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Black hole attractor varieties and complex multiplication. (English) Zbl 1043.81057
Yui, Noriko (ed.) et al., Calabi-Yau varieties and mirror symmetry. Providence, RI: American Mathematical Society (AMS) (ISBN 0-8218-3355-3/hbk). Fields Inst. Commun. 38, 209-222 (2003).
Summary: Black holes in string theory compactified on Calabi-Yau varieties a priori might be expected to have moduli dependent features. For example the entropy of the black hole might be expected to depend on the complex structure of the manifold. This would be inconsistent with known properties of black holes. Supersymmetric black holes appear to evade this inconsistency by having moduli fields that flow to fixed points in the moduli space that depend only on the charges of the black hole. Moore observed in the case of compactifications with elliptic curve factors that these fixed points are arithmetic, corresponding to curves with complex multiplication. The main goal of this talk is to explore the possibility of generalizing such a characterization to Calabi-Yau varieties with finite fundamental groups.
For the entire collection see [Zbl 1022.00014].

##### MSC:
 81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory 14K22 Complex multiplication and abelian varieties 11G15 Complex multiplication and moduli of abelian varieties 14H81 Relationships between algebraic curves and physics 11R42 Zeta functions and $$L$$-functions of number fields 14K30 Picard schemes, higher Jacobians 58D27 Moduli problems for differential geometric structures 83C57 Black holes 14J32 Calabi-Yau manifolds (algebro-geometric aspects)
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