It is known that for some modified theories of gravity such as Palatini $f(R)$ Theory, we have two kinds of the connections: Affine connection and the Christoffel symbol, which are related to each other by variating the action with respect to the connection. For example for the Palatini $f(R)$ we have

$$\Gamma^{a}_{bc}= \{^{a}_{bc} \} +\Delta^{a}_{bc}$$

where $\{^{a}_{bc} \}$ is the Christoffel symbol and $\Delta^{a}_{bc}$ is a function of the derivative of the $f(R)$.

Now, I want to know which of these connections should be considered for the su(2) Yang-Mills algebra? Since the matter section of the Palatini theory is not a function of connection, contrary to metric-affine theory, does it make any difference in our chosen connection for the related Yang-Mills theory?



Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.