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 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.

scholarly journals Defect CFT techniques in the 6d $$ \mathcal{N} $$ = (2, 0) theory

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Nadav Drukker ◽  
Malte Probst ◽  
Maxime Trépanier
Keyword(s):  
Stress Tensor ◽  
Unitary Representations ◽  
Point Function ◽  
Displacement Operator ◽  
Expectation Value ◽  
Operator Expansion ◽  
Bulk Stress ◽  
Defect Operator ◽  
Tensor Multiplet

Abstract Surface operators are among the most important observables of the 6d $$ \mathcal{N} $$ N = (2, 0) theory. Here we apply the tools of defect CFT to study local operator insertions into the 1/2-BPS plane. We first relate the 2-point function of the displacement operator to the expectation value of the bulk stress tensor and translate this relation into a constraint on the anomaly coefficients associated with the defect. Secondly, we study the defect operator expansion of the stress tensor multiplet and identify several new operators of the defect CFT. Technical results derived along the way include the explicit supersymmetry tranformations of the stress tensor multiplet and the classification of unitary representations of the superconformal algebra preserved by the defect.

scholarly journals Hyperbolic cylinders and entanglement entropy: gravitons, higher spins, p-forms

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Justin R. David ◽  
Jyotirmoy Mukherjee
Keyword(s):  
Stress Tensor ◽  
Entanglement Entropy ◽  
Partition Functions ◽  
Point Function ◽  
Expectation Value ◽  
Massive Spin ◽  
Twist Operator ◽  
Higher Spins ◽  
Hyperbolic Cylinders ◽  
Kaluza Klein

Abstract We show that the entanglement entropy of D = 4 linearized gravitons across a sphere recently computed by Benedetti and Casini coincides with that obtained using the Kaluza-Klein tower of traceless transverse massive spin-2 fields on S1× AdS3. The mass of the constant mode on S1 saturates the Brietenholer-Freedman bound in AdS3. This condition also ensures that the entanglement entropy of higher spins determined from partition functions on the hyperbolic cylinder coincides with their recent conjecture. Starting from the action of the 2-form on S1× AdS5 and fixing gauge, we evaluate the entanglement entropy across a sphere as well as the dimensions of the corresponding twist operator. We demonstrate that the conformal dimensions of the corresponding twist operator agrees with that obtained using the expectation value of the stress tensor on the replica cone. For conformal p-forms in even dimensions it obeys the expected relations with the coefficients determining the 3-point function of the stress tensor of these fields.

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 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 Variational inequalities of Bingham type in three dimensions

1993 ◽  
Vol 129 ◽  
pp. 53-95 ◽  
Author(s):  
Yoshio Kato
Keyword(s):  
Variational Inequalities ◽  
Stress Tensor ◽  
Velocity Vector ◽  
Dimensional Space ◽  
Three Dimensions ◽  
Plastic Fluid

The flow of Bingham type through a domain Ω in the d-th dimensional space Rd (d ≥ 2) during the time (0, T) is a flow of an incompressible visco-plastic fluid governed by the equations for a velocity vector u = (u1,…,ud) and a stress tensor

scholarly journals Quantum fluctuation of stress tensor and black holes in three dimensions

1994 ◽  
Vol 49 (10) ◽  
pp. 5286-5294 ◽  
Author(s):  
Kiyoshi Shiraishi ◽  
Takuya Maki
Keyword(s):  
Black Holes ◽  
Stress Tensor ◽  
Quantum Fluctuation ◽  
Three Dimensions

scholarly journals A LUTTINGER LIQUID CORE INSIDE HELIUM-4 FILLED NANOPORES

2012 ◽  
Vol 26 (22) ◽  
pp. 1244002 ◽  
Author(s):  
ADRIAN DEL MAESTRO
Keyword(s):  
Quantum Monte Carlo ◽  
Large Scale ◽  
Liquid Core ◽  
Luttinger Liquid ◽  
Three Dimensions ◽  
Dimensional System ◽  
Hydrodynamic Description ◽  
One Dimensional ◽  
Helium 4 ◽  
State Of Matter

As helium-4 is cooled below 2.17 K it undergoes a phase transition to a fundamentally quantum mechanical state of matter known as a superfluid which supports flow without viscosity. This type of dissipationless transport can be observed by forcing helium to travel through a narrow constriction that the normal liquid could not penetrate. Recent experiments have highlighted the feasibility of fabricating smooth pores with nanometer radii, that approach the truly one-dimensional limit where it is believed that a system of bosons (like helium-4) may have startlingly different behavior than in three dimensions. The one-dimensional system is predicted to have a linear hydrodynamic description known as Luttinger liquid (LL) theory, where no type of long range order can be sustained. In the limit where the pore radius is small, LL theory would predict that helium inside the channel behaves as a sort of quasi-supersolid with all correlations decaying as power-law functions of distance at zero temperature. We have performed large scale quantum Monte Carlo simulations of helium-4 inside nanopores of varying radii at low temperature with realistic helium–helium and helium-pore interactions. The results indicate that helium inside the nanopore forms concentric cylindrical shells surrounding a core that can be described via LL theory and provides insights into the exciting possibility of the experimental detection of this intriguing low-dimensional state of matter.

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