scholarly journals Supersymmetry anomalies and the Wess–Zumino model in a supergravity background

2021 ◽  
Vol 36 (11) ◽  
pp. 2150076
Author(s):  
Giorgos Eleftheriou ◽  
Peter West
Keyword(s):  
Ward Identity ◽  
Dimensional Regularization ◽  
Counter Term ◽  
Ward Identities ◽  
Zumino Model

We briefly recall the procedure for computing the Ward identities in the presence of a regulator which violates the symmetry being considered. We compute the first nontrivial correction to the supersymmetry Ward identity of the Wess–Zumino model in the presence of background supergravity using dimensional regularization. We find that the result can be removed using a finite local counter term and so there is no supersymmetry anomaly.

PROBING TOPOLOGICAL FEATURES IN PERTURBATIVE CHERN-SIMONS GAUGE THEORY

1990 ◽  
Vol 05 (23) ◽  
pp. 1833-1839 ◽  
Author(s):  
WEI CHEN ◽  
G. W. SEMENOFF ◽  
YONG-SHI WU
Keyword(s):  
Perturbation Theory ◽  
Gauge Theory ◽  
Ward Identity ◽  
Beta Function ◽  
Dimensional Regularization ◽  
Coupling Constant ◽  
Topological Features ◽  
Chern Simons

The topological Chern-Simons gauge theory is studied in the framework of perturbation theory. Both dimensional and F2 regularizations are used. We demonstrate the vanishing of the beta function up to three loops, the absence of diffeomorphism anomaly in the calculation of two- and three-point functions, and the validity of a topological Ward identity by finite renormalization of the coupling constant. The regularization dependence of the finite renormalization and an ambiguity in the dimensional regularization are also discussed.

Transversality of the Rarita-Schwinger self-energy, Ward identities, and dimensional regularization

1980 ◽  
Vol 22 (12) ◽  
pp. 2995-3002 ◽  
Author(s):  
M. K. Fung ◽  
P. van Nieuwenhuizen ◽  
D. R. T. Jones
Keyword(s):  
Dimensional Regularization ◽  
Ward Identities ◽  
Self Energy

OPERATOR REGULARIZATION AND THE COMPONENT WESS-ZUMINO MODEL

1990 ◽  
Vol 05 (10) ◽  
pp. 1919-1949 ◽  
Author(s):  
D.G.C. McKEON ◽  
S.S. SAMANT ◽  
T.N. SHERRY
Keyword(s):  
Symmetry Breaking ◽  
Energy Tensor ◽  
Stress Energy Tensor ◽  
Loop Order ◽  
Ward Identities ◽  
Model Calculations ◽  
Stress Energy ◽  
Component Field ◽  
Spinor Current ◽  
Zumino Model

Operator regularization has been shown to provide a method for computing Green’s functions without introducing any symmetry breaking regulating parameters, and without the occurrence of explicit infinities at any stage of the calculation. In this paper, we apply this technique to the component field Wess-Zumino model. Calculations to two-loop order of the two-point functions show that the supersymmetric Ward identities are satisfied, and that infinities do not arise. One-loop anomalous processes involving the chiral current, the spinor current and the stress-energy tensor are computed.

scholarly journals ANOMALIES IN WARD IDENTITIES FOR THREE-POINT FUNCTIONS REVISITED

2002 ◽  
Vol 17 (15) ◽  
pp. 1979-2017 ◽  
Author(s):  
O. A. BATTISTEL ◽  
O. L. BATTISTEL
Keyword(s):  
Traditional Approach ◽  
Axial Vector ◽  
Dimensional Regularization ◽  
Point Of View ◽  
Ward Identities ◽  
Calculational Method ◽  
Free Fermion Model ◽  
Traditional Work ◽  
Symmetry Relations ◽  
Natural Way

