# Dimension of gamma matrices in dimensional regularization

When performing loop integrals in theories containing Dirac fermions, one almost always confronts terms of the form

$$\text{Tr}\left[\gamma^{\mu_1}\cdots\gamma^{\mu_n}\right].$$

For instance, in $$d$$ dimensions, we could compute the simple trace $$\text{Tr}\left[\gamma^{\mu}\gamma_{\mu}\right]$$ as

$$\text{Tr}\left[\gamma^{\mu}\gamma_{\mu}\right]=\frac{1}{2}g_{\mu\nu}\left\{\gamma^{\mu},\gamma^{\nu}\right\}=d\,\text{Tr}[\textbf{1}].$$

Typically, at this point, textbooks set $$\text{Tr}[\textbf{1}]$$. However, it is well known that the size of the $$\gamma$$ matrices in various dimensions is not always $$4$$, but is given by

$$\textbf{dim}(\gamma)=2^{\lfloor d/2\rfloor}.$$

Since this is clearly not an analytic function, how does one deal with this in dimensional regularization? Do we need to define a smooth function that interpolates between all of the integer $$d$$ values of this equation?

I have a slight feeling that the answer is going to be something along the lines of "It doesn't matter, because the order $$\epsilon$$ term in the trace can only contribute a constant to the $$\mathcal{O}(1)$$ terms in the full answer (after being multiplied by a $$1/\epsilon$$ term), and such constants can be absorbed by the counter-term, or in the definition of $$\mu$$." And I feel like that might be right, but I'm having a hard time convincing myself that this works.