Abstract
Basis tensor gauge theory is a vierbein analog reformulation of ordinary gauge theories in which the difference of local field degrees of freedom has the interpretation of an object similar to a Wilson line. Here we present a non-Abelian basis tensor gauge theory formalism. Unlike in the Abelian case, the map between the ordinary gauge field and the basis tensor gauge field is nonlinear. To test the formalism, we compute the beta function and the two-point function at the one-loop level in non-Abelian basis tensor gauge theory and show that it reproduces the well-known results from the usual formulation of non-Abelian gauge theory.
Highlights
The Standard Model (SM) of particle physics [1,2,3,4,5,6,7,8,9,10] is usually formulated with gauge fields that transform inhomogeneously under the gauge group; i.e., they are connections on principal bundles
This mechanism is used to construct covariant derivatives acting on matter fields, which allows a simple recipe for constructing kinetic terms for local field theories living on principal bundles
It was shown that the vierbein analog field Gαβ transforms homogeneously under the Uð1Þ gauge group and satisfies certain constraints, in contrast with the ordinary formulation in which the gauge field transforms inhomogeneously
Summary
The Standard Model (SM) of particle physics [1,2,3,4,5,6,7,8,9,10] is usually formulated with gauge fields that transform inhomogeneously under the gauge group; i.e., they are connections on principal bundles (see e.g., [11,12]) This mechanism is used to construct covariant derivatives acting on matter fields, which allows a simple recipe for constructing kinetic terms for local field theories living on principal bundles. We find that before introducing the counterterms, the divergence that is obtained using the θAa formalism is the same as in the usual AAμ ðxÞ formalism This is an indication that the UV structure of ordinary gauge theories are faithfully reproduced by the non-Abelian BTGT theory. In Appendix D, we list the Feynman rules for the theory
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