Expansion of the one-loop effective action in covariant derivatives

1986 ◽  
Vol 33 (12) ◽  
pp. 3645-3653 ◽  
Author(s):  
Josef A. Zuk
Keyword(s):  
Effective Action ◽  
Covariant Derivatives ◽  
The One

scholarly journals On a structure of the one-loop divergences in 4D harmonic superspace sigma-model

2022 ◽  
Vol 82 (1) ◽  
Author(s):  
I. L. Buchbinder ◽  
A. S. Budekhina ◽  
B. S. Merzlikin
Keyword(s):  
Effective Action ◽  
Sigma Model ◽  
Proper Time ◽  
Kähler Manifold ◽  
Quantum Structure ◽  
Harmonic Superspace ◽  
Component Structure ◽  
Covariant Derivatives ◽  
The One ◽  
Quantum Splitting

AbstractWe study the quantum structure of four-dimensional $${{\mathcal {N}}}=2$$ N = 2 superfield sigma-model formulated in harmonic superspace in terms of the omega-hypermultiplet superfield $$\omega $$ ω . The model is described by harmonic superfield sigma-model metric $$g_{ab}(\omega )$$ g ab ( ω ) and two potential-like superfields $$L^{++}_{a}(\omega )$$ L a + + ( ω ) and $$L^{(+4)}(\omega )$$ L ( + 4 ) ( ω ) . In bosonic component sector this model describes some hyper-Kähler manifold. The manifestly $${{\mathcal {N}}}=2$$ N = 2 supersymmetric covariant background-quantum splitting is constructed and the superfield proper-time technique is developed to calculate the one-loop effective action. The one-loop divergences of the superfield effective action are found for arbitrary $$g_{ab}(\omega ), L^{++}_{a}(\omega ), L^{(+4)}(\omega )$$ g ab ( ω ) , L a + + ( ω ) , L ( + 4 ) ( ω ) , where some specific analogy between the algebra of covariant derivatives in the sigma-model and the corresponding algebra in the $${{\mathcal {N}}}=2$$ N = 2 SYM theory is used. The component structure of divergences in the bosonic sector is discussed.

scholarly journals Supergraph calculation of one-loop divergences in higher-derivative 6D SYM theory

2020 ◽  
Vol 2020 (8) ◽  
Author(s):  
I. L. Buchbinder ◽  
E. A. Ivanov ◽  
B. S. Merzlikin ◽  
K. V. Stepanyantz
Keyword(s):  
Effective Action ◽  
A Priori ◽  
Coupling Constant ◽  
Harmonic Superspace ◽  
Classical Action ◽  
Higher Derivative ◽  
Component Approach ◽  
Dimensionless Coupling ◽  
The One ◽  
Dimensionless Coupling Constant

Abstract We apply the harmonic superspace approach for calculating the divergent part of the one-loop effective action of renormalizable 6D, $$ \mathcal{N} $$ N = (1, 0) supersymmetric higher-derivative gauge theory with a dimensionless coupling constant. Our consideration uses the background superfield method allowing to carry out the analysis of the effective action in a manifestly gauge covariant and $$ \mathcal{N} $$ N = (1, 0) supersymmetric way. We exploit the regularization by dimensional reduction, in which the divergences are absorbed into a renormalization of the coupling constant. Having the expression for the one-loop divergences, we calculate the relevant β-function. Its sign is specified by the overall sign of the classical action which in higher-derivative theories is not fixed a priori. The result agrees with the earlier calculations in the component approach. The superfield calculation is simpler and provides possibilities for various generalizations.

THE VILKOVISKY EFFECTIVE ACTION IN THE EVEN-DIMENSIONAL QUANTUM GRAVITY

1989 ◽  
Vol 04 (07) ◽  
pp. 633-644 ◽  
Author(s):  
I. L. BUCHBINDER ◽  
E. N. KIRILLOVA ◽  
S. D. ODINTSOV
Keyword(s):  
Numerical Calculation ◽  
Effective Potential ◽  
Effective Action ◽  
Equations Of Motion ◽  
Flat Space ◽  
Einstein Gravity ◽  
Quantum Field ◽  
Dimensional Torus ◽  
Spontaneous Compactification ◽  
The One

The one-loop Vilkovisky effective potential which is not dependent on a gauge and a parametrization of quantum field, is investigated. We have considered Einstein gravity on a background manifold of (flat space) × (d−4- sphere) or × (d−4- dimensional torus ), d is even, and of R3 × (1- sphere ), where R3 is flat space. The numerical calculation for the cases R4 × Td−4 (d = 6,8,10) and R3 × S1 is done. The solution to the one-loop corrected equations of motion is found, although the spontaneous compactification is not stable in these cases.

scholarly journals Nonperturbative one-loop effective action for QED with Yukawa couplings

2018 ◽  
Vol 33 (27) ◽  
pp. 1850157 ◽  
Author(s):  
Theodore N. Jacobson ◽  
Tonnis ter Veldhuis
Keyword(s):  
Effective Action ◽  
Proper Time ◽  
Background Field ◽  
Field Approximation ◽  
Chiral Anomaly ◽  
Dirac Fermion ◽  
Yukawa Couplings ◽  
Time Formalism ◽  
The One ◽  
The Relationship

