Stochastic quantization of the nonlinear sigma model and the background field method

1994 ◽  
Vol 33 (6) ◽  
pp. 1241-1250
Author(s):  
E. Abdalla ◽  
F. M. de Carvalho Filho ◽  
Ricardo L. Viana
Keyword(s):  
Sigma Model ◽  
Background Field ◽  
Field Method ◽  
Nonlinear Sigma Model ◽  
Stochastic Quantization ◽  
Background Field Method

scholarly journals Beta functions for the duality-invariant sigma model

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
Roberto Bonezzi ◽  
Tomas Codina ◽  
Olaf Hohm
Keyword(s):  
String Theory ◽  
Sigma Models ◽  
Sigma Model ◽  
Equations Of Motion ◽  
Background Field ◽  
Field Method ◽  
Bosonic String ◽  
Two Dimensional ◽  
Background Field Method ◽  
Bosonic String Theory

Abstract The O(d, d) invariant worldsheet theory for bosonic string theory with d abelian isometries is employed to compute the beta functions and Weyl anomaly at one-loop. We show that vanishing of the Weyl anomaly coefficients implies the equations of motion of the Maharana-Schwarz action. We give a self-contained introduction into the required techniques, including beta functions, the Weyl anomaly for two-dimensional sigma models and the background field method. This sets the stage for a sequel to this paper on generalizations to higher loops and α′ corrections.

SUPERSPACE FORMULATION OF STOCHASTIC BACKGROUND FIELD METHOD

1989 ◽  
Vol 04 (06) ◽  
pp. 569-579 ◽  
Author(s):  
NAOHITO NAKAZAWA
Keyword(s):  
Background Field ◽  
Field Method ◽  
General Covariance ◽  
Stochastic Quantization ◽  
Stochastic Background ◽  
Background Field Method

We formulate the background field method for a nonlinear σ-model in stochastic quantization based on the superspace formulation. In addition to the general covariance, the BRS invariance of the system is manifestly maintained in our formulation.

scholarly journals NONCOMMUTATIVITY AND NON-ANTICOMMUTATIVITY PERTURBATIVE QUANTUM GRAVITY

2012 ◽  
Vol 27 (13) ◽  
pp. 1250075 ◽  
Author(s):  
MIR FAIZAL
Keyword(s):  
Quantum Gravity ◽  
Lagrangian Density ◽  
Background Field ◽  
Field Method ◽  
Gauge Fixing ◽  
Perturbative Quantum ◽  
Background Field Method

In this paper, we will study perturbative quantum gravity on supermanifolds with both noncommutativity and non-anticommutativity of spacetime coordinates. We shall first analyze the BRST and the anti-BRST symmetries of this theory. Then we will also analyze the effect of shifting all the fields of this theory in background field method. We will construct a Lagrangian density which apart from being invariant under the extended BRST transformations is also invariant under on-shell extended anti-BRST transformations. This will be done by using the Batalin–Vilkovisky (BV) formalism. Finally, we will show that the sum of the gauge-fixing term and the ghost term for this theory can be elegantly written down in superspace with a two Grassmann parameter.

scholarly journals FIELD DECOMPOSITION AND THE GROUND STATE STRUCTURE OF SU(2) YANG–MILLS THEORY

2002 ◽  
Vol 17 (25) ◽  
pp. 3681-3688 ◽  
Author(s):  
LISA FREYHULT
Keyword(s):  
Effective Potential ◽  
Ground State ◽  
Scalar Fields ◽  
Background Field ◽  
Field Method ◽  
Gauge Fields ◽  
Ground State Structure ◽  
State Structure ◽  
Yang Mills ◽  
Background Field Method

We compute the effective potential of SU(2) Yang–Mills theory using the background field method and the Faddeev–Niemi decomposition of the gauge fields. In particular, we find that the potential will depend on the values of two scalar fields in the decomposition and that its structure will give rise to a symmetry breaking.

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