CHIRAL ANOMALY IN d=4, N=1 SUPERGRAVITY

1995 ◽  
Vol 10 (31) ◽  
pp. 2313-2321 ◽  
Author(s):  
SATOSHI YAJIMA ◽  
YOJI HIGASIDA ◽  
HIDEO TAIRA
Keyword(s):  
Heat Kernel ◽  
Explicit Form ◽  
Kernel Method ◽  
Background Field ◽  
Field Method ◽  
Chiral Anomaly ◽  
Minimal Coupling ◽  
Gravitational Fields ◽  
Background Field Method

The chiral U (1) anomaly in d=4, N=1 supergravity is evaluated on the basis of the heat kernel method. We consider all gravitino interactions of the theory, i.e. not only the minimal coupling of gravitino and gravitational fields, but also four-gravitino interactions which are treated as two-gravitino interactions in the background field method. We show the explicit form of a new contribution from the four-gravitino interactions to the anomaly.

scholarly journals Super heat kernel and one-loop divergence of super Yang–Mills theory in conformal supergravity

2019 ◽  
Vol 2019 (10) ◽  
Author(s):  
Ka-Hei Leung
Keyword(s):  
Heat Kernel ◽  
Iterative Scheme ◽  
Kernel Method ◽  
Background Field ◽  
Field Method ◽  
Conformal Supergravity ◽  
Quantum Theories ◽  
Yang Mills ◽  
Background Field Method ◽  
The One

Abstract We consider super Yang–Mills (SYM) theory in $N=1$ conformal supergravity. Using the background field method and the Faddeev–Popov procedure, the quantized action of the theory is presented. Its one-loop effective action is studied using the heat kernel method. We shall develop a non-iterative scheme, generalizing the non-supersymmetric case, to obtain the super heat kernel coefficients. In particular, the first three coefficients, which govern the one-loop divergence, will be calculated. We shall also demonstrate how to schematically derive the higher-order coefficients. The method presented here can be readily applied to various quantum theories. We shall, as an application, derive the full one-loop divergence of SYM in conformal supergravity.

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.

scholarly journals Boundary contributions of on-shell recursion relations with multiple-line deformation

2020 ◽  
Vol 80 (10) ◽  
Author(s):  
Chang Hu ◽  
Xiao-Di Li ◽  
Yi Li
Keyword(s):  
Recursion Relation ◽  
Background Field ◽  
Field Method ◽  
Tree Level ◽  
Link Type ◽  
Multiple Line ◽  
Boundary Operators ◽  
Background Field Method ◽  
The Right ◽  
Boundary Behaviors

AbstractThe on-shell recursion relation has been recognized as a powerful tool for calculating tree-level amplitudes in quantum field theory, but it does not work well when the residue of the deformed amplitude $$\hat{A}(z)$$ A ^ ( z ) does not vanish at infinity of z. However, in such a situation, we still can get the right amplitude by computing the boundary contribution explicitly. In Arkani-Hamed and Kaplan (JHEP 04:076. 10.1088/1126-6708/2008/04/076. arXiv:0801.2385, 2008), the background field method was first used to analyze the boundary behaviors of amplitudes with two deformed external lines in different theories. The same method has been generalized to calculate the explicit boundary operators of some amplitudes with BCFW-like deformation in Jin and Feng (JHEP 04:123. 10.1007/JHEP04(2016)123. arXiv:1507.00463, 2016). In this paper, we will take a step further to generalize the method to the case of multiple-line deformation, and to show how the boundary behaviors (even the boundary contributions) can be extracted in the method.

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