sułkowski dual quantum curve conjecture
arXiv@arxiv
Consider curves with $y=\log z$ of the form … where $P_1$ and $P_2$ are coprime polynomials. Let $\psi^{\vee}(z;b)$ be the dual wavefunction, and write $\hat{x}^{\vee}=y\cdot$ and…
Conjectureopenknot-theory mirror-symmetry quantum-curves
0
Topological recursion/quantum curve correspondence
arXiv@arxiv
Let $\mathcal{S}$ be an admissible spectral curve with $x,y$ satisfying … A quantisation of $P$ is an operator $\hat{P}(\hat{x},\hat{y};\hbar)$ of the form … where…
Conjectureopenquantum-curves spectral-curves topological-recursion
0
Grassi–Hatsuda–Mariño spectral determinant conjecture
arXiv@arxiv
Let $\rho$ be the operator whose Fredholm determinant is denoted by $\Xi(\kappa)$ , with $\kappa$ identified with a complex modulus of the mirror curve. Let $\mu$ satisfy the corres…
Conjectureopenquantum-curves spectral-theory topological-strings
2
Bergère–Eynard determinantal reconstruction conjecture for topological-recursion correlators
arXiv@arxiv
Bergère–Eynard determinantal reconstruction conjecture. These correlators are equal to the correlators $\tilde{W}_n$ generated by topological recursion. This determinantal formula…
Conjecturesolvedquantum-curves topological-recursion
0
Quantum-curve mirror correspondence for Sp(N) gauge theories
arXiv@arxiv
Let a 5d $\mathcal{N}=1$ theory with gauge group $\mathrm{Sp}(N)$ have quantum curve Hamiltonians with eigenvalues $H_j$ , and let $z_i$ denote the B-model complex structure paramet…
Conjectureopengauge-theory mirror-symmetry quantum-curves
0
Trace-class conjecture for quantum mirror-curve operators
arXiv@arxiv
Trace-class conjecture. The operator $\widehat{\mathcal O}^{-1}$ is trace class; equivalently, $\operatorname{tr}\widehat{\mathcal O}^{-n}$ is finite for every $n=1,2,\ldots$ . This…
Conjectureopenquantum-curves spectral-theory topological-strings
0
Theta-divisor description of the twisted spectral determinant
arXiv@arxiv
Let $\Delta$ satisfy the condition referred to as, let $F$ be integrally tempered, let $\bm{\mathcal{M}}$ be the relevant moduli space, let $\bm{\nu}(\bm{\mathcal{M}})$ be the imag…
Conjectureopennormal-functions quantum-curves theta-divisors
1
Quantum mirror map and spectral determinant conjecture
arXiv@arxiv
Let $X$ be a noncompact toric Calabi–Yau threefold with mirror curve $\mathcal{C}$ , generalized spectral determinant $\Xi_{\mathcal{C}}(\underline{a};\hbar)$ , quantum mirror map…
Conjectureopenenumerative-geometry mirror-symmetry quantum-curves
1
The quantum-curve conjecture for peacock patterns
arXiv@arxiv
A peacock pattern is a resurgent structure involving infinitely many integer Stokes constants. A quantum curve is the quantum-geometric structure underlying a theory based on a qua…
Conjectureopenquantum-curves resurgence topological-string-theory
0
Dequantization conjecture for quantum spectral curves
arXiv@arxiv
Let ${\mathcal W}$ be a point of the Sato Grassmannian with wave function $\Psi$ and quantum spectral curve operator ${\mathtt P}_{\mathcal W}$ , so that … For a tau-function with a…
Conjecturesolvedintegrable-systems quantum-curves
0
Canonical determination conjecture for quantum-curve partition functions
arXiv@arxiv
Consider the non-perturbatively defined partition functions associated with the quantum curves studied in the paper, together with exact WKB and topological recursion. Canonical de…
Conjectureopenexact-wkb quantum-curves topological-recursion
0
Finite Laurent-series conjecture for the quantized Seiberg–Witten geometry
arXiv@arxiv
Finite Laurent-series conjecture. $T$ is a finite Laurent series in $e^M$ ; equivalently, the number $i$ of parameters $\{e_i^{\epsilon_1,\epsilon_2}\}$ is finite.
