scholarly journals Flow equation of N $$ \mathcal{N} $$ = 1 supersymmetric O(N ) nonlinear sigma model in two dimensions

2018 ◽  
Vol 2018 (2) ◽  
Author(s):  
Sinya Aoki ◽  
Kengo Kikuchi ◽  
Tetsuya Onogi
Keyword(s):  
Sigma Model ◽  
Flow Equation ◽  
Two Dimensions ◽  
Nonlinear Sigma Model

STOCHASTIC QUANTIZATION AND 1/N EXPANSION

1993 ◽  
Vol 08 (02) ◽  
pp. 115-128
Author(s):  
J.C. BRUNELLI ◽  
R.S. MENDES
Keyword(s):  
Perturbation Theory ◽  
Sigma Model ◽  
Functional Approach ◽  
Two Dimensions ◽  
Field Theories ◽  
Nonlinear Sigma Model ◽  
Stochastic Quantization ◽  
Quantization Method ◽  
Systematic Procedure

We study the 1/N expansion of field theories in the stochastic quantization method of Parisi and Wu using the supersymmetric functional approach. This formulation provides a systematic procedure to implement the 1/N expansion which resembles the ones used in the equilibrium. The 1/N perturbation theory for the nonlinear sigma-model in two dimensions is worked out as an example.

scholarly journals Statistical inference and string theory

2015 ◽  
Vol 30 (26) ◽  
pp. 1550160 ◽  
Author(s):  
Jonathan J. Heckman
Keyword(s):  
String Theory ◽  
Statistical Inference ◽  
Sigma Model ◽  
Two Dimensions ◽  
Nonlinear Sigma Model ◽  
Dimensional Manifold ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Lorentzian Signature ◽  
Stability Under Perturbations

In this paper, we expose some surprising connections between string theory and statistical inference. We consider a large collective of agents sweeping out a family of nearby statistical models for an [Formula: see text]-dimensional manifold of statistical fitting parameters. When the agents making nearby inferences align along a [Formula: see text]-dimensional grid, we find that the pooled probability that the collective reaches a correct inference is the partition function of a nonlinear sigma model in [Formula: see text] dimensions. Stability under perturbations to the original inference scheme requires the agents of the collective to distribute along two dimensions. Conformal invariance of the sigma model corresponds to the condition of a stable inference scheme, directly leading to the Einstein field equations for classical gravity. By summing over all possible arrangements of the agents in the collective, we reach a string theory. We also use this perspective to quantify how much an observer can hope to learn about the internal geometry of a superstring compactification. Finally, we present some brief speculative remarks on applications to the AdS/CFT correspondence and Lorentzian signature space–times.

THE BOSONIC SIGMA MODEL ON A COMPACT SURFACE

1990 ◽  
Vol 05 (25) ◽  
pp. 2031-2037 ◽  
Author(s):  
M. LEBLANC ◽  
P. MADSEN ◽  
R. B. MANN ◽  
D. G. C. McKEON
Keyword(s):  
Sigma Model ◽  
Stereographic Projection ◽  
Two Dimensions ◽  
Compact Surface ◽  
Three Dimensions ◽  
Dimensional Euclidean Space ◽  
Nonlinear Sigma Model ◽  
Β Function ◽  
The One ◽  
Infrared Divergences

A stereographic projection is used to map the bosonic nonlinear sigma model with torsion from two-dimensional Euclidean space onto a sphere-S2 embedded in three dimensions. The one-loop β-function of the torsionless σ-model is determined using operator regularization to handle ultraviolet divergences. Only by excluding the lowest eigenstate of the rotation operator on the sphere can the usual β-function be recovered; inclusion of this eigenstate leads to severe infrared divergences. Both the ultraviolet and infrared divergences can be regulated by working in n, rather than two, dimensions, in which case the contribution of the lowest mode cancels exactly against the contribution of all other modes, resulting in a vanishing β-function.

scholarly journals NONCOMMUTATIVE U(1) GAUGE THEORY AS A NONLINEAR SIGMA MODEL

2004 ◽  
Vol 19 (29) ◽  
pp. 2205-2213 ◽  
Author(s):  
BADIS YDRI
Keyword(s):  
Gauge Theory ◽  
Sigma Model ◽  
Beta Function ◽  
Scaling Limit ◽  
Two Dimensions ◽  
Nonlinear Sigma Model ◽  
Matrix Size ◽  
Gauge Groups ◽  
Four Dimensions ◽  
The Matrix

