Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
@Prallax "sign depends on whether you move clockwise or counterclockwise", that is true. But Pedro has already specified he's traversing the loop counterclockwise, so the signs are fixed, and so the question of whether it should be $\epsilon^2[\nabla_{\mu},\nabla_{\nu}]$ or the other way around is not a matter of convention anymore.
