Rational conformal field theory with matrix level and strings on a torus
Keyword(s):
Study of the matrix-level affine algebra Um,K is motivated by conformal field theory and the fractional quantum Hall effect. Gannon completed the classification of Um,K modular-invariant partition functions. Here we connect the algebra U2,K to strings on 2-tori describable by rational conformal field theories. As Gukov and Vafa proved, rationality selects the complex-multiplication tori. We point out that the rational conformal field theories describing strings on complex-multiplication tori have characters and partition functions identical to those of the matrix-level algebra Um,K. This connection makes it obvious that the rational theories are dense in the moduli space of strings on Tm, and may prove useful in other ways.
2003 ◽
Vol 18
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pp. 4497-4591
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1990 ◽
Vol 05
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pp. 2903-2952
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1990 ◽
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pp. 2343-2358
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1991 ◽
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pp. 2045-2074
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1989 ◽
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pp. 161-168
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2001 ◽
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pp. 2165-2173
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Vol 12
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pp. 739-748
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2008 ◽
Vol 23
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pp. 2184-2186