International Journal of Modern Physics A

SU (2)k MODULAR-INVARIANT PARTITION FUNCTIONS FROM ORBIFOLDS

Farhad Ardalan A, H. Arfaei, Shahin Rouhani

Published Nov 10, 1991• 0 citations

Abstract

We present a method which generates the modular-invariant partition functions of the ADE series of SU(2)k. Dividing the diagonal theory by discrete subgroups of the conformal group, we construct all the modular-invariant partition functions, thus proving that orbifold construction generates all the partition functions of SU(2)k.

DOI: 10.1142/s0217751x91002264

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International Journal of Modern Physics A

SU (2)k MODULAR-INVARIANT PARTITION FUNCTIONS FROM ORBIFOLDS

Farhad Ardalan A, H. Arfaei, Shahin Rouhani

Published Nov 10, 1991• 0 citations

Publisher

Abstract

DOI: 10.1142/s0217751x91002264

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N

the partition functions for string orbifolds on

\mathbb{C}/\mathbb{Z}_N

conical spaces, known for all odd integer

N

. In the concrete example of ten-dimensional Type-IIB strings, the one-loop partition function can be computed explicitly and the one-loop entropy can be expressed as a manifestly modular invariant series in terms of the Weierstrass

\wp

function. The convergence of the series is not evident but, from physical arguments based on holography, it is expected to yield a finite answer together with the tree level contribution. This method has a natural generalization to other string compactifications and to higher genus Riemann surfaces; it can provide a modular invariant definition of generalized entropy in a given string vacuum to all orders, of potential interest for the generalized second law of thermodynamics.