scholarly journals Integrability in sigma-models

2019 ◽  
pp. 205-247 ◽  
Author(s):  
K. Zarembo
Keyword(s):  
Sigma Models ◽  
Homogeneous Spaces ◽  
Beta Function ◽  
Background Field ◽  
Field Method ◽  
Two Dimensions ◽  
S Matrix ◽  
Background Field Method ◽  
Coset Models

The following topics are covered in this chapter: (1) Homogeneous spaces, (2) Classical integrability of sigma-models in two dimensions, (3) Topological terms, (4) Background-field method and beta-function, (5) S-matrix bootstrap in the O(N) model, (6) Supersymmetric coset models and strings on AdS(d) x X.

The background field method and the S-matrix

1983 ◽  
Vol 229 (2) ◽  
pp. 372-380 ◽  
Author(s):  
L.F. Abbott ◽  
M.T. Grisaru ◽  
R.K. Schaefer
Keyword(s):  
Background Field ◽  
Field Method ◽  
S Matrix ◽  
Background Field Method

scholarly journals Revisit of renormalization of Einstein-Maxwell theory at one-loop

2020 ◽  
Author(s):  
I Y Park
Keyword(s):  
Beta Function ◽  
Background Field ◽  
Field Method ◽  
Maxwell Theory ◽  
Vector Coupling ◽  
Gauge Choice ◽  
Graviton Propagator ◽  
Careful Handling ◽  
Background Field Method ◽  
Field Redefinition

Abstract In a series of the recent works based on foliation-based quantization in which renormalizability has been achieved for the physical sector of the theory, we have shown that the use of the standard graviton propagator interferes, due to the presence of the trace mode, with the 4D covariance. A subtlety in the background field method also requires careful handling. This status of the matter motivated us to revisit an Einstein-scalar system in one of the sequels. Continuing the endeavors, we revisit the one-loop renormalization of an Einstein-Maxwell system in the present work. The systematic renormalization of the cosmological and Newton’s constants is carried out by applying the refined background field method. One-loop beta function of the vector coupling constant is explicitly computed and compared with the literature. The longstanding problem of gauge choice-dependence of the effective action is addressed and the manner in which the gauge-choice independence is restored in the present framework is discussed. The formalism also sheds light on background independent analysis. The renormalization involves a metric field redefinition originally introduced by ‘t Hooft; with the field redefinition the theory should be predictive.

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.

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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