Related papers: Elliptic Quantum Curves of Class $\mathcal{S}_k$
Starting with a gentle approach to the AGT correspondence from its 6d origin, these notes provide a wide (albeit shallow) survey of the literature on numerous extensions of the correspondence up to early 2020. This is an extended writeup of…
We study the low energy effective dynamics of four-dimensional $\mathcal{N}=1$ supersymmetric gauge theories of class $\mathcal{S}_k$ on the generalized Coulomb branch. The low energy effective gauge couplings are naturally encoded in…
We use mirror symmetry, quantum geometry and modularity properties of elliptic curves to calculate the refined free energies in the Nekrasov-Shatashvili limit on non-compact toric Calabi-Yau manifolds, based on del Pezzo surfaces. Quantum…
This article consists of two parts. In Part 1, we present a formulation of two-dimensional topological quantum field theories in terms of a functor from a category of Ribbon graphs to the endofuntor category of a monoidal category. The key…
We study the quantum Seiberg-Witten (SW) curves for $(A_1, G)$-type Argyres-Douglas (AD) theory by taking the scaling limit of the quantum SW curve of $N=2$ gauge theory with gauge group $G$. For $G=A_r$, the quantum SW curve of the AD…
The classical limit $\hbar$->0 of quantum mechanics is known to be delicate, in particular there seems to be no simple derivation of the classical Hamilton equation, starting from the Schr\"odinger equation. In this paper I elaborate on an…
We solve for the effective actions on the Coulomb branches of a class of N=2 supersymmetric theories by finding the complex structure of an M5 brane in an appropriate background hyperkahler geometry corresponding to the lift of two O6^-…
We propose a procedure to derive quantum spectral curves of AdS/CFT type by requiring that a specially designed analytic continuation around the branch point results in an automorphism of the underlying algebraic structure. In this way we…
We consider all 4d $\mathcal{N}=2$ theories of class $\mathcal{S}$ arising from the compactification of exceptional 6d $(2,0)$ SCFTs on a three-punctured sphere with a simple puncture. We find that each of these 4d theories has another…
We consider 5d Sp(1) gauge theory with $E_{N_f+1}$ global symmetries based on toric(-like) diagram constructed from (p,q)-web with 7-branes. We propose a systematic procedure to compute the Seiberg-Witten curve for generic toric-like…
Four-dimensional N=2 gauge theories may be obtained from configurations of D-branes in type IIA string theory. Unitary gauge theories with two-index representations, and orthogonal and symplectic gauge theories, are constructed from…
When N = 2 gauge theories are compactified on $S^4$, the large $N_c$ limit then selects a unique vacuum of the theory determined by saddle-point equations, which remains determined even in the flat-theory limit. We show that exactly the…
We consider a class of 6D superconformal field theories (SCFTs) which have a large $N$ limit and a semi-classical gravity dual description. Using the quiver-like structure of 6D SCFTs we study a subsector of operators protected from large…
We discuss the relation between quantum curves (defined as solutions of equation $[P,Q]=\hbar$, where $P,Q$ are ordinary differential operators) and classical curves. We illustrate this relation for the case of quantum curve that…
We determine the quantum multiplication with divisor classes on the Hilbert scheme of points on an elliptic surface $S \to \Sigma$ for all curve classes which are contracted by the induced fibration $S^{[n]} \to \Sigma^{[n]}$. The formula…
We consider some general aspects of the new noncommutative or quantum geometry coming out of the theory of quantum groups, in connection with Planck scale physics. A generalisation of Fourier or wave-particle duality on curved spaces…
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…
Using geometric quantization, we represent curve operators in the TQFT of Witten-Reshetikhin-Turaev with jauge group SU_2 as Toeplitz operators with symbols corresponding to trace functions. As an application, we show that eigenvectors of…
We show how the modular symmetries that have been found to be consistent with most available scaling data from quantum Hall systems, derive from a rigid family of algebraic curves of the elliptic type. The complicated special functions…
This is the second of the two related papers analysing origins and possible explanations of a paradoxical phenomenon of the quantum potential (QP). It arises in quantum mechanics'(QM) of a particle in the Riemannian $n$-dimensional…