Σ Model, from not obvious to obvious?

[PhyAmateur]

Georgi in his book, for reference: http://www.people.fas.harvard.edu/~hgeorgi/weak.pdf he says that it is not obvious that the form of $$\Sigma = \sigma + i\tau_a\pi_a$$ is preserved under (2.6.6) $$ \delta \Sigma = i \epsilon_L^aT_a \Sigma - i \Sigma \epsilon_R^aT_a$$

But then he said, "But it is true, and you can work out by explicit calculation the transformations of the $\sigma$ and $\pi _a$ fields":

$$\delta \sigma = \epsilon_5^a \pi_a$$
$$\delta \pi_a = - \epsilon_{abc}\epsilon^b\pi_c - \epsilon_5^a \sigma$$

But I have no idea how after what he wrote it became obvious? It is still not obvious to me how it is preserved though he saying it must be.

 

[Einj]

I don't think he wants to say that it becomes obvious but simply that if you actually do the calculation with the change of the $\sigma$ and $\pi_a$ fields that you listed before you'll find that it is actually invariant. By ''obvious'' he probably means that can be seen by eye, without doing the explicit calculation.