Representation of the power-series expansion coefficients for the one-point correlation function in the grand canonical ensemble

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.

Download Full-text

CRITICAL BEHAVIOR IN THE ROTATING D-BRANES

Modern Physics Letters A ◽

10.1142/s0217732399001966 ◽

1999 ◽

Vol 14 (27) ◽

pp. 1895-1907 ◽

Cited By ~ 68

Author(s):

RONG-GEN CAI ◽

KWANG-SUP SOH

Keyword(s):

Correlation Function ◽

Critical Behavior ◽

Critical Exponents ◽

Correlation Functions ◽

Scaling Laws ◽

Canonical Ensemble ◽

Stable Boundary ◽

Conformal Fields ◽

Point Correlation ◽

Point Correlation Function

We investigate the critical behavior near the thermodynamically stable boundary for the rotating D3-, M5- and M2-branes. The static scaling laws are found to hold. The critical exponents characterizing the scaling behaviors of susceptibilities are the same and all equal 1/2 in all cases. Using the scaling laws related to the correlation functions, we predict the critical exponents of the two-point correlation function of the corresponding conformal fields. We find that the stable boundary is shifted in the different ensembles and there does not exist the stable boundary in the canonical ensemble for the rotating M2-branes.

Download Full-text

The two-point correlation function of the one-dimensional matrix model

Nuclear Physics B ◽

10.1016/0550-3213(91)90158-t ◽

1991 ◽

Vol 350 (3) ◽

pp. 621-634 ◽

Cited By ~ 73

Author(s):

David J. Gross ◽

Igor R. Klebanov ◽

Michael J. Newman

Keyword(s):

Correlation Function ◽

Matrix Model ◽

One Dimensional ◽

Dimensional Matrix ◽

Point Correlation ◽

Point Correlation Function ◽

The One

Download Full-text

Grand-canonical-ensemble representability problem for the one-electron reduced density matrix

Physical Review A ◽

10.1103/physreva.75.012509 ◽

2007 ◽

Vol 75 (1) ◽

Cited By ~ 8

Author(s):

D. R. Alcoba ◽

R. C. Bochicchio ◽

G. E. Massacessi ◽

L. Lain ◽

A. Torre

Keyword(s):

Density Matrix ◽

Canonical Ensemble ◽

Grand Canonical Ensemble ◽

Reduced Density Matrix ◽

The One ◽

Reduced Density ◽

Grand Canonical

Download Full-text

A grand canonical ensemble Monte Carlo study of confined planar and homeotropically anchored Gay—Berne films

Molecular Physics ◽

10.1080/00268979809482254 ◽

1998 ◽

Vol 93 (4) ◽

pp. 681-692

Author(s):

THOMAS GRUHN ◽

MARTIN SCHOEN

Keyword(s):

Monte Carlo ◽

Canonical Ensemble ◽

Monte Carlo Study ◽

Grand Canonical Ensemble ◽

Ensemble Monte Carlo ◽

Grand Canonical

Download Full-text

From correlation functions to event shapes in QCD

Journal of High Energy Physics ◽

10.1007/jhep02(2021)053 ◽

2021 ◽

Vol 2021 (2) ◽

Cited By ~ 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.

Download Full-text