String theory
Final Report Abstract
Regarding BPS-states and wall-crossing may research results cover the following topics: • BPS string states, their moduli spaces, their Witten index, and relations to partition functions of M5-branes • Three-dimensional gauge theories and three-dimensionsal mirror symmetