# 2 dimensional chiral boson theory

1. Nov 23, 2012

### rbwang1225

I am reading the paper "Covariant Action for a D=11 Five-Brane with the Chiral Field" and want to make an analog for the chiral field in 2 dimensions.
But I don't know at the starting point, for if I take the local coordinates of the worldvolume to be $x^m (m=0,1)$, the dual field strength $F_{mnl}$ will be zero and the action $S$ becomes $S=\int d^2x\sqrt{-g}$.
Could anyone give me some advices?

Best Regards.

2. Dec 5, 2012

### xepma

The chiral boson in 2D was introduced e.g. by Floreanini and Jackiw (see here: http://prl.aps.org/abstract/PRL/v59/i17/p1873_1 ). In particular eq. 20 is the Lagrangian of the 2D chiral boson.

There is also a relativistic version I believe (or, at least, a more covoriant notation), which is I believe due to Siegel. I'm not sure, but I think he treats it in this paper:

http://www.sciencedirect.com/science/article/pii/055032138490453X

but I can't access it, because of the paywall...

Now, keep in mind that the chiral boson is plagued by a lot of subtleties. It's a constrained system, which requires constrained quantization to turn it into a quantum theory. The theory may or may not have gauge invariance, depending on the boundary conditions. Finally, the theory has an annoying infrared divergence, which needs to be regularized using either a finite system size or the introduction of a mass term.

3. Feb 21, 2013

Dear xepma: