scholarly journals One-point function estimates for loop-erased random walk in three dimensions

2019 ◽  
Vol 24 (0) ◽  
Author(s):  
Xinyi Li ◽  
Daisuke Shiraishi
Keyword(s):  
Random Walk ◽  
Three Dimensions ◽  
Point Function

scholarly journals Mixed scalar-current bootstrap in three dimensions

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Marten Reehorst ◽  
Emilio Trevisani ◽  
Alessandro Vichi
Keyword(s):  
Stress Tensor ◽  
Quantum Monte Carlo ◽  
Three Dimensions ◽  
Mixed System ◽  
Point Function ◽  
Function Coefficient ◽  
Rigorous Bounds ◽  
Usual Scalar ◽  
Scalar Singlet ◽  
Scalar Current

Abstract We study the mixed system of correlation functions involving a scalar field charged under a global U(1) symmetry and the associated conserved spin-1 current Jμ. Using numerical bootstrap techniques we obtain bounds on new observables not accessible in the usual scalar bootstrap. We then specialize to the O(2) model and extract rigorous bounds on the three-point function coefficient of two currents and the unique relevant scalar singlet, as well as those of two currents and the stress tensor. Using these results, and comparing with a quantum Monte Carlo simulation of the O(2) model conductivity, we give estimates of the thermal one-point function of the relevant singlet and the stress tensor. We also obtain new bounds on operators in various sectors.

scholarly journals BMS modular diaries: torus one-point function

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Arjun Bagchi ◽  
Poulami Nandi ◽  
Amartya Saha ◽  
Zodinmawia
Keyword(s):  
Cosmological Solution ◽  
Three Dimensions ◽  
Field Theories ◽  
Point Function ◽  
Asymptotic Structure ◽  
Highest Weight ◽  
Structure Constants ◽  
Flat Spacetimes ◽  
Geodesic Approximation ◽  
Highest Weight Representation

Abstract Two dimensional field theories invariant under the Bondi-Metzner-Sachs (BMS) group are conjectured to be dual to asymptotically flat spacetimes in three dimensions. In this paper, we continue our investigations of the modular properties of these field theories. In particular, we focus on the BMS torus one-point function. We use two different methods to arrive at expressions for asymptotic structure constants for general states in the theory utilising modular properties of the torus one-point function. We then concentrate on the BMS highest weight representation, and derive a host of new results, the most important of which is the BMS torus block. In a particular limit of large weights, we derive the leading and sub-leading pieces of the BMS torus block, which we then use to rederive an expression for the asymptotic structure constants for BMS primaries. Finally, we perform a bulk computation of a probe scalar in the background of a flatspace cosmological solution based on the geodesic approximation to reproduce our field theoretic results.

scholarly journals Wind Accretion by Compact Objects: The “Flip-Flop” Instability

1992 ◽  
Vol 151 ◽  
pp. 185-194
Author(s):  
Mario Livio
Keyword(s):  
Random Walk ◽  
Accretion Rate ◽  
Compact Object ◽  
Two Dimensions ◽  
Compact Objects ◽  
Numerical Calculations ◽  
Three Dimensions ◽  
Flip Flop ◽  
Accretion Flows ◽  
The Stability

The problem of the stability of wind accretion onto compact objects is examined. Recent analytical and numerical calculations show that in two dimensions, Bondi-Hoyle accretion flows are unstable to a “flip-flop” instability. The instability can manifest itself as bursts in the accretion rate and as a random walk-type spin-up, spin-down behaviour of the accreting compact object. The nature of the flow in three dimensions needs further clarification. Possible observational implications are reviewed.

TURBULENT DIFFUSION IN TWO AND THREE DIMENSIONS BY THE RANDOM-WALK MODEL WITH MEMORY

1961 ◽  
Vol 39 (1) ◽  
pp. 133-140 ◽  
Author(s):  
R. C. Bourret
Keyword(s):  
Random Walk ◽  
Lattice Model ◽  
Turbulent Diffusion ◽  
Telegraph Equation ◽  
Three Dimensions ◽  
Autocorrelation Functions ◽  
Fine Grained ◽  
Velocity Autocorrelation ◽  
With Memory ◽  
Velocity Autocorrelation Functions

A lattice model used for the derivation of the telegraph equation for diffusion is extended to two and three dimensions. Appropriate generalizations of the telegraph equation are obtained. These equations give a fine-grained chronological description of diffusion. From these equations, the velocity autocorrelation functions of the diffusing particles are obtained.

scholarly journals Anomalies from correlation functions in defect conformal field theory

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Christopher P. Herzog ◽  
Itamar Shamir
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Effective Action ◽  
Three Dimensions ◽  
Two Dimensional ◽  
Point Function ◽  
Perfect Agreement ◽  
Conformal Field ◽  
Density Anomaly ◽  
The One

Abstract In previous work, we showed that an anomaly in the one point function of marginal operators is related by the Wess-Zumino condition to the Euler density anomaly on a two dimensional defect or boundary. Here we analyze in detail the two point functions of marginal operators with the stress tensor and with the displacement operator in three dimensions. We show how to get the boundary anomaly from these bulk two point functions and find perfect agreement with our anomaly effective action. For a higher dimensional conformal field theory with a four dimensional defect, we describe for the first time the anomaly effective action that relates the Euler density term to the one point function anomaly, generalizing our result for two dimensional defects.

scholarly journals The O(N ) model with ϕ6 potential in ℝ2 × ℝ+

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Christopher P. Herzog ◽  
Nozomu Kobayashi
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Stress Tensor ◽  
The Other ◽  
Three Dimensions ◽  
Planar Boundary ◽  
Point Function ◽  
Conformal Blocks ◽  
Boundary Limit ◽  
The Stability

Abstract We study the large N limit of O(N ) scalar field theory with classically marginal ϕ6 interaction in three dimensions in the presence of a planar boundary. This theory has an approximate conformal invariance at large N . We find different phases of the theory corresponding to different boundary conditions for the scalar field. Computing a one loop effective potential, we examine the stability of these different phases. The potential also allows us to determine a boundary anomaly coefficient in the trace of the stress tensor. We further compute the current and stress-tensor two point functions for the Dirichlet case and decompose them into boundary and bulk conformal blocks. The boundary limit of the stress tensor two point function allows us to compute the other boundary anomaly coefficient. Both anomaly coefficients depend on the approximately marginal ϕ6 coupling.

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