scholarly journals One-loop calculations in Lorentz-breaking theories and proper-time method

2021 ◽  
Author(s):  
Alysson Ferrari ◽  
Job Furtado Neto ◽  
Jose F. Assunção ◽  
Tiago Mariz ◽  
Albert Yu. Petrov
Keyword(s):  
Effective Action ◽  
Proper Time ◽  
Axial Vector ◽  
Constant Tensor ◽  
The One

Abstract We discuss applications of the proper-time method in various minimal Lorentz violating modifications of QED and present new results obtained with its use. Explicitly we calculate the complete one-loop Heisenberg-Euler effective action involving all orders in $F_{\mu\nu}$, for two of the most studied minimal Lorentz-violating extensions of QED, the one characterized by the axial vector $b^{\mu}$ and the one involving the second-rank constant tensor $c^{\mu\nu}$.

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 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 Harmonic Superspace Approach to the Effective Action in Six-Dimensional Supersymmetric Gauge Theories

Symmetry ◽  
2019 ◽  
Vol 11 (1) ◽  
pp. 68 ◽  
Author(s):  
Ioseph Buchbinder ◽  
Evgeny Ivanov ◽  
Boris Merzlikin ◽  
Konstantin Stepanyantz
Keyword(s):  
Effective Action ◽  
Gauge Theories ◽  
Proper Time ◽  
Background Field ◽  
Field Method ◽  
Quantum Corrections ◽  
Supersymmetric Gauge Theories ◽  
Loop Approximation ◽  
Supersymmetric Gauge ◽  
The One

We review the recent progress in studying the quantum structure of 6 D , N = ( 1 , 0 ) , and N = ( 1 , 1 ) supersymmetric gauge theories formulated through unconstrained harmonic superfields. The harmonic superfield approach allows one to carry out the quantization and calculations of the quantum corrections in a manifestly N = ( 1 , 0 ) supersymmetric way. The quantum effective action is constructed with the help of the background field method that secures the manifest gauge invariance of the results. Although the theories under consideration are not renormalizable, the extended supersymmetry essentially improves the ultraviolet behavior of the lowest-order loops. The N = ( 1 , 1 ) supersymmetric Yang–Mills theory turns out to be finite in the one-loop approximation in the minimal gauge. Furthermore, some two-loop divergences are shown to be absent in this theory. Analysis of the divergences is performed both in terms of harmonic supergraphs and by the manifestly gauge covariant superfield proper-time method. The finite one-loop leading low-energy effective action is calculated and analyzed. Furthermore, in the Abelian case, we discuss the gauge dependence of the quantum corrections and present its precise form for the one-loop divergent part of the effective action.

scholarly journals The UL(3) × UR(3) Extended Nambu–Jona-Lasinio Model in Differential Regularization

1997 ◽  
Vol 12 (13) ◽  
pp. 2361-2371
Author(s):  
Yaw-Hwang Chen ◽  
Su-Long Nyeo ◽  
Yeou-Wei Yang
Keyword(s):  
Effective Action ◽  
Vector Fields ◽  
Axial Vector ◽  
The One

We employ the method of differential regularization to calculate explicitly the one-loop effective action of a bosonized UL(3) × UR(3) extended Nambu–Jona-Lasinio model consisting of scalar, pseudoscalar, vector and axial vector fields.

scholarly journals The fermionic universal one-loop effective action

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Sebastian A. R. Ellis ◽  
Jérémie Quevillon ◽  
Pham Ngoc Hoa Vuong ◽  
Tevong You ◽  
Zhengkang Zhang
Keyword(s):  
Path Integral ◽  
Effective Action ◽  
Covariant Derivative ◽  
Heavy Fermion ◽  
Axial Vector ◽  
Derivative Expansion ◽  
Universal Structure ◽  
Pseudo Scalar ◽  
Matching Techniques ◽  
Analytical Expressions

Abstract Recent development of path integral matching techniques based on the covariant derivative expansion has made manifest a universal structure of one-loop effective Lagrangians. The universal terms can be computed once and for all to serve as a reference for one-loop matching calculations and to ease their automation. Here we present the fermionic universal one-loop effective action (UOLEA), resulting from integrating out heavy fermions (Dirac or Majorana) with scalar, pseudo-scalar, vector and axial-vector couplings. We also clarify the relation of the new terms computed here to terms previously computed in the literature and those that remain to complete the UOLEA. Our results can be readily used to efficiently obtain analytical expressions for effective operators arising from heavy fermion loops [13].

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 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 Electroweak fermion triangle loop contributions to the muon anomalous magnetic moment revisited

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Ken Sasaki
Keyword(s):  
Magnetic Moment ◽  
Top Quark ◽  
Anomalous Magnetic Moment ◽  
Ward Identity ◽  
Axial Vector ◽  
Goldstone Boson ◽  
Muon Anomalous Magnetic Moment ◽  
Feynman Gauge ◽  
Unitary Gauge ◽  
The One

Abstract The contribution to the muon anomalous magnetic moment from the fermion triangle loop diagrams connected to the muon line by a photon and a $Z$ boson is re-analyzed in both the unitary gauge and the ’t Hooft–Feynman gauge. With use of the anomalous axial-vector Ward identity, it is shown that the calculation in the unitary gauge exactly coincides with the one in the ’t Hooft–Feynman gauge. The part which arises from the ordinary axial-vector Ward identity corresponds to the contribution of the neutral Goldstone boson. For the top-quark contribution, the one-parameter integral form is obtained up to the order of $m_\mu^2/m_Z^2$. The results are compared with those obtained by the asymptotic expansion method.

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