Ab initio wall crossing
SCIE
SCOPUS
- Title
- Ab initio wall crossing
- Authors
- Kim, H; Park, J; Wang, Z; Yi, P
- Date Issued
- 2011-09
- Publisher
- Springer
- Abstract
- We derive supersymmetric quantum mechanics of n BPS objects with 3n position degrees of freedom and 4n fermionic partners with SO(4) R-symmetry. The potential terms, essential and sufficient for the index problem for non-threshold BPS states, are universal, and 2(n - 1) dimensional classical moduli spaces M-n emerge from zero locus of the potential energy. We emphasize that there is no natural reduction of the quantum mechanics to M-n, contrary to the conventional wisdom. Nevertheless, via an index-preserving deformation that breaks supersymmetry partially, we derive a Dirac index on M-n as the fundamental state counting quantity. This rigorously fills a missing link in the "Coulomb phase" wall-crossing formula in literature. We then impose Bose/Fermi statistics of identical centers, and derive the general wall-crossing formula, applicable to both BPS black holes and BPS dyons. Also explained dynamically is how the rational invariant similar to Omega(beta)/p(2), appearing repeatedly in wall-crossing formulae, can be understood as the universal multiplicative factor due to p identical, coincident, yet unbound, BPS particles of charge beta. Along the way, we also clarify relationships between field theory state countings and quantum mechanical indices.
- Keywords
- Supersymmetric gauge theory; Solitons Monopoles and Instantons; Black Holes in String Theory; FIXED POINT FORMULA; ELLIPTIC COMPLEXES; QUANTUM-MECHANICS; INDEX THEOREMS; BPS MONOPOLES; MODULI SPACE; ORBIFOLDS; DUALITY; STRINGS; STATES
- URI
- https://oasis.postech.ac.kr/handle/2014.oak/17115
- DOI
- 10.1007/JHEP09(2011)079
- ISSN
- 1126-6708
- Article Type
- Article
- Citation
- Journal of high enrgy physics, vol. 2011, no. 9, page. 1 - 79, 2011-09
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