scholarly journals MIRROR SYMMETRY AND AN EXACT CALCULATION OF AN (N–2)-POINT CORRELATION FUNCTION ON A CALABI-YAU MANIFOLD EMBEDDED IN CPN−1

1996 ◽  
Vol 11 (07) ◽  
pp. 1217-1252 ◽  
Author(s):  
MASAO JINZENJI ◽  
MASARU NAGURA
Keyword(s):  
Correlation Function ◽  
Yukawa Coupling ◽  
Mirror Symmetry ◽  
Rational Curves ◽  
Holomorphic Curves ◽  
Holomorphic Maps ◽  
Point Function ◽  
Point Correlation ◽  
Point Correlation Function ◽  
Zero Locus

We consider an (N–2)-dimensional Calabi-Yau manifold which is defined as the zero locus of the polynomial of degree N (of the Fermat type) in CPN−1 and its mirror manifold. We introduce an (N–2)-point correlation function (generalized Yukawa coupling) and evaluate it both by solving the Picard-Fuchs equation for period integrals in the mirror manifold and by explicitly calculating the contribution of holomorphic maps of degree 1 to the Yukawa coupling in the Calabi-Yau manifold using the method of algebraic geometry. In enumerating the holomorphic curves in the general-dimensional Calabi-Yau manifolds, we extend the method of counting rational curves on the Calabi-Yau three-fold using the Shubert calculus on Gr (2, N). The agreement of the two calculations for the (N–2)-point function establishes “the mirror symmetry at the correlation function level” in the general-dimensional case.

scholarly journals MIRROR SYMMETRY OF THE K3 SURFACE

1995 ◽  
Vol 10 (02) ◽  
pp. 233-252 ◽  
Author(s):  
MASARU NAGURA ◽  
KATSUYUKI SUGIYAMA
Keyword(s):  
Correlation Function ◽  
Algebraic Geometry ◽  
Yukawa Coupling ◽  
Mirror Symmetry ◽  
K3 Surface ◽  
Complex Torus ◽  
Point Correlation ◽  
Point Correlation Function ◽  
Mirror Map

We discuss the K3 surface and the complex torus from the viewpoint of “mirror symmetry.” We calculate the periods of some K3 surface and construct a mirror map for the two-point correlation function and the prepotential. We find that there are no instanton corrections of the Yukawa coupling for K3 (also torus), which is expected from the viewpoint of algebraic geometry.

scholarly journals TOWARDS THE PROOF OF AGT-W RELATION: TODA 3-POINT FUNCTION AND ${\mathcal W}_{1+\infty}$ ALGEBRA

2013 ◽  
Vol 21 ◽  
pp. 138-139
Author(s):  
SHOTARO SHIBA
Keyword(s):  
Field Theory ◽  
Correlation Function ◽  
Point Function ◽  
Gauge Groups ◽  
Promising Direction ◽  
Quiver Gauge Theory ◽  
Conformal Theory ◽  
Conformal Field ◽  
Point Correlation ◽  
Point Correlation Function

The AGT-W relation is a conjecture of the nontrivial duality between 4-dim quiver gauge theory and 2-dim conformal field theory. We verify a part of this conjecture for all the cases of quiver gauge groups by studying on the property of 3-point correlation function of conformal theory. We also mention the relation to [Formula: see text] algebra as one of the promising direction towards the proof of the remaining part.

FOUR-POINT FUNCTION OF THE SUPER-WZW MODEL ON THE SPHERE

1990 ◽  
Vol 05 (29) ◽  
pp. 2413-2422 ◽  
Author(s):  
KENICHIRO AOKI
Keyword(s):  
Field Theory ◽  
Correlation Function ◽  
Scalar Field ◽  
Explicit Expression ◽  
Point Function ◽  
Scalar Field Theory ◽  
Identical Structure ◽  
Point Correlation ◽  
Point Correlation Function ◽  
Background Charge

The superspace formulation of the super-WZW model is used to obtain an explicit expression for the four-point correlation function on the super-sphere given that of the Bose case, for general groups. The correlation function is compared with that of the free super-scalar field theory with background charge and is shown to have an identical structure for the case of SU(2).

scholarly journals Operator expansions, layer susceptibility and two-point functions in BCFT

