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Register a new userA graphic approach to gauge invariance induced identity
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All tree-level amplitudes in Einstein-Yang-Mills (EYM) theory and gravity (GR) can be expanded in terms of color ordered Yang-Mills (YM) ones whose coefficients are polynomial functions of Lorentz inner products and are constructed by a graphic rule. Once the gauge invariance condition of any graviton is imposed, the expansion of a tree level EYM or gravity amplitude induces a nontrivial identity between color ordered YM amplitudes. Being different from traditional Kleiss-Kuijf (KK) and Bern-Carrasco-Johansson (BCJ) relations, the gauge invariance induced identity includes polarizations in the coefficients. In this paper, we investigate the relationship between the gauge invariance induced identity and traditional BCJ relations. By proposing a refined graphic rule, we prove that all the gauge invariance induced identities for single trace tree-level EYM amplitudes can be precisely expanded in terms of traditional BCJ relations, without referring any property of polarizations. When further considering the transversality of polarizations and momentum conservation, we prove that the gauge invariance induced identity for tree-level GR (or pure YM) amplitudes can also be expanded in terms of traditional BCJ relations for YM (or bi-scalar) amplitudes. As a byproduct, a graph-based BCJ relation is proposed and proved.
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Symmetries of Einstein-Yang-Mills (EYM) amplitudes, together with the recursive expansions, induce nontrivial identities for pure Yang-Mills amplitudes. In the previous work cite{Hou:2018bwm}, we have already proven that the identities induced from tree level single-trace EYM amplitudes can be precisely expanded in terms of BCJ relations. In this paper, we extend the discussions to those identities induced from all tree level emph{multi-trace} EYM amplitudes. Particularly, we establish a refined graphic rule for multi-trace EYM amplitudes and then show that the induced identities can be fully decomposed in terms of BCJ relations.
On the basis of recent results extending non-trivially the Poincare symmetry, we investigate the properties of bosonic multiplets including $2-$form gauge fields. Invariant free Lagrangians are explicitly built which involve possibly $3-$ and $4-$form fields. We also study in detail the interplay between this symmetry and a U(1) gauge symmetry, and in particular the implications of the automatic gauge-fixing of the latter associated to a residual gauge invariance, as well as the absence of self-interaction terms.
Basis tensor gauge theory (BTGT) is a vierbein analog reformulation of ordinary gauge theories in which the vierbein field describes the Wilson line. After a brief review of the BTGT, we clarify the Lorentz group representation properties associated with the variables used for its quantization. In particular, we show that starting from an SO(1,3) representation satisfying the Lorentz-invariant U(1,3) matrix constraints, BTGT introduces a Lorentz frame choice to pick the Abelian group manifold generated by the Cartan subalgebra of u(1,3) for the convenience of quantization even though the theory is frame independent. This freedom to choose a frame can be viewed as an additional symmetry of BTGT that was not emphasized before. We then show how an $S_4$ permutation symmetry and a parity symmetry of frame fields natural in BTGT can be used to construct renormalizable gauge theories that introduce frame dependent fields but remain frame independent perturbatively without any explicit reference to the usual gauge field.
In Lagrangian gauge systems, the vector space of global reducibility parameters forms a module under the Lie algebra of symmetries of the action. Since the classification of global reducibility parameters is generically easier than the classification of symmetries of the action, this fact can be used to constrain the latter when knowing the former. We apply this strategy and its generalization for the non-Lagrangian setting to the problem of conformal symmetry of various free higher spin gauge fields. This scheme allows one to show that, in terms of potentials, massless higher spin gauge fields in Minkowski space and partially-massless fields in (A)dS space are not conformal for spin strictly greater than one, while in terms of curvatures, maximal-depth partially-massless fields in four dimensions are also not conformal, unlike the closely related, but less constrained, maximal-depth Fradkin--Tseytlin fields.
The radiative induction of the CPT and Lorentz violating Chern-Simons (CS) term is reassessed. The massless and massive models are studied. Special attention is given to the preservation of gauge symmetry at higher orders in the background vector $b_mu$ when radiative corrections are considered. Both the study of the odd and even parity sectors of the complete vacuum polarization tensor at one-loop order and a non-perturbative analysis show that this symmetry must be preserved by the quantum corrections. As a complement we obtain that transversality of the polarization tensor does not fix the value of the coefficient of the induced CS term.
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