A general calculational method is applied to investigate symmetry relations among divergent amplitudes in a free fermion model. A very traditional work on this subject is revisited. A systematic study of one, two and three-point functions associated to scalar, pseudoscalar, vector and axial-vector densities is performed. The divergent content of the amplitudes are left in terms of five basic objects (external momentum independent). No specific assumptions about a regulator is adopted in the calculations. All ambiguities and symmetry violating terms are shown to be associated with only three combinations of the basic divergent objects. Our final results can be mapped in the corresponding Dimensional Regularization calculations (in cases where this technique could be applied) or in those of Gertsein and Jackiw which we will show in detail. The results emerging from our general approach allow us to extract, in a natural way, a set of reasonable conditions (e.g. crucial for QED consistency) that could lead us to obtain all Ward Identities satisfied. Consequently, we conclude that the traditional approach used to justify the famous triangular anomalies in perturbative calculations could be questionable. An alternative point of view, dismissed of ambiguities, which lead to a correct description of the associated phenomenology, is pointed out.

scholarly journals ANOMALY AND ANOMALY-FREE TREATMENT OF QFT's BASED ON SYMMETRY-PRESERVING LOOP REGULARIZATION

2006 ◽  
Vol 21 (31) ◽  
pp. 6383-6456 ◽  
Author(s):  
YONG-LIANG MA ◽  
YUE-LIANG WU
Keyword(s):  
Ward Identity ◽  
Axial Vector ◽  
Dimensional Regularization ◽  
Direct Calculation ◽  
Vector Current ◽  
Explicit Calculation ◽  
Abelian Gauge ◽  
Free Treatment ◽  
Definition Of ◽  
Villars Regularization

The triangle anomaly in massless and massive QED is investigated by adopting the symmetry-preserving loop regularization method proposed recently in Refs. 1 and 2. The method is realized in the initial dimension of theory without modifying the original Lagrangian, it preserves symmetries under non-Abelian gauge and Poincaré transformations in spite of the existence of two intrinsic mass scales Mc and μs which actually play the roles of UV- and IR-cutoff respectively. The axial-vector–vector-vector (AVV) triangle diagrams in massless and massive QED are evaluated explicitly by using the loop regularization. It is shown that when the momentum k of external state is soft with [Formula: see text], m2 (m is the mass of loop fermions) and Mc → ∞, both massless and massive QED become anomaly free. The triangle anomaly is found to appear as quantum corrections in the case that m2, [Formula: see text] and Mc → ∞. Especially, it is justified that in the massless QED with μs = 0 and Mc → ∞, the triangle anomaly naturally exists as quantum effects in the axial-vector current when the ambiguity caused by the trace of gamma matrices with γ5 is eliminated by simply using the definition of γ5. It is explicitly demonstrated how the Ward identity anomaly of currents depends on the treatment for the trace of gamma matrices, which enables us to make a clarification whether the ambiguity of triangle anomaly is caused by the regularization scheme in the perturbation calculations or by the trace of gamma matrices with γ5. For comparison, an explicit calculation based on the Pauli–Villars regularization and dimensional regularization is carried out and the possible ambiguities of Ward identity anomalies caused from these two regularization schemes are carefully discussed, which include the ambiguities induced by the treatment of the trace of gamma matrices with γ5 and the action of the external momentum on the amplitude before the direct calculation of the AVV diagram.

scholarly journals Feynman Rules, Ward Identities and Loop Corrections in Very Special Relativity Standard Model

Universe ◽  
2019 ◽  
Vol 5 (1) ◽  
pp. 16 ◽  
Author(s):  
Jorge Alfaro
Keyword(s):  
Standard Model ◽  
Special Relativity ◽  
Effective Action ◽  
Dimensional Regularization ◽  
External Momentum ◽  
Ward Identities ◽  
Feynman Rules ◽  
Very Special Relativity ◽  
Charged Leptons ◽  
The Masses

In this paper, we want to study one loop corrections in Very Special Relativity Standard Model(VSRSM). In order to satisfy the Ward identities and the S i m ( 2 ) symmetry of the model, we have to specify the Feynman rules, including the infrared regulator. To do this, we adapt the Mandelstam–Leibbrandt (ML) prescription to incorporate external momentum-dependent null vectors. As an example, we use the new S i m ( 2 ) invariant dimensional regularization to compute one loop corrections to the effective action in the subsector of the VSRSM that describe the interaction of photons with charged leptons. New stringent bounds for the masses of ν e and ν μ are obtained.

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