We derive the one-loop effective action for scalar, pseudoscalar, and electromagnetic fields coupled to a Dirac fermion in an extension of QED with Yukawa couplings. Using the Schwinger proper-time formalism and zeta-function regularization, we calculate the full nonperturbative effective action to one loop in the constant background field approximation. Our result is nonperturbative in the external fields, and goes beyond existing results in the literature which treat only the first nontrivial order involving the pseudoscalar. The result has an even and odd part, which are related to the modulus and phase of the fermion functional determinant. The even contribution to the effective action involves the modulus of the effective Yukawa couplings and is invariant under global chiral transformations while the odd contribution is proportional to the angle between the scalar and pseudoscalar couplings. In different limits the effective action reduces either to the Euler–Heisenberg effective action or the Coleman–Weinberg potential. We also comment on the relationship between the odd part of the effective action and the chiral anomaly in QED.

scholarly journals Radiative corrections in 2 + 1 dimensional supergravity

2018 ◽  
Vol 96 (12) ◽  
pp. 1409-1412 ◽  
Author(s):  
D.G.C. McKeon
Keyword(s):  
Gauge Theory ◽  
Radiative Correction ◽  
Effective Action ◽  
Spin Connection ◽  
Dynamical Generation ◽  
Effective Lagrangian ◽  
Majorana Spinor ◽  
The One ◽  
Brst Invariance ◽  
Topological Mass

Supergravity in 2 + 1 dimensions has a set of first-class constraints that result in two bosonic and one fermionic gauge invariances. When one uses Faddeev–Popov quantization, these gauge invariances result in four fermionic scalar ghosts and two bosonic Majorana spinor ghosts. The BRST invariance of the effective Lagrangian is found. As an example of a radiative correction, we compute the phase of the one-loop effective action in the presence of a background spin connection, and show that it vanishes. This indicates that unlike a spinor coupled to a gauge field in 2 + 1 dimensions, there is no dynamical generation of a topological mass in this model. An additional example of how a BRST invariant effective action can arise in a gauge theory is provided in Appendix B where the BRST effective action for the classical Palatini action in 1 + 1 dimensions is examined.

scholarly journals Paramagnetic versus Diamagnetic Interaction in the SU(2) Higgs Model

Symmetry ◽  
2019 ◽  
Vol 11 (10) ◽  
pp. 1237
Author(s):  
Dmitry Antonov
Keyword(s):  
Gauge Boson ◽  
Effective Action ◽  
Dimensional Reduction ◽  
Higgs Model ◽  
Analytic Calculation ◽  
Standard Result ◽  
Correlation Lengths ◽  
Yang Mills ◽  
Diamagnetic Contribution ◽  
The One

We present an analytic calculation of the paramagnetic and diamagnetic contributions to the one-loop effective action in the SU(2) Higgs model. The paramagnetic contribution is produced by the gauge boson, while the diamagnetic contribution is produced by the gauge boson and the ghost. In the limit, where these particles are massless, the standard result of - 12 for the ratio of the paramagnetic to the diamagnetic contribution is reproduced. If the mass of the gauge boson and the ghost become much larger than the inverse vacuum correlation lengths of the Yang–Mills vacuum, the value of the ratio goes to - 8 . We also find that the same values of the ratio are achieved in the deconfinement phase of the model, up to the temperatures at which the dimensional reduction occurs.

scholarly journals EULER–HEISENBERG LAGRANGIAN THROUGH KREIN REGULARIZATION

2013 ◽  
Vol 28 (14) ◽  
pp. 1350056 ◽  
Author(s):  
A. REFAEI
Keyword(s):  
Electromagnetic Field ◽  
Effective Action ◽  
Light Cone ◽  
Krein Space ◽  
Renormalization Procedure ◽  
Constant Electromagnetic Field ◽  
Kreĭn Space ◽  
The One ◽  
Convergent Solution ◽  
Krein Regularization

The Euler–Heisenberg effective action at the one-loop for a constant electromagnetic field is derived in Krein space quantization with Ford's idea of fluctuated light-cone. In this work, we present a perturbative but convergent solution of the effective action. Without using any renormalization procedure, the result coincides with the famous renormalized Euler–Heisenberg action.

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.

scholarly journals Anomalies from correlation functions in defect conformal field theory

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Christopher P. Herzog ◽  
Itamar Shamir
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Effective Action ◽  
Three Dimensions ◽  
Two Dimensional ◽  
Point Function ◽  
Perfect Agreement ◽  
Conformal Field ◽  
Density Anomaly ◽  
The One

Abstract In previous work, we showed that an anomaly in the one point function of marginal operators is related by the Wess-Zumino condition to the Euler density anomaly on a two dimensional defect or boundary. Here we analyze in detail the two point functions of marginal operators with the stress tensor and with the displacement operator in three dimensions. We show how to get the boundary anomaly from these bulk two point functions and find perfect agreement with our anomaly effective action. For a higher dimensional conformal field theory with a four dimensional defect, we describe for the first time the anomaly effective action that relates the Euler density term to the one point function anomaly, generalizing our result for two dimensional defects.

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