Hi, anyone knows what the sign of the metric determinant sgn($g$) mean?

For example the raised levi civita symbol e^{ijk} = sgn(g) e_{ijk}

@TaeNyFan A metric of signature $(p,q)$ will have determinant sign $(-1)^p$ or $(-1)^q$ depending on your sign convention. It doesn't really have a physical meaning if that's what you're asking.

I was wondering about this earlier, the question I asked a while ago here was said by qmechanic to be "not about string theory per se". I don't really want to @ them to ask a semantic question, but in what sense is the question not really about string theory?

the only thing I can think of is that an identical question could be asked for a different theory that isn't ST

@Charlie you can ask the same question even for regular (SU)GRA QFT, the existence of both a background field and a graviton is not specific to string theory in any way

ok that's fair, ty

it's not even specific to gravity - this occurs every time that you have a non-zero VEV of a field - you have both the "particle" and its VEV as the "background"