The Extended Algebra of the Minimal Models

Details The Extended Algebra of the Minimal Models The Extended Algebra of the Minimal Models

2007-01-29

arxiv.org/abs/hep-th/0701250v2

Nucl.Phys.B776:365-404,2007

Physics

High Energy Physics

High Energy Physics - Theory

43 pages, 1 figure. Added reference, clarification to proof of Thm 5.1, and several paragraphs to Sec 3.2 addressing modules c

Scientific paper

10.1016/j.nuclphysb.2007.03.030

The minimal models M(p',p) with p' > 2 have a unique (non-trivial) simple current of conformal dimension h = (p' - 2) (p - 2) / 4. The representation theory of the extended algebra defined by this simple current is investigated in detail. All highest weight representations are proved to be irreducible: There are thus no singular vectors in the extended theory. This has interesting structural consequences. In particular, it leads to a recursive method for computing the various terms appearing in the operator product expansion of the simple current with itself. The simplest extended models are analysed in detail and the question of equivalence of conformal field theories is carefully examined.

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