scholarly journals Stochastic quantization and holographic Wilsonian renormalization group of massless fermions in AdS

2014 ◽  
Vol 29 (17) ◽  
pp. 1450082 ◽  
Author(s):  
Jae-Hyuk Oh
Keyword(s):  
Renormalization Group ◽  
Radial Flow ◽  
Natural Extension ◽  
High Energy ◽  
Stochastic Quantization ◽  
Point Function ◽  
Fermionic Fields ◽  
Point Correlation ◽  
Point Correlation Function ◽  
Euclidean Action

We have studied holographic Wilsonian renormalization group (HWRG) of free massless fermionic fields in AdS space and its stochastic quantization (SQ) by identifying the Euclidean action with its boundary on-shell action. The natural extension of the relation between stochastic two-point correlation function and double trace coupling obtained from HWRG computation conjectured in [J.-H. Oh and D. P. Jatkar, J. High Energy Phys. 1211, 144 (2012) arXiv:1209.2242] to fermionic fields is established. We have confirmed that the stochastic two-point function precisely captures the radial flow of the double trace coupling via this relation.

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.

scholarly journals Computing three-point correlation function randoms counts without the randoms catalogue

2019 ◽  
Vol 486 (1) ◽  
pp. L105-L109 ◽  
Author(s):  
David W Pearson ◽  
Lado Samushia
Keyword(s):  
Cosmological Parameters ◽  
Synthetic Data ◽  
Function Estimation ◽  
Point Function ◽  
Simple Method ◽  
Galaxy Surveys ◽  
Counting Algorithms ◽  
Data Points ◽  
Point Correlation ◽  
Point Correlation Function

ABSTRACT As we move towards future galaxy surveys, the three-point statistics will be increasingly leveraged to enhance the constraining power of the data on cosmological parameters. An essential part of the three-point function estimation is performing triplet counts of synthetic data points in random catalogues. Since triplet counting algorithms scale at best as $\mathcal {O}(N^2\log N)$ with the number of particles and the random catalogues are typically at least 50 times denser than the data; this tends to be by far the most time-consuming part of the measurements. Here, we present a simple method of computing the necessary triplet counts involving uniform random distributions through simple one-dimensional integrals. The method speeds up the computation of the three-point function by orders of magnitude, eliminating the need for random catalogues, with the simultaneous pair and triplet counting of the data points alone being sufficient.

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.

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.

A CRITICAL VIEW ON THE PERTURBATIVE RG METHOD

2012 ◽  
Vol 27 (21) ◽  
pp. 1250114 ◽  
Author(s):  
J. KAUPUŽS
Keyword(s):  
Correlation Function ◽  
Renormalization Group ◽  
Critical Surface ◽  
Ginzburg Landau ◽  
Landau Model ◽  
Critical View ◽  
Flow Equations ◽  
Point Correlation ◽  
Point Correlation Function ◽  
Perturbative Renormalization

The perturbative renormalization group (RG) treatment of the Ginzburg–Landau model is reconsidered based on the Feynman diagram technique. We derive RG flow equations, exactly calculating all vertices appearing in the perturbative RG transformation of the φ4 model up to the ε3 order of the ε-expansion. The Fourier-transformed two-point correlation function G(k) has been considered. Although the ε-expansion of X(k) = 1/G(k) is well defined on the critical surface, we have revealed an inconsistency with the exact rescaling of X(k), represented as an expansion in powers of k at k →0. This new result can serve as a basis to challenge the correctness of the ε-expansion-based perturbative RG method.

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 Correlation functions in finite temperature CFT and black hole singularities

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
D. Rodriguez-Gomez ◽  
J.G. Russo
Keyword(s):  
Black Hole ◽  
Event Horizon ◽  
Correlation Functions ◽  
Finite Temperature ◽  
Proper Time ◽  
Black Brane ◽  
Point Function ◽  
Black Hole Singularity ◽  
Point Correlation ◽  
Scaling Dimension

Abstract We compute thermal 2-point correlation functions in the black brane AdS5 background dual to 4d CFT’s at finite temperature for operators of large scaling dimension. We find a formula that matches the expected structure of the OPE. It exhibits an exponentiation property, whose origin we explain. We also compute the first correction to the two-point function due to graviton emission, which encodes the proper time from the event horizon to the black hole singularity.

scholarly journals THE CASE OF ASYMPTOTIC SUPERSYMMETRY

2013 ◽  
Vol 28 (14) ◽  
pp. 1350053 ◽  
Author(s):  
BRUCE L. SÁNCHEZ-VEGA ◽  
ILYA L. SHAPIRO
Keyword(s):  
Fixed Point ◽  
Renormalization Group ◽  
Gauge Coupling ◽  
High Energy ◽  
Systematic Investigation ◽  
Coupling Constants ◽  
Scalar Coupling ◽  
Asymptotic State ◽  
Stable Fixed Point ◽  
Scalar Couplings

We start systematic investigation for the possibility to have supersymmetry (SUSY) as an asymptotic state of the gauge theory in the high energy (UV) limit, due to the renormalization group running of coupling constants of the theory. The answer on whether this situation takes place or not, can be resolved by dealing with the running of the ratios between Yukawa and scalar couplings to the gauge coupling. The behavior of these ratios does not depend too much on whether gauge coupling is asymptotically free (AF) or not. It can be shown that the UV stable fixed point for the Yukawa coupling is not supersymmetric. Taking this into account, one can break down SUSY only in the scalar coupling sector. We consider two simplest examples of such breaking, namely N = 1 supersymmetric QED and QCD. In one of the cases one can construct an example of SUSY being restored in the UV regime.

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