Beyond wild walls there is algebraicity and exponential growth (of BPS indices)
| dc.contributor.advisor | Neitzke, Andrew | en |
| dc.contributor.advisor | Distler, Jacques | en |
| dc.contributor.committeeMember | Kaplunovsky, Vadim | en |
| dc.contributor.committeeMember | Fischler, Willy | en |
| dc.contributor.committeeMember | Keel, Sean | en |
| dc.creator | Mainiero, Thomas Joseph | en |
| dc.date.accessioned | 2015-10-09T18:37:07Z | en |
| dc.date.accessioned | 2018-01-22T22:28:22Z | |
| dc.date.available | 2015-10-09T18:37:07Z | en |
| dc.date.available | 2018-01-22T22:28:22Z | |
| dc.date.issued | 2015-05 | en |
| dc.date.submitted | May 2015 | en |
| dc.date.updated | 2015-10-09T18:37:07Z | en |
| dc.description | text | en |
| dc.description.abstract | The BPS spectrum of pure SU(3) four-dimensional super Yang-Mills with N=2 supersymmetry (a theory of class S(A)) exhibits a surprising phenomenon: there are regions of the Coulomb branch where the growth of BPS-indices with the charge is exponential. We show this using spectral networks and, independently, using wall-crossing formulae and quiver methods. The technique using spectral networks hints at a general property dubbed "algebraicity": generating series for BPS-indices in theories of class S(A) (a class of N=2 four-dimensional field theories) are secretly algebraic functions over the rational numbers. Kontsevich and Soibelman have an independent understanding of algebraicity using indirect techniques, however, spectral networks give a distinct reason for algebraicity with the advantage of providing explicit algebraic equations obeyed by generating series; along these lines, we provide a novel example of such an algebraic equation, and explore some relationships to Euler characteristics of Kronecker quiver stable moduli. We conclude by proving that exponential asymptotic growth is a corollary of algebraicity, leading to the slogan "there are either finitely many BPS indices or exponentially many" (in theories of class S(A)). | en |
| dc.description.department | Physics | en |
| dc.format.mimetype | application/pdf | en |
| dc.identifier | doi:10.15781/T27881 | en |
| dc.identifier.uri | http://hdl.handle.net/2152/31637 | en |
| dc.language.iso | en | en |
| dc.subject | N=2 supersymmetry | en |
| dc.subject | BPS-indices | en |
| dc.subject | Donaldson-Thomas invariants | en |
| dc.subject | Theories of class s | en |
| dc.subject | SU(3) super yang mills | en |
| dc.subject | Kontsevich and Soibelman wall crossing formula | en |
| dc.subject | Wild wall crossing | en |
| dc.subject | Spectral networks | en |
| dc.subject | Algebraic generating series | en |
| dc.subject | Exponential degeneracy | en |
| dc.subject | Asymptotics of BPS-indices | en |
| dc.title | Beyond wild walls there is algebraicity and exponential growth (of BPS indices) | en |
| dc.type | Thesis | en |