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.

SCALAR FIELD THEORY IN THE AdS/CFT CORRESPONDENCE: AN OPERATOR FORMULATION

2007 ◽  
Vol 22 (30) ◽  
pp. 2287-2295 ◽  
Author(s):  
G. A. KERIMOV
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Scalar Fields ◽  
De Sitter Space ◽  
De Sitter ◽  
Point Function ◽  
Scalar Field Theory ◽  
Arbitrary Mass ◽  
Boundary Limit ◽  
Operator Formulation

Starting with a scalar field theory in Euclidean anti-de Sitter space constructed in an earlier paper, we examine the boundary limit of the quantized bulk field. Our AdS/CFT correspondence is generally valid for interacting fields, and is illustrated by a treatment of three-point function for scalar fields of arbitrary mass.

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 A smooth constant-roll to a slow-roll modular inflation transition

2018 ◽  
Vol 27 (02) ◽  
pp. 1850009 ◽  
Author(s):  
V. K. Oikonomou
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Dynamical Evolution ◽  
Smooth Transition ◽  
The Novel ◽  
Scalar Theory ◽  
Stability Properties ◽  
Slow Roll ◽  
Stable Attractor ◽  
The Stability

In this work, we investigate how a smooth transition from a constant-roll to a slow-roll inflationary era may be realized in the context of a canonical scalar field theory. We study in some detail the dynamical evolution of the cosmological system, and we investigate whether a stable attractor exists, both numerically and analytically. We also investigate the slow-roll era and as we demonstrate, the partially compatibility of the resulting scalar theory may be achieved with the potential of the latter belonging to a class of modular inflationary potentials. The novel features of the constant-roll to slow-roll transition which we achieved are firstly that it is not compelling for the slow-roll era to last for [Formula: see text]–60 [Formula: see text]-foldings, but it may last for a smaller number of [Formula: see text]-foldings, since some [Formula: see text]-foldings may occur during the constant-roll era. Secondly, when the slow-roll era occurs after the constant-roll era, the graceful exit from inflation may occur, a feature absent in the constant-roll scenario, due to the stability properties of the final attractor in the constant-roll case.

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.

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).

Metastable vacua in quantum field theory (QFT)

2021 ◽  
pp. 919-941
Author(s):  
Jean Zinn-Justin
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Scalar Field ◽  
Imaginary Part ◽  
Classical Limit ◽  
Three Dimensions ◽  
Quantum Field ◽  
Field Equations ◽  
Barrier Penetration ◽  
General Scalar

The methods to evaluate barrier penetration effects, in the semi-classical limit are generalized to quantum field theory (QFT). Since barrier penetration is associated with classical motion in imaginary time, the QFT is considered in its Euclidean formulation. In the representation of QFT in terms of field integrals, in the semi-classical limit, barrier penetration is related to finite action solutions (instantons) of the classical field equations. The evaluation of instanton contributions at leading order is explained, the main new problem arising from ultraviolet divergences. The lifetime of metastable states is related to the imaginary part of the ‘ground state’ energy. However, for later purpose, it is useful to calculate the imaginary part not only of the vacuum amplitude, but also of correlation functions. In the case of the vacuum amplitude, the instanton contribution is proportional to the space–time volume. Therefore, dividing by the volume, one obtains the probability per unit time and unit volume of a metastable pseudo-vacuum to decay. A scalar field theory with a φ4 interaction, generalization of the quartic anharmonic oscillator is discussed in two and three dimensions, dimensions in which the theory is super-renormalizable, then more general scalar field theories are considered.

scholarly journals Field Equations and Lagrangian for the Kaluza Metric Evaluated with Tensor Algebra Software

2015 ◽  
Vol 2015 ◽  
pp. 1-6 ◽  
Author(s):  
L. L. Williams
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Computer Algebra ◽  
Data File ◽  
The Other ◽  
Tensor Algebra ◽  
Field Equations ◽  
Scalar Field Theory ◽  
Computer Package ◽  
Self Consistency

This paper calculates the Kaluza field equations with the aid of a computer package for tensor algebra, xAct. The xAct file is provided with this paper. We find that Thiry’s field equations are correct, but only under limited circumstances. The full five-dimensional field equations under the cylinder condition are provided here, and we see that most of the other references miss at least some terms from them. We go on to establish the remarkable Kaluza Lagrangian, and verify that the field equations calculated from it match those calculated with xAct, thereby demonstrating self-consistency of these results. Many of these results can be found scattered throughout the literature, and we provide some pointers for historical purposes. But our intent is to provide a definitive exposition of the field equations of the classical, five-dimensional metric ansatz of Kaluza, along with the computer algebra data file to verify them, and then to recover the unique Lagrangian for the theory. In common terms, the Kaluza theory is an “ω=0” scalar field theory, but with unique electrodynamic couplings.

scholarly journals GRAVITATIONAL RENORMALIZATION OF QUANTUM FIELD THEORY

2012 ◽  
Vol 27 (32) ◽  
pp. 1250186 ◽  
Author(s):  
ROBERTO CASADIO
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Scalar Field ◽  
Feynman Graph ◽  
The Other ◽  
Quantum Field ◽  
High Momentum ◽  
Feynman Propagator ◽  
Virtual Particle ◽  
Virtual Particles

We propose to include gravity in quantum field theory nonperturbatively, by modifying the propagators so that each virtual particle in a Feynman graph move in the space–time determined by the four-momenta of the other particles in the same graph. By making additional working assumptions, we are able to put this idea at work in a simplified context, and obtain a modified Feynman propagator for the massless neutral scalar field. Our expression shows a suppression at high momentum, strong enough to entail finite results, to all loop orders, for processes involving at least two virtual particles.

scholarly journals Polymer quantization, stability and higher-order time derivative terms

2016 ◽  
Vol 31 (09) ◽  
pp. 1650040 ◽  
Author(s):  
Patricio Cumsille ◽  
Carlos M. Reyes ◽  
Sebastian Ossandon ◽  
Camilo Reyes
Keyword(s):  
Field Theory ◽  
Stability Problem ◽  
Time Derivative ◽  
Negative Energy ◽  
Higher Order ◽  
The Other ◽  
Harmonic Oscillators ◽  
Positive Energy ◽  
Quantum Field ◽  
The Stability

The possibility that fundamental discreteness implicit in a quantum gravity theory may act as a natural regulator for ultraviolet singularities arising in quantum field theory has been intensively studied. Here, along the same expectations, we investigate whether a nonstandard representation called polymer representation can smooth away the large amount of negative energy that afflicts the Hamiltonians of higher-order time derivative theories, rendering the theory unstable when interactions come into play. We focus on the fourth-order Pais–Uhlenbeck model which can be reexpressed as the sum of two decoupled harmonic oscillators one producing positive energy and the other negative energy. As expected, the Schrödinger quantization of such model leads to the stability problem or to negative norm states called ghosts. Within the framework of polymer quantization we show the existence of new regions where the Hamiltonian can be defined well bounded from below.

Sign in / Sign up

Export Citation Format

Share Document