Noncommutative U (1) gauge theory in four dimensions is shown to be equivalent in some scaling limit to an ordinary nonlinear sigma model in two dimensions. The model in this regime is solvable and the corresponding exact beta function is found. We also show that classical U (n) gauge theory on [Formula: see text] can be approximated by a sequence of ordinary (d-2)-dimensional Georgi–Glashow models with gauge groups U (n(L+1)), where L+1 is the matrix size of the regularized noncommutative plane [Formula: see text].

scholarly journals N=2 Supersymmetry with Central Charge: A Twofold Implementation

2019 ◽  
Vol 2019 ◽  
pp. 1-9
Author(s):  
L. P. R. Ospedal ◽  
R. C. Terin
Keyword(s):  
Sigma Model ◽  
Central Charge ◽  
Classical Mechanics ◽  
Theoretical Framework ◽  
Two Dimensions ◽  
Nonlinear Sigma Model ◽  
Two Dimensional ◽  
One Dimensional ◽  
Matter Model

In this work, we analyze an extended N=2 supersymmetry with central charge and develop its superspace formulation under two distinct viewpoints. Initially, in the context of classical mechanics, we discuss the introduction of deformed supersymmetric derivatives and their consequence on the deformation of one-dimensional nonlinear sigma model. After that, considering a field-theoretical framework, we present an implementation of this superalgebra in two dimensions, such that one of the coordinates is related to the central charge. As an application, in this two-dimensional scenario, we consider topological (bosonic) configurations of a special self-coupled matter model and present a nontrivial fermionic solution.

scholarly journals Symmetry restoration and the gluon mass in the Landau gauge

2021 ◽  
Vol 10 (2) ◽  
Author(s):  
Urko Reinosa ◽  
Julien Serreau ◽  
Rodrigo Carmo Terin ◽  
Matthieu Tissier
Keyword(s):  
Field Theory ◽  
Sigma Model ◽  
Landau Gauge ◽  
Two Dimensions ◽  
Nonlinear Sigma Model ◽  
Yang Mills ◽  
Local Field Theory ◽  
Gauge Fixing ◽  
Gribov Ambiguity ◽  
Gribov Copies

We investigate the generation of a gluon screening mass in Yang-Mills theory in the Landau gauge. We propose a gauge-fixing procedure where the Gribov ambiguity is overcome by summing over all Gribov copies with some weight function. This can be formulated in terms of a local field theory involving constrained, nonlinear sigma model fields. We show that a phenomenon of radiative symmetry restoration occurs in this theory, similar to what happens in the standard nonlinear sigma model in two dimensions. This results in a nonzero gluon screening mass, as seen in lattice simulations.

scholarly journals Some applications of Ricci flow in physics

2008 ◽  
Vol 86 (4) ◽  
pp. 645-651 ◽  
Author(s):  
E Woolgar
Keyword(s):  
General Relativity ◽  
Renormalization Group ◽  
Ricci Flow ◽  
Sigma Model ◽  
Final Section ◽  
Higher Dimensions ◽  
Ricci Soliton ◽  
Two Dimensions ◽  
Nonlinear Sigma Model

I discuss certain applications of the Ricci flow in physics. I first review how it arises in the renormalization group (RG) flow of a nonlinear sigma model. I then review the concept of a Ricci soliton and recall how a soliton was used to discuss the RG flow of mass in two dimensions. I then present recent results obtained with Oliynyk on the flow of mass in higher dimensions. The final section discusses how Ricci flow may arise in general relativity, particularly for static metrics.PACS Nos.: 02.40Ky, 02.30Ik, 04.20.–q

scholarly journals Strings in bimetric spacetimes

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Ziqi Yan
Keyword(s):  
Gravitational Field ◽  
Sigma Model ◽  
Flow Equation ◽  
Target Space ◽  
Nonlinear Sigma Model ◽  
Field Equations ◽  
Gravitational Field Equations ◽  
Weyl Invariance ◽  
Massless Spin ◽  
Renormalization Group Flows

Abstract We put forward a two-dimensional nonlinear sigma model that couples (bosonic) matter fields to topological Hořava gravity on a nonrelativistic worldsheet. In the target space, this sigma model describes classical strings propagating in a curved spacetime background, whose geometry is described by two distinct metric fields. We evaluate the renormalization group flows of this sigma model on a flat worldsheet and derive a set of beta-functionals for the bimetric fields. Imposing worldsheet Weyl invariance at the quantum level, we uncover a set of gravitational field equations that dictate the dynamics of the bimetric fields in the target space, where a unique massless spin-two excitation emerges. When the bimetric fields become identical, the sigma model gains an emergent Lorentz symmetry. In this single metric limit, the beta-functionals of the bimetric fields reduce to the Ricci flow equation that arises in bosonic string theory, and the bimetric gravitational field equations give rise to Einstein’s gravity.

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