Related papers: Conformal TBA for resolved conifolds

We study correlation functions in topologically twisted $\mathcal{N}=2, d=4$ supersymmetric Yang-Mills theory for gauge groups of rank larger than one on compact four-manifolds $X$. We find that the topological invariance of the generator…

We study a class of flat bundles, of finite rank $N$, which arise naturally from the Donaldson-Thomas theory of a Calabi-Yau threefold $X$ via the notion of a variation of BPS structure. We prove that in a large $N$ limit their flat…

We prove conformal versions of the local decomposition theorems of de Rham and Hiepko of a Riemannian manifold as a Riemannian or a warped product of Riemannian manifolds. Namely, we give necessary and sufficient conditions for a Riemannian…

Quasinormal modes of usual, four dimensional, Kerr black holes are described by certain solutions of a confluent Heun differential equation. In this work, we express these solutions in terms of the connection matrices for a Riemann-Hilbert…

Several expansions of the solutions to the confluent Heun equation in terms of incomplete Beta functions are constructed. A new type of expansion involving certain combinations of the incomplete Beta functions as expansion functions is…

Riemannian Geometry, Topology and Dynamics permit to introduce partially defined holomorphic functions on the variety of representations of the fundamental group of a manifold. The functions we consider are the complex valued Ray-Singer…

We develop theoretical aspects of refined Donaldson-Thomas theory for threefold flops, and use these to determine all DT invariants for a doubly infinite family of length 2 flopping contractions. Our results show that a refined version of…

The conformable double ARA decomposition approach is presented in this current study to solve one-dimensional regular and singular conformable functional Burger's equations. We investigate the conformable double ARA transform's definition,…

We present a theorem on taking the repeated indefinite summation of a holomorphic function $\phi(z)$ in a vertical strip of $\mathbb{C}$ satisfying exponential bounds as the imaginary part grows. We arrive at this result using transforms…

This is a short version of math.DG/0505537. For an acyclic representation of the fundamental group of a compact oriented odd-dimensional manifold, which is close enough to a unitary representation, we define a refinement of the Ray-Singer…

Quantizing the mirror curve of certain toric Calabi-Yau (CY) three-folds leads to a family of trace class operators. The resolvent function of these operators is known to encode topological data of the CY. In this paper, we show that in…

We extend the results of Riemannian geometry over finite groups and provide a full classification of all linear connections for the minimal noncommutative differential calculus over a finite cyclic group. We solve the torsion-free and…

We present a simple systematic algorithm for construction of expansions of the solutions of ordinary differential equations with rational coefficients in terms of mathematical functions having indefinite integral representation. The…

We develop a universal distributional calculus for regulated volumes of metrics that are singular along hypersurfaces. When the hypersurface is a conformal infinity we give simple integrated distribution expressions for the divergences and…

In this paper we introduce the class of infinite infimal convolution functionals and apply these functionals to the regularization of ill-posed inverse problems. The proposed regularization involves an infimal convolution of a continuously…

We consider partition functions with insertions of surface operators of topologically twisted N=2, SU(2) supersymmetric Yang-Mills theory, or Donaldson-Witten theory for short, on a four-manifold. If the metric of the compact four-manifold…

Rubin's generalized Minkowski--Funk transforms $M_t^\alpha$ on the sphere $\mathbb{S}^n$ give rise, for irrational radii $t=\cos(\beta\pi)$, to a small denominator problem governed by the asymptotic behavior of their spectral multipliers.…

We consider partial sum rules for the homogeneous limit of the solution of the q-deformed Knizhnik--Zamolodchikov equation with reflecting boundaries in the Dyck path representation. We show that these partial sums arise in a solution of…

We study the open string integrality invariants (LMOV invariants) for toric Calabi-Yau 3-folds with Aganagic-Vafa brane (AV-brane). In this paper, we focus on the case of the resolved conifold with one out AV-brane in any integer framing…

We analyse the transverse dynamical two-point correlation function of the XX chain by means of a thermal form factor series. The series is rewritten in terms of the resolvent and the Fredholm determinant of an integrable integral operator.…