nn-th parafermion WN\mathcal{W}_N characters from U(N)U(N) instanton counting on C2/Zn{\mathbb {C}}^2/{\mathbb {Z}}_n

We propose, following the AGT correspondence, how the $\mathcal{W}^{\, para}_{N, n}$ ($n$-th parafermion $\mathcal{W}_N$) minimal model characters are obtained from the $U(N)$ instanton counting on ${\mathbb {C}}^2/{\mathbb {Z}}_n$ with $\Omega$-deformation by imposing specific conditions which remove the minimal model null states.Comment: 25 pages, 2 figures; v2: minor changes, references added; I would like to dedicate this paper to the memory of Professor Omar Fod

Determinantal Calabi-Yau varieties in Grassmannians and the Givental II-functions

We examine a class of Calabi-Yau varieties of the determinantal type in Grassmannians and clarify what kind of examples can be constructed explicitly. We also demonstrate how to compute their genus-0 Gromov-Witten invariants from the analysis of the Givental $I$-functions. By constructing $I$-functions from the supersymmetric localization formula for the two dimensional gauged linear sigma models, we describe an algorithm to evaluate the genus-0 A-model correlation functions appropriately. We also check that our results for the Gromov-Witten invariants are consistent with previous results for known examples included in our construction.Comment: 50 page

Probability Distribution Function of the Coarse-grained Scalar Field at Finite Temperature

We present a formalism to calculate the probability distribution function of a scalar field coarse-grained over some spatial scales with a Gaussian filter at finite temperature. As an application, we investigate the role of subcritical fluctuations in the electroweak phase transition in the minimal standard model. It is concluded that the universe was in a mixed state of true and false vacua already at the critical temperature.Comment: 15 pages, uuencode, gzipped tar file including LaTeX text and 4 postscript figures. Nuclear Physics B, in pres

Quantum curves and conformal field theory

To a given algebraic curve we assign an infinite family of quantum curves (Schr\"odinger equations), which are in one-to-one correspondence with, and have the structure of, Virasoro singular vectors. For a spectral curve of a matrix model we build such quantum curves out of an appropriate representation of the Virasoro algebra, encoded in the structure of the $\alpha/\beta$-deformed matrix integral and its loop equation. We generalize this construction to a large class of algebraic curves by means of a refined topological recursion. We also specialize this construction to various specific matrix models with polynomial and logarithmic potentials, and among other results, show that various ingredients familiar in the study of conformal field theory (Ward identities, correlation functions and a representation of Virasoro operators acting thereon, BPZ equations) arise upon specialization of our formalism to the multi-Penner matrix model.Comment: 90 pages, published versio

Multiphoton discrimination at telecom wavelength with charge integration photon detector

We present a charge integration photon detector (CIPD) that enables the efficient measurement of photon number states at the telecom-fiber wavelengths with a quantum efficiency of 80% and a resolution less than 0.5 electrons at 1 Hz sampling. The CIPD consists of an InGaAs PIN photodiode and a GaAs JFET in a charge integration amplifier, which is cooled to 4.2 K to reduce thermal noise and leakage current. The charge integration amplifier exhibits a low noise level of 470 nV/Hz1/2. The dark count is as low as 500 electrons/hour.Comment: 4 pages, 4 figures, accepted for Applied Physics letter

Multi-Point Virtual Structure Constants and Mirror Computation of CP^2-model

In this paper, we propose a geometrical approach to mirror computation of genus 0 Gromov-Witten invariants of CP^2. We use multi-point virtual structure constants, which are defined as intersection numbers of a compact moduli space of quasi maps from CP^1 to CP^2 with 2+n marked points. We conjecture that some generating functions of them produce mirror map and the others are translated into generating functions of Gromov-Witten invariants via the mirror map. We generalize this formalism to open string case. In this case, we have to introduce infinite number of deformation parameters to obtain results that agree with some known results of open Gromov-Witten invariants of CP^2. We also apply multi-point virtual structure constants to compute closed and open Gromov-Witten invariants of a non-nef hypersurface in projective space. This application simplifies the computational process of generalized mirror transformation.Comment: 26 pages, Late