相关论文: Quantum Curves, Resurgence and Exact WKB

In this paper we demonstrate that the Stokes constants of unrefined free energies and the Stokes constants of Nekrasov-Shatashvili free energies of topological string on a non-compact Calabi-Yau threefold are identical, possibly up to a…

Given a log Calabi--Yau surface $(Y,D)$, Bousseau has constructed a quantization of the mirror algebra of this pair. We give a formula for structure constants of this quantization in terms of higher genus descendant logarithmic…

We show that there is a natural universal limit of the topological string free energies at the large radius point. The new free energies keep a nonholomorphic dependence on the complex structure moduli space and their functional form is the…

We interpret the $q$-refined theta function $\vartheta_1$ of a log Calabi-Yau surface $(\mathbb{P},E)$ as a natural $q$-refinement of the open mirror map, defined by quantum periods of mirror curves for outer Aganagic-Vafa branes on the…

We investigate the nonperturbative structure of Jackiw-Teitelboim gravity at finite cutoff, as given by its proposed formulation in terms of a $T\bar{T}$-deformed Schwarzian quantum mechanics. Our starting point is a careful computation of…

The core of this thesis is the path-integral formulation of quantum field theory and its ability to describe strongly-coupled quantum many-body systems of finite size. Collective behaviors can be efficiently described in such systems…

We derive quantum spectral curve equation for (q,t)-matrix model, which turns out to be a certain difference equation. We show that in Nekrasov-Shatashvili limit this equation reproduces the Baxter TQ equation for the quantum XXZ spin…

We investigate aspects of Kauffman bracket skein algebras of surfaces and modules of 3-manifolds using quantum torus methods. These methods come in two flavors: embedding the skein algebra into a quantum torus related to quantum Teichmuller…

We study the thermodynamics of near horizon near extremal Kerr (NHNEK) geometry within the framework of $AdS_2/CFT_1$ correspondence. We start by shifting the horizon of near horizon extremal Kerr (NHEK) geometry by a general finite mass.…

We apply the recently proposed quantum spectral curve technique to the study of twist operators in planar N=4 SYM theory. We focus on the small spin expansion of anomalous dimensions in the sl(2) sector and compute its first two orders…

In this work we present an experimental demonstration of the Contextual Subspace Variational Quantum Eigensolver on superconducting quantum hardware. In particular, we compute the potential energy curve for molecular nitrogen, where a…

The topological recursion of Eynard and Orantin governs a variety of problems in enumerative geometry and mathematical physics. The recursion uses the data of a spectral curve to define an infinite family of multidifferentials. It has been…

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…

We prove that the topological recursion formalism can be used to compute the WKB expansion of solutions of second order differential operators obtained by quantization of any hyper-elliptic curve. We express this quantum curve in terms of…

We use super-spectral curve to investigate irregular conformal states of integer and half-odd integer rank. The spectral curve is the loop equation of supersymmetrized irregular matrix model. The case of integer rank corresponds to the…

We adapt the Bender-Wu algorithm to solve perturbatively but very efficiently the eigenvalue problem of "relativistic" quantum mechanical problems whose Hamiltonians are difference operators of the exponential-polynomial type. We implement…

We find an explicit matrix model computing the refined topological vertex, starting from its representation in terms of plane partitions. We then find the spectral curve of that matrix model, and thus the mirror symmetry of the refined…

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…

Accurate calculations of the spectral density in a strongly correlated quantum many-body system are of fundamental importance to study its dynamics in the linear response regime. Typical examples are the calculation of inclusive and…

Localization methods have recently led to a plethora of new exact results in supersymmetric gauge theories, as certain observables may be computed in terms of matrix integrals. These can then be evaluated by making use of standard large N…