scholarly journals Perturbative expansion around the Gaussian effective action: The background field method

1997 ◽  
Vol 56 (10) ◽  
pp. 6573-6578 ◽  
Author(s):  
Geon Hyoung Lee ◽  
Jae Hyung Yee
Keyword(s):  
Effective Action ◽  
Background Field ◽  
Field Method ◽  
Perturbative Expansion ◽  
Background Field Method

scholarly journals Relationship between Fujikawa’s Method and the Background Field Method for the Scale Anomaly

2016 ◽  
Vol 2016 ◽  
pp. 1-6 ◽  
Author(s):  
Chris L. Lin ◽  
Carlos R. Ordóñez
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Effective Potential ◽  
Effective Action ◽  
Background Field ◽  
Field Method ◽  
Scale Dependence ◽  
Classical Action ◽  
Loop Expansion ◽  
Background Field Method

We show the equivalence between Fujikawa’s method for calculating the scale anomaly and the diagrammatic approach to calculating the effective potential via the background field method, for anO(N)symmetric scalar field theory. Fujikawa’s method leads to a sum of terms, each one superficially in one-to-one correspondence with a vacuum diagram of the 1-loop expansion. From the viewpoint of the classical action, the anomaly results in a breakdown of the Ward identities due to scale-dependence of the couplings, whereas, in terms of the effective action, the anomaly is the result of the breakdown of Noether’s theorem due to explicit symmetry breaking terms of the effective potential.

THE BACKGROUND FIELD METHOD AND THE ANOMALIES OF THE HETEROTIC σ-MODEL IN A CURVED (1, 0) SUPERSPACE

1991 ◽  
Vol 06 (17) ◽  
pp. 2971-2998 ◽  
Author(s):  
S.V. KETOV ◽  
O.A. SOLOVIEV
Keyword(s):  
Effective Action ◽  
Background Field ◽  
Field Method ◽  
Low Energy ◽  
Heterotic String ◽  
Explicit Calculation ◽  
Two Dimensional ◽  
Gauge Bosons ◽  
Background Field Method ◽  
Background Fields

The covariant (in the σ-model sense) background field method for calculating the anomalies of the heterotic string propagating on the background of its massless modes is developed in a curved superspace of the two-dimensional (1, 0) supergravity. As the massless background fields, we use a metric, an antisymmetric tensor, a dilaton and gauge bosons. Explicit calculation of the anomalies up to five loops is performed and the results are found to be in agreement with the known facts about the heterotic string low-energy effective action. The dilaton-dependent corrections to the anomalies at the two- and three-loop levels are shown to be absent.

scholarly journals COMMENTS ON THE BACKGROUND FIELD METHOD IN HARMONIC SUPERSPACE: NON-HOLOMORPHIC CORRECTIONS IN N=4 SYM

1998 ◽  
Vol 13 (20) ◽  
pp. 1623-1635 ◽  
Author(s):  
IOSEPH L. BUCHBINDER ◽  
SERGEI M. KUZENKO
Keyword(s):  
Effective Action ◽  
Background Field ◽  
Field Method ◽  
Vector Multiplet ◽  
Harmonic Superspace ◽  
Background Field Method ◽  
Field Formalism ◽  
The One

We analyze the one-loop effective action of N=4 SYM theory in the framework of the bakground field formalism in N=2 harmonic superspace. For the case of onshell background N=2 vector multiplet we prove that the effective action is free of harmonic singularities. When the lowest N=1 superspace component of the N=2 vector multiplet is switched off, the effective action of N=4 SYM theory is shown to coincide with obtained by Grisaru et al. on the base of the N=1 background field method. We compute the leading non-holomorphic corrections to the N=4 SU (2) SYM effective action.

scholarly journals OPTIMIZED POST GAUSSIAN APPROXIMATION IN THE BACKGROUND FIELD METHOD

2004 ◽  
Vol 19 (10) ◽  
pp. 1589-1607 ◽  
Author(s):  
ABDULLA RAKHIMOV ◽  
JAE HYUNG YEE
Keyword(s):  
Effective Potential ◽  
Effective Action ◽  
Gaussian Approximation ◽  
Background Field ◽  
Field Method ◽  
New Method ◽  
Background Field Method ◽  
Gaussian Effective Potential ◽  
Correction Terms

We have extended the variational perturbative theory based on the background field method to include the optimized expansion of Okopinska and the post Gaussian effective potential of Stansu and Stevenson. This new method provides a much simpler way to compute the correction terms to the Gaussian effective action (or potential). We have also renormalized the effective potential in 3+1 dimensions by introducing appropriate counterterms in the Lagrangian.

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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