3
$\begingroup$

In string theory worldsheet path integral, integral is done over all possible topologies, metric and coordinates.

And I was wondering if there is something in string theory similar to quantum field theory in fixed curved background spacetime - and came up with the idea of not integrating over all possible metric and considering worldsheet metric as fixed.

Would such an idea be inconsistent? If so, why would it be?

Improve this question
$\endgroup$
1
  • 1
    $\begingroup$ if you want to be able to scatter strings then if you don't sum over metrics you violate unitarity $\endgroup$
    – Wakabaloola
    Commented May 7, 2020 at 8:36

1 Answer 1

Reset to default
3
$\begingroup$

What you get for fixed worldsheet metric is a 2d quantum field theory known as the nonlinear sigma model. It's not inconsistent -- it's even sort of interesting -- but it's not string theory. String theory lives in the target space. The sum over worldsheet embeddings is just one way to describe it.

I think what you're after -- "something in string theory similar to quantum field theory in fixed curved background spacetime" -- is the idea of a decoupling limit. In general, in string theory, you can't turn off gravity without making the theory inconsistent, but there are special circumstances where you can. The simplest of these is the low energy supergravity approximation; in this limit, it's fine to fix the spacetime metric and just look at the behavior of the other fields. But there are other, more 'stringy' decoupling limits like OM theory and the 6d (2,0) theory.

Improve this answer
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.