Abstract
We investigate the properties of chiral operators in N = 2 superconformal theories. In particular, we study the spectral flow of such models under a one-parameter family of twists generated by the U(1) current, and use this to deduce various properties of the ring of chiral primary fields. We furthermore investigate under what conditions a given superconformal theory can be represented as the fixed point of an N = 2 Landau-Ginzburg theory and show how to determine the superpotential. We also investigate the coset models of Kazama and Suzuki and find a simple cohomological characterization for the elements of the chiral primary ring. Moreover we show how some of them can be represented as LG models.
Highlights
The conformal models in two dimensions possessing N = 2 world-sheet supersymmetry form a special class of conformal theories, that is, they comprise the only known solutions to string theory at the perturbative level
We find the conditions for an N = 2 superconformal model to be representable as the fixed point of a Landau-Ginzburg theory
If we look at the anticommutator ( Go, Go~), we deduce that h >1c/24 for any state in the R sector
Summary
The property (2.22) implies in particular that there exists an unique primary chiral field with the highest possible left and right charges qL = qR = C/3 and dimensions h L = h R = c/6. By flowing with (0, - 1 ) we see that there is one and only one (chiral, chiral) state with charge (0, d) These two states correspond to the local operators PL = e x p [ i ~ 3 d P L ] and OR = e x p [ - i c ~ '~R] that generate independent, integral spectral flows in the left- and right-moving sectors*. The ground states of the Ramond sector and its connection with the spectral flow are easy to work out for this example, and we leave it as an instructive exercise to the reader
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