In Fujikawa's 'Path integrals and Quantum Anomalies', Eq.(10.26) in the derivation of gravitational anomaly in Chapter 10.1 is puzzling for me.
$A_{\mu}^{mn}(x_0^{\mu}+\frac{y^{\mu}}{M})=\frac{1}{2M}y^{\nu}{R_{\nu\mu}}^{mn}+...$
The author antisymmetrized $\mu,\nu$ by hand in the first derivative of spin connection and the explanation in the book is "the symmetric components are eliminated by using the gauge freedom". I do not know what that exactly means, what is the 'gauge' here refering to and how it eliminates the symmetric component.
If anybody has also gone through the derivation, could you please give me a hand?
