Related papers: Quantum spectral curve for (q,t)-matrix model

We construct the quantum curve for the Gromov-Witten theory of the complex projective line.

The spectral curve is the key ingredient in the modern theory of classical integrable systems. We develop a construction of the ``quantum spectral curve'' and argue that it takes the analogous structural and unifying role on the quantum…

We describe relationships between integrable systems with N degrees of freedom arising from the AGT conjecture. Namely, we prove the equivalence (spectral duality) between the N-cite Heisenberg spin chain and a reduced gl(N) Gaudin model…

We give a derivation of quantum spectral curve (QSC) - a finite set of Riemann-Hilbert equations for exact spectrum of planar N=4 SYM theory proposed in our recent paper Phys.Rev.Lett. 112 (2014). We also generalize this construction to all…

Based on properties of the universal R-matrix, we derive universal Baxter TQ-relations for quantum integrable systems with (diagonal) open boundaries associated with $U_{q}(\widehat{sl_{2}})$. The Baxter TQ-relations for the open XXZ-spin…

We propose that the Baxter's $Q$-operator for the XYZ quantum spin chain with open boundary conditions is given by the $j\to \infty$ limit of the corresponding transfer matrix with spin-$j$ (i.e., $(2j+1)$-dimensional) auxiliary space. The…

The spectrum of planar N=6 superconformal Chern-Simons theory, dual to type IIA superstring theory on $AdS_4 \times CP^3$, is accessible at finite coupling using integrability. Starting from the results of [arXiv:1403.1859], we study in…

We write the loop equations for the $\beta$ two-matrix model, and we propose a topological recursion algorithm to solve them, order by order in a small parameter. We find that to leading order, the spectral curve is a "quantum" spectral…

In the correspondence between spectral problems and topological strings, it is natural to consider complex values for the string theory moduli. In the spectral theory side, this corresponds to non-Hermitian quantum curves with complex…

The off-diagonal Bethe Ansatz method [1] is used to revisit the periodic XXX Heisenberg spin-1/2 chain. It is found that the spectrum of the transfer matrix can be characterized by an inhomogeneous T-Q relation, a natural but nontrivial…

We derive the spectral curves for $q$-part double Hurwitz numbers, $r$-spin simple Hurwitz numbers, and arbitrary combinations of these cases, from the analysis of the unstable (0,1)-geometry. We quantize this family of spectral curves and…

We give an introduction to the Quantum Spectral Curve in AdS/CFT. This is an integrability-based framework which provides the exact spectrum of planar N = 4 super Yang-Mills theory (and of the dual string model) in terms of a solution of a…

A lattice model of interacting q-oscillators, proposed in [V. Bazhanov, S. Sergeev, arXiv:hep-th/0509181], is the quantum mechanical integrable model in 2+1 dimensional space-time. Its layer-to-layer transfer-matrix is a polynomial of two…

The spectral problem for the ${\rm AdS}_5\times {\rm S}^5$ superstring and its dual planar maximally supersymmetric Yang-Mills theory can be efficiently solved through a set of functional equations known as the quantum spectral curve. We…

In this thesis we discuss how one can derive the quantum spectral curve for the $\eta$-deformed AdS$_5 \times S^5$ superstring, an integrable deformation of the AdS$_5 \times $S$^5$ superstring with quantum group symmetry. This model can be…

We study Baxter's T-Q equation of XXX spin-chain models under the semiclassical limit where an intriguing SU(N)/SU(2)^{N-3} correspondence emerges. That is, two kinds of 4D \mathcal{N}=2 superconformal field theories having the above…

We consider quantum difference equation (QDE) for equivariant quantum K-theory of the Grassmannian. In this paper we obtain a solution to the QDE and use the solution to asymptotically derive the Bethe ansatz equations. In the limit, we…

We define and study the quantum equivariant $K$-theory of cotangent bundles over Grassmannians. For every tautological bundle in the $K$-theory we define its one-parametric deformation, referred to as quantum tautological bundle. We prove…

We review the quantum spectral curve (QSC) formalism for anomalous dimensions of planar ${\cal\ N}=4$ SYM, including its $\gamma$-deformation. Leaving aside its derivation, we concentrate on formulation of the "final product" in its most…

We consider the Quantum Inverse Scattering Method with a new R-matrix depending on two parameters $q$ and $t$. We find that the underlying algebraic structure is the two-parameter deformed algebra $SU_{q,t}(2)$ enlarged by introducing an…