Related papers: Elliptic Quantum Curves of Class $\mathcal{S}_k$

Any two infinite-dimensional (separable) Hilbert spaces are unitarily isomorphic. The sets of all their self-adjoint operators are also therefore unitarily equivalent. Thus if all self-adjoint operators can be observed, and if there is no…

We construct classes of ${\cal N}=1$ superconformal theories elements of which are labeled by punctured Riemann surfaces. Degenerations of the surfaces correspond, in some cases, to weak coupling limits. Different classes are labeled by two…

We study the quantization of the curved spacetime created by ultrarelativistic particles at Planckian energies. We consider a minisuperspace model based on the classical shock wave metric generated by these particles, and for which the…

For a finite field $\mathbb{F}_q$ of characteristic $p\geq 5$ and $K=\mathbb{F}_q(t)$, we consider the family of elliptic curves $E_d$ over $K$ given by $y^2+xy - t^dy=x^3$ for all integers $d$ coprime to $q$. We provide an explicit…

We construct the quantum double ramification hierarchy associated with the Gromov-Witten theory of elliptic curves. We use results of Oberdieck and Pixton on the intersection numbers of the double ramification cycle, the Gromov-Witten…

We propose a construction of some canonical bases for quantum loop algebras of Kac-Moody algebras. We consider a smooth projective curve X, a group of automorphism G of X such that X/G=P^1, and we consider some Quot schemes of G-equivariant…

Exact solution to many problems in mathematical physics and quantum field theory often can be expressed in terms of an algebraic curve equipped with a meromorphic differential. Typically, the geometry of the curve can be seen most clearly…

Alternative versions of the Klein-Gordon and Dirac equations in a curved spacetime are got by applying directly the classical-quantum correspondence.

We determine the low energy description of N=2 supersymmetric SU(k) product group theories with bifundamental and fundamental matter based on M-theory fivebrane configurations. The dependence on moduli and scales of the coefficients in the…

A group $H \cong {\mathbb Z}_{2}^{n}$, $n \geq 3$, of conformal automorphisms of a closed Riemann surface $S$ such that $S/H$ has genus zero and exactly $(n+1)$ cone points is called a generalized Humbert group of type $n$, in which case,…

In this paper a construction of quantum codes from self-orthogonal algebraic geometry codes is provided. Our method is based on the CSS construction as well as on some peculiar properties of the underlying algebraic curves, named Swiss…

We develop a diagrammatic calculus for representations of unrolled quantum $\mathfrak{sl}_2$ at a fourth root of unity. This allows us to prove Seifert-Torres type formulas for certain splice links using quantum algebraic methods, rather…

Six-dimensional superconformal field theories (SCFTs) give rise to four-dimensional (4d) ones when compactified on Riemann surfaces. In the $\mathcal{N}=(2,0)$ case, this yields the famous class S family. For $\mathcal{N}=(1,0)$ theories…

We consider the multiple M2-branes wrapped on a compact Riemann surface and study the arising quantum mechanics by taking the limit where the size of the Riemann surface goes to zero. The IR quantum mechanical models resulting from the…

We present supersymmetric, curved space, quantum mechanical models based on deformations of a parabolic subalgebra of osp(2p+2|Q). The dynamics are governed by a spinning particle action whose internal coordinates are Lorentz vectors…

We study 2d $\mathcal{N}=(0,2)$ and $\mathcal{N}=(0,4)$ theories derived from compactifying class $\mathcal{S}$ theories on $S^2$ with a topological twist. We present concise expressions for the elliptic genera of both classes of theories,…

We present a quantum theory of distances along a curve, based on a linear line element that is equal to the operator square root of the quadratic metric of Riemannian geometry. Since the linear line element is an operator, we treat it…

We investigate the quantum geometry of $2d$ surface $S$ bounding the Cauchy slices of 4d gravitational system. We investigate in detail and for the first time the symplectic current that naturally arises boundary term in the first order…

We consider the sector of N=8 five-dimensional gauged supergravity with non-trivial scalar fields in the coset space SL(6,R)/SO(6), plus the metric. We find that the most general supersymmetric solution is parametrized by six real moduli…

Given an oriented $2$-manifold $M$, a locally constant sheaf of lattices $\Lambda$ over $M$, and a pointed morphism $q : \textsf B^2\Lambda \rightarrow \textsf B^4\mathbf C^{\times}$, we define an $\mathbb E_M$-category…