Want to take part in these discussions? Sign in if you have an account, or apply for one below
Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.
Added to T-duality a section with the discussion of the usual path-integral heuristics for why the two sigma-models on T-dual backgrounds yield equivalent quantum field theories.
Dear Urs,
the path integral heuristics behind path-integral sigma-models T-duality should actually be simpler (at least at the level of the naive idea). Namely, everything boils down to saying that the 2-torus obtained by opposite sides identification of and the one obtained by opposite sides identification of (both with the standard flat metric obtained by restriction from ) are conformally equivalent.
A way of seeing this is to recall that up to conformal equivalence a 2-torus can be seen as a parallelogram in with a vertex in , a vertex in and the other vertex in , where denotes the upper half-plane. The torus of parameter and the one of parameter are conformally equivalent iff
with
in . The two parameters and are related by the matrix
True, but I do not quite see how you’d derive T-duality of the target space this way.
Also, one point of the computation I posted is that it also applies to the open string and shows the action of T-duality on D-branes.
Right, I misunderstood what you were referring to. now I see that what I wrote could have something to do with what you were saying, but at the moment I could not say exactly what.. :)
I think you are certainly right that the basic mechanism underlying T-duality is at least morally that of the -transformation on a torus. But I don’t quite see how one can upgrade this observation to a proof that two T-dual backgrounds give equivalent sigma-model QFTs. Possibly there is a way, though.
Correcting some typos at T-duality, I don’t know how to fix
A quick way to get an indication for this is to notice that the center-of-mass energy of the string in such a circle-bundle background is In terms of the worldsheet theory.
Thanks for catching this. Not sure what happened there. I have changed the sentence to
A quick way to get an indication for this is to consider the center-of-mass energy of the string in such a circle-bundle background.
added pointer to today’s
Added a new reference
added pointer to:
adding reference
Anonymous
added pointer to today’s preprint (replacement)
and grouped together all the reference on super-space T-duality
A propos, we now keep here a streamlined account of the computations of super-space T-duality (for anyone who found the original article hard to read).
1 to 13 of 13