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 CANCELLATION OF UV DIVERGENCES IN THE ${\mathcal N} = 4$ SUSY NONLINEAR SIGMA MODEL IN THREE DIMENSIONS

2001 ◽  
Vol 16 (25) ◽  
pp. 1643-1650 ◽  
Author(s):  
TAKEO INAMI ◽  
YORINORI SAITO ◽  
MASAYOSHI YAMAMOTO
Keyword(s):  
Cotangent Bundle ◽  
Sigma Model ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Target Space ◽  
Quantum Corrections ◽  
Nonlinear Sigma Model ◽  
Leading Order ◽  
Β Function

We study the uv properties of the three-dimensional [Formula: see text] SUSY nonlinear sigma model whose target space is T*(CPN-1) (the cotangent bundle of CPN-1) to higher orders in the 1/N expansion. We calculate the β-function to next-to-leading order and verify that it has no quantum corrections at leading and next-to-leading orders.

Joint inversion of seismic traveltime and frequency-domain airborne electromagnetic data for hydrocarbon exploration

Geophysics ◽  
2018 ◽  
Vol 83 (2) ◽  
pp. U9-U22 ◽  
Author(s):  
Jide Nosakare Ogunbo ◽  
Guy Marquis ◽  
Jie Zhang ◽  
Weizhong Wang
Keyword(s):  
Frequency Domain ◽  
Joint Inversion ◽  
Sedimentary Environment ◽  
Computational Cost ◽  
Velocity Model ◽  
Two Dimensions ◽  
Hydrocarbon Exploration ◽  
Three Dimensions ◽  
Data Sets ◽  
The One

Geophysical joint inversion requires the setting of a few parameters for optimum performance of the process. However, there are yet no known detailed procedures for selecting the various parameters for performing the joint inversion. Previous works on the joint inversion of electromagnetic (EM) and seismic data have reported parameter applications for data sets acquired from the same dimensional geometry (either in two dimensions or three dimensions) and few on variant geometry. But none has discussed the parameter selections for the joint inversion of methods from variant geometry (for example, a 2D seismic travel and pseudo-2D frequency-domain EM data). With the advantage of affordable computational cost and the sufficient approximation of a 1D EM model in a horizontally layered sedimentary environment, we are able to set optimum joint inversion parameters to perform structurally constrained joint 2D seismic traveltime and pseudo-2D EM data for hydrocarbon exploration. From the synthetic experiments, even in the presence of noise, we are able to prescribe the rules for optimum parameter setting for the joint inversion, including the choice of initial model and the cross-gradient weighting. We apply these rules on field data to reconstruct a more reliable subsurface velocity model than the one obtained by the traveltime inversions alone. We expect that this approach will be useful for performing joint inversion of the seismic traveltime and frequency-domain EM data for the production of hydrocarbon.

scholarly journals ELECTRODYNAMICS IN A BACKGROUND CHIRAL FIELD

2011 ◽  
Vol 26 (38) ◽  
pp. 2879-2887
Author(s):  
F. T. BRANDT ◽  
D. G. C. MCKEON ◽  
A. PATRUSHEV
Keyword(s):  
Vector Field ◽  
Euclidean Space ◽  
Effective Action ◽  
Exact Expression ◽  
Two Dimensions ◽  
Perturbative Expansion ◽  
Dimensional Euclidean Space ◽  
Chiral Field ◽  
Axial Field ◽  
The One

We consider the one-loop effective action in four-dimensional Euclidean space for a background chiral field coupled to a spinor field. It proves possible to find an exact expression for this action if the mass m of the spinor vanishes. If m does not vanish, one can make a perturbative expansion in powers of the axial field that contributes to the chiral field, while treating the contribution of the vector field exactly when it is a constant. The analogous problem in two dimensions is also discussed.

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 On the finiteness of the SUSY nonlinear sigma model in three dimensions

2000 ◽  
Vol 495 (1-2) ◽  
pp. 245-250 ◽  
Author(s):  
Takeo Inami ◽  
Yorinori Saito ◽  
Masayoshi Yamamoto
Keyword(s):  
Sigma Model ◽  
Three Dimensions ◽  
Nonlinear Sigma Model

THE BOSONIC SIGMA MODEL ON A TOROIDAL SURFACE

2004 ◽  
Vol 19 (16) ◽  
pp. 2713-2720
Author(s):  
D. G. C. McKEON
Keyword(s):  
Riemannian Manifold ◽  
Sigma Model ◽  
Three Dimensional ◽  
The Other ◽  
Target Space ◽  
Dimensional Euclidean Space ◽  
Nonlinear Sigma Model ◽  
Two Dimensional ◽  
Toroidal Surface ◽  
Spherical Basis

The nonlinear sigma model with a two-dimensional basis space and an n-dimensional target space is considered. Two different basis spaces are considered; the first is an 0(2)×0(2) subspace of the 0(2,2) projective space related to the Minkowski basis space, and the other is a toroidal space embedded into three-dimensional Euclidean space, characterized by radii R and r. The target space is taken to be an arbitrarily curved Riemannian manifold. One-loop dependence on the renormalization induced scale μ is shown in the toroidal basis space to be the same as in a flat or spherical basis space.

RENORMALIZATION GROUP FLOW AND OPEN STRING DYNAMICS

1988 ◽  
Vol 03 (18) ◽  
pp. 1797-1805 ◽  
Author(s):  
NAOHITO NAKAZAWA ◽  
KENJI SAKAI ◽  
JIRO SODA
Keyword(s):  
Renormalization Group ◽  
Sigma Model ◽  
Open String ◽  
Tree Level ◽  
Nonlinear Sigma Model ◽  
Renormalization Group Flow ◽  
Point Solution ◽  
Β Function ◽  
Group Flow ◽  
Model Approach

The renormalization group flow in the nonlinear sigma model approach is explicitly solved to the fourth order in the case of an open string propagating in the tachyon background. Using a regularization different from the original one used by Klebanov and Susskind (K-S), we show that its fixed point solution produces the tree-level 5-point tachyon amplitude. Furthermore we prove K-S’s conjecture, i.e., the equivalence between the vanishing β-function defined by our regularization and the equation of motion arising from the effective action, up to all orders.

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.

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