Related papers: Spectral equations for the modular oscillator
We consider four dimensional heterotic compactifications on smooth elliptic Calabi-Yau threefolds. Using spectral cover techniques, we study bundle cohomology groups corresponding to charged matter multiplets. The analysis shows that in…
In [6] Cho and Tanahashi showe new spectral mapping theorem of the taylor spectrum for doubly commuting pairs of p-hyponormal operators and log-hyponormal operators. In this paper, we will show that same spectral mapping theorem holds for…
We study the regularity properties of the Hausdorff distance between spectra of continuous Harper-like operators. As a special case we obtain H\"{o}lder continuity of this Hausdorff distance with respect to the intensity of the magnetic…
The authors study the spectral theory of self-adjoint operators that are subject to certain types of perturbations. An iterative introduction of infinitely many randomly coupled rank-one perturbations is one of our settings. Spectral…
We construct a hyperbolic modular double -- an algebra lying in between the Faddeev modular double for $U_q(sl_2)$ and the elliptic modular double. The intertwining operator for this algebra leads to an integral operator solution of the…
We present an efficient algorithm for computing the prepotential in compactifications of type II string theory on mirror pairs of Calabi-Yau threefolds in toric varieties. Applying this method, we exhibit the first systematic computation of…
The aim of this paper is to extend the notion of the spectral order for finite families of pairwise commuting bounded and unbounded selfadjoint operators in Hilbert space. It is shown that the multidimensional spectral order $\preccurlyeq$…
We study aspects of Calabi-Yau four-folds as compactification manifolds of F-theory, using mirror symmetry of toric hypersurfaces. Correlation functions of the topological field theory are determined directly in terms of a natural ring…
We address the computational spectral theory of Jacobi operators that are compact perturbations of the free Jacobi operator via the asymptotic properties of a connection coefficient matrix. In particular, for finite-rank perturbation we…
We give some remarks on exact quantization conditions associated with quantized mirror curves of local Calabi-Yau threefolds, conjectured in arXiv:1410.3382. It is shown that they characterize a non-perturbative completion of the refined…
We study a problem related to Kontsevich's homological mirror symmetry conjecture for the case of a generic curve $\cal Y$ with bi-degree (2,2) in a product of projective lines ${\Bbb P}^{1} \times {\Bbb P}^{1}$. We calculate two…
We show that certain superpotential and Kahler potential couplings of N=1 supersymmetric compactifications with branes or bundles can be computed from Hodge theory and mirror symmetry. This applies to F-theory on a Calabi-Yau four-fold and…
We consider the heterotic string on Calabi-Yau manifolds admitting a Strominger-Yau-Zaslow fibration. Upon reducing the system in the $T^3$-directions, the Hermitian Yang-Mills conditions can then be reinterpreted as a complex flat…
We study black hole attractor equations for one-(complex structure)modulus Calabi-Yau spaces which are the mirror dual of Fermat Calabi-Yau threefolds (CY_{3}s). When exploring non-degenerate solutions near the Landau-Ginzburg point of the…
We investigate the non-perturbative equivalence of some heterotic/type II dual pairs with N=2 supersymmetry. The perturbative heterotic scalar manifolds are respectively SU(1, 1)/U(1) x SO(2, 2+NV)/ SO(2) x SO(2+NV) and SO(4, 4+NH)/ SO(4) x…
In this work we review a systematic, algorithmic construction of dual heterotic/F-theory geometries corresponding to 4-dimensional, N = 1 supersymmetric compactifications. We look in detail at a class of well-defined Calabi-Yau fourfolds…
We consider semi-infinite Jacobi matrices with discrete spectrum. We prove that the Jacobi operator can be uniquely recovered from one spectrum and subsets of another spectrum and norming constants corresponding to the first spectrum. We…
We study the Harmonic and Dirac Oscillator problem extended to a three-dimensional noncom- mutative space where the noncommutativity is induced by a shift of the dynamical variables with generators of SL(2;R) in a unitary irreducible…
In this note we study several conditions to be imposed on a mirror symmetry candidate to the generic multi-quasihomogeneous Calabi-Yau variety defined in the product of the quasihomogeneous projective spaces. We propose several properties…
Quasiperiodic Jacobi operators arise as mathematical models of quasicrystals and in more general studies of structures exhibiting aperiodic order. The spectra of these self-adjoint operators can be quite exotic, such as Cantor sets, and…