Timeline for CFTs corresponding to affine Lie algebras
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 2, 2013 at 18:10 | vote | accept | Anirbit | ||
| Apr 1, 2013 at 18:11 | comment | added | Anton Nazarov | @Anirbit Yes, of course. I've just written what kind of conformal field theory one can get for affine Lie algebra. I've omited the details. We can use radial quantization or path-integral formulation. Commutation relations can be obtained from Ward identities, that correspond to gauge transformations. I have not mentioned that because of topological term the action is not gauge-invariant. But the theory is well-defined when action have integer values. So we obtain the requirement for k to be integer. The details on compactification procedure can be found in Di Francesco starting from p.657 | |
| Apr 1, 2013 at 16:56 | comment | added | Anirbit | @Anton Nazarov Aren't you needing to do a QFT of the action you have written? I mean - your currents need to be normal ordered or something? What is the fundamental Dirac bracket from which you are getting the $[J,J]$ commutation? (..also about your comment about comapactified Boson picture - thats part of my question - in closed Bosonic string theory compactified on a $(S^1)^{rank}$ isn't the affine algebra of the massless states restricted to be in the A, D, E?...And in that case what is Lagrangian?..) | |
| Mar 31, 2013 at 17:37 | history | answered | Anton Nazarov | CC BY-SA 3.0 |