2
$\begingroup$

I have heard people use the terminology D-brane wrapping around A-cycle and B-cycle when talking about compactifications on a torus. What do A-cycle, and B-cycle means here, and how it's related to T-duality?

Improve this question
$\endgroup$
4
  • 1
    $\begingroup$ The first homology group of the torus is $\mathbb Z\oplus\mathbb Z$, a and b are the two generators, i.e. single loops around each of the periodic dimensions. $\endgroup$
    – Nihar Karve
    Commented Nov 29, 2022 at 13:54
  • $\begingroup$ So it simply means they are two different loops going around two independent circular paths on the torus? Not related to A(1-form), B(2-form), which we find in string theory usually? $\endgroup$
    – htr
    Commented Nov 29, 2022 at 17:57
  • $\begingroup$ Yep, nothing to do with gauge fields $\endgroup$
    – Nihar Karve
    Commented Nov 29, 2022 at 23:38
  • $\begingroup$ Thank you for the answer. $\endgroup$
    – htr
    Commented Nov 30, 2022 at 18:54

0

Reset to default

Your Answer

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

Browse other questions tagged or ask your own question.