Conjectureopenquantum-curves seiberg-witten-geometry
0
The quantum-curve conjecture for Baker–Akhiezer functions of KP reductions
arXiv@arxiv
Quantum-curve conjecture.
Conjectureopengromov-witten-theory integrable-systems quantum-curves
0
Existence of quantum curves for topological recursion spectral curves
arXiv@arxiv
A spectral curve is the input of topological recursion, whose output defines a wave function through its WKB asymptotic expansion. Quantum-curve conjecture. Every such spectral cur…
Conjectureopenquantum-curves spectral-curves topological-recursion
0
Independence of the Hamiltonian spectrum and eigenvectors from the auxiliary parameter
arXiv@arxiv
Let $\zeta$ be the auxiliary parameter appearing in the construction of the wavefunction $\Psi(x)$ , and let the admissible values of $\sigma$ determine the corresponding Hamiltonia…
Conjectureopenquantum-curves spectral-theory
1
Infinitely sheeted spectrum conjecture for quantum mirror curves
arXiv@arxiv
The mass parameters of a quantum mirror curve may be complex, and the exact solution of the associated spectral problem depends logarithmically on these parameters. Infinitely shee…
Conjectureopenquantum-curves spectral-theory topological-strings
0
Exponential formula for reconstructing the wave function by topological recursion
arXiv@arxiv
Exponential formula. The solution should have the WKB expansion
Conjectureopenintegrable-systems quantum-curves topological-recursion
1
Weierstrass quantum-curve conjecture
arXiv@arxiv
Consider the Weierstrass spectral curve … Let $\hat{P}(\hat{x},\hat{y};\hbar)$ be a quantum curve of the form … where the $A_i(x)$ and $B_j(x)$ are polynomials in $x$ . A Weierstras…
Conjectureopenelliptic-curves quantum-curves topological-recursion
0
Borot–Eynard conjecture that the non-perturbative partition function is a tau-function
arXiv@arxiv
Let the non-perturbative partition function be the partition function constructed from the non-perturbative topological recursion formalism for an algebraic spectral curve. A tau-f…
Conjectureopenquantum-curves tau-functions topological-recursion
0
The topological-recursion conjecture for constructing quantum curves
arXiv@arxiv
Topological-recursion conjecture. In all the situations mentioned in the paper, quantum curves can be constructed by means of the topological recursion; in many cases they can also…
Conjectureopenmatrix-models quantum-curves topological-recursion
0
Grand-potential formula for the quantum mirror-curve wavefunction
arXiv@arxiv
Let $\psi(x;\kappa)$ be the wavefunction associated to the quantum mirror curve, let $X$ be the corresponding open-string coordinate, and let $\mathsf{J}_\sigma(\mu,\hbar,X)$ denot…
Conjectureopenquantum-curves topological-strings wavefunctions
0
All-orders open topological-string wavefunction conjecture
arXiv@arxiv
Consider the first saddle point of the canonical transformation from the quantum-mechanical variables to the large-radius open coordinates. Its leading term agrees with the Abelian…
Conjectureopenquantum-curves topological-strings wavefunctions
1
Exact Fredholm determinant conjecture for quantum mirror curves
arXiv@arxiv
Let a toric Calabi–Yau manifold have a mirror curve of genus $g_\Sigma$ , and let the quantized mirror curve define $g_\Sigma$ trace-class operators on $L^2(\mathbb{R})$ . Their gene…
Conjectureopenquantum-curves spectral-theory topological-strings
0
The topological-recursion reconstruction conjecture for quantum curves
arXiv@arxiv
Topological-recursion reconstruction conjecture. The topological recursion reconstructs the WKB asymptotic solution of quantum curves.
Conjectureopenquantum-curves topological-recursion wkb-analysis
1
The quantum mirror-curve conjecture for open topological string partition functions
arXiv@arxiv
Let $X$ be a toric geometry, and consider its open topological string partition function in the Nekrasov–Shatashvili limit. Let ${\cal O}_{\boldsymbol{C}}$ denote the difference op…
Conjectureopendifference-equations quantum-curves topological-strings
1