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Parijat Dey ◽  
Tobias Hansen ◽  
Mykola Shpot
Keyword(s):  
Correlation Function ◽  
Power Series Expansion ◽  
Operator Product ◽  
Point Function ◽  
Direct Identification ◽  
Boundary Spectrum ◽  
Anomalous Dimensions ◽  
Point Correlation ◽  
Point Correlation Function ◽  
Expansion Coefficients

Abstract We show that in boundary CFTs, there exists a one-to-one correspondence between the boundary operator expansion of the two-point correlation function and a power series expansion of the layer susceptibility. This general property allows the direct identification of the boundary spectrum and expansion coefficients from the layer susceptibility and opens a new way for efficient calculations of two-point correlators in BCFTs. To show how it works we derive an explicit expression for the correlation function 〈ϕiϕi〉 of the O(N) model at the extraordinary transition in 4 − ϵ dimensional semi-infinite space to order O(ϵ). The bulk operator product expansion of the two-point function gives access to the spectrum of the bulk CFT. In our example, we obtain the averaged anomalous dimensions of scalar composite operators of the O(N) model to order O(ϵ2). These agree with the known results both in ϵ and large-N expansions.

scholarly journals From correlation functions to event shapes in QCD

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
D. Chicherin ◽  
J. M. Henn ◽  
E. Sokatchev ◽  
K. Yan
Keyword(s):  
Correlation Function ◽  
Correlation Functions ◽  
Event Shape ◽  
Proof Of Concept ◽  
Yang Mills ◽  
Point Correlation ◽  
Point Correlation Function ◽  
Event Shapes ◽  
A Charge ◽  
Conserved Currents

Abstract We present a method for calculating event shapes in QCD based on correlation functions of conserved currents. The method has been previously applied to the maximally supersymmetric Yang-Mills theory, but we demonstrate that supersymmetry is not essential. As a proof of concept, we consider the simplest example of a charge-charge correlation at one loop (leading order). We compute the correlation function of four electromagnetic currents and explain in detail the steps needed to extract the event shape from it. The result is compared to the standard amplitude calculation. The explicit four-point correlation function may also be of interest for the CFT community.

scholarly journals A two-point correlation function for Galactic halo stars

2011 ◽  
Vol 417 (3) ◽  
pp. 2206-2215 ◽  
Author(s):  
A. P. Cooper ◽  
S. Cole ◽  
C. S. Frenk ◽  
A. Helmi
Keyword(s):  
Correlation Function ◽  
Galactic Halo ◽  
Halo Stars ◽  
Point Correlation ◽  
Point Correlation Function

scholarly journals A general treatment of snow microstructure exemplified by an improved relation for the thermal conductivity

2012 ◽  
Vol 6 (6) ◽  
pp. 4673-4693 ◽  
Author(s):  
H. Löwe ◽  
F. Riche ◽  
M. Schneebeli
Keyword(s):  
Thermal Conductivity ◽  
Correlation Function ◽  
Pore Space ◽  
Anisotropy Parameter ◽  
Micro Computed Tomography ◽  
Data Set ◽  
Microstructural Parameters ◽  
Point Correlation ◽  
Point Correlation Function ◽  
Snow Microstructure

Abstract. Finding relevant microstructural parameters beyond the density is a longstanding problem which hinders the formulation of accurate parametrizations of physical properties of snow. Towards a remedy we address the effective thermal conductivity tensor of snow via known anisotropic, second-order bounds. The bound provides an explicit expression for the thermal conductivity and predicts the relevance of a microstructural anisotropy parameter Q which is given by an integral over the two-point correlation function and unambiguously defined for arbitrary snow structures. For validation we compiled a comprehensive data set of 167 snow samples. The set comprises individual samples of various snow types and entire time series of metamorphism experiments under isothermal and temperature gradient conditions. All samples were digitally reconstructed by micro-computed tomography to perform microstructure-based simulations of heat transport. The incorporation of anisotropy via Q considerably reduces the root mean square error over the usual density-based parametrization. The systematic quantification of anisotropy via the two-point correlation function suggests a generalizable route to incorporate microstructure into snowpack models. We indicate the inter-relation of the conductivity to other properties and outline a potential impact of Q on dielectric constant, permeability and adsorption rate of diffusing species in the pore space.

Sign in / Sign up

Export Citation Format

Share Document