A twist in the dyon partition function

2009/11/30 by Ashoke Sen · 1 citation
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Attractor #Black Holes and Theoretical Physics #Diffeomorphism #Dyon #Moduli space #Orbifold #Partition function (quantum field theory) #Quantum Chromodynamics and Particle Interactions #String duality #String theory #Supersymmetry #Twist #hep-th

paper · pdf · doi:10.1007/jhep05(2010)028

published as JHEP 1005:028,2010 · LaTeX file, 35 pages; v2: references added

arxiv created 2010/02/20 · openalex publication_date 2010/05/01 · arxiv updated 2010/05/25 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

In four dimensional string theories with N = 4 and N = 8 supersymmetries one can often define twisted index in a subspace of the moduli space which captures additional information on the partition function than the ones contained in the usual helicity trace index. We compute several such indices in type IIB string theory on K3 × T 2 and T 6, and find that they share many properties with the usual helicity trace index that captures the spectrum of quarter BPS states in N = 4 supersymmetric string theories. In particular the partition function is a modular form of a subgroup of Sp( 2;ℤ ) and the jumps across the walls of marginal stability are controlled by the residues at the poles of the partition function. However for large charges the logarithm of this index grows as 1/N times the entropy of a black hole carrying the same charges where N is the order of the symmetry generator that is used to define the twisted index. We provide a macroscopic explanation of this phenomenon using quantum entropy function formalism. The leading saddle point corresponding to the attractor geometry fails to contribute to the twisted index, but a ℤ_N orbifold of the attractor geometry produces the desired contribution.

Citations

• Arithmetic of N = 8 black holes
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• Dyon spectrum in Script N = 4 supersymmetric type II string theories
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Cited by

• BKM Lie superalgebras from counting twisted CHL dyons

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