scholarly journals An extension of stochastic hierarchy equations of motion for the equilibrium correlation functions

2017 ◽  
Vol 146 (21) ◽  
pp. 214105 ◽  
Author(s):  
Yaling Ke ◽  
Yi Zhao
Keyword(s):  
Correlation Functions ◽  
Equations Of Motion ◽  
Equilibrium Correlation ◽  
Hierarchy Equations

scholarly journals Two point functions in defect CFTs

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Christopher P. Herzog ◽  
Abhay Shrestha
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Correlation Functions ◽  
Equations Of Motion ◽  
Physical Space ◽  
Arbitrary Spin ◽  
Momentum Tensor ◽  
Maxwell Theory ◽  
Conformal Field ◽  
Point Correlation

Abstract This paper is designed to be a practical tool for constructing and investigating two-point correlation functions in defect conformal field theory, directly in physical space, between any two bulk primaries or between a bulk primary and a defect primary, with arbitrary spin. Although geometrically elegant and ultimately a more powerful approach, the embedding space formalism gets rather cumbersome when dealing with mixed symmetry tensors, especially in the projection to physical space. The results in this paper provide an alternative method for studying two-point correlation functions for a generic d-dimensional conformal field theory with a flat p-dimensional defect and d − p = q co-dimensions. We tabulate some examples of correlation functions involving a conserved current, an energy momentum tensor and a Maxwell field strength, while analysing the constraints arising from conservation and the equations of motion. A method for obtaining bulk-to-defect correlators is also explained. Some explicit examples are considered: free scalar theory on ℝp× (ℝq/ℤ2) and a free four dimensional Maxwell theory on a wedge.

Bilinear Contributions to Equilibrium Correlation Functions

1973 ◽  
Vol 7 (4) ◽  
pp. 1384-1395 ◽  
Author(s):  
T. Keyes ◽  
Irwin Oppenheim
Keyword(s):  
Correlation Functions ◽  
Equilibrium Correlation

Correlation Structure and Time Scale of Simple Hydrologic Systems

1977 ◽  
Vol 8 (3) ◽  
pp. 129-140 ◽  
Author(s):  
Lars Gottschalk
Keyword(s):  
River Runoff ◽  
Groundwater Level ◽  
Correlation Functions ◽  
Time Scale ◽  
Equations Of Motion ◽  
Nonlinear Effects ◽  
Correlation Structure ◽  
Linearized Equations ◽  
Hydrologic Systems ◽  
Meteorological Input

Correlation structure of river runoff is a complicated set of different persistence phenomena in the watershed itself and in the meteorological input to the watershed. Correlation functions and time scale of isolated processes in a watershed (groundwater level and river runoff) are derived analytically from the linearized equations of motion for these processes. Nonlinear effects on the correlation functions are shown for river runoff and for the watershed as a whole.

scholarly journals CFT in AdS and boundary RG flows

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Simone Giombi ◽  
Himanshu Khanchandani
Keyword(s):  
Free Energy ◽  
Correlation Functions ◽  
Equations Of Motion ◽  
Flat Space ◽  
De Sitter ◽  
Conformal Field ◽  
Anomalous Dimensions ◽  
Epsilon Expansion ◽  
Boundary Operators ◽  
Renormalization Group Flows

Abstract Using the fact that flat space with a boundary is related by a Weyl transformation to anti-de Sitter (AdS) space, one may study observables in boundary conformal field theory (BCFT) by placing a CFT in AdS. In addition to correlation functions of local operators, a quantity of interest is the free energy of the CFT computed on the AdS space with hyperbolic ball metric, i.e. with a spherical boundary. It is natural to expect that the AdS free energy can be used to define a quantity that decreases under boundary renormalization group flows. We test this idea by discussing in detail the case of the large N critical O(N) model in general dimension d, as well as its perturbative descriptions in the epsilon-expansion. Using the AdS approach, we recover the various known boundary critical behaviors of the model, and we compute the free energy for each boundary fixed point, finding results which are consistent with the conjectured F-theorem in a continuous range of dimensions. Finally, we also use the AdS setup to compute correlation functions and extract some of the BCFT data. In particular, we show that using the bulk equations of motion, in conjunction with crossing symmetry, gives an efficient way to constrain bulk two-point functions and extract anomalous dimensions of boundary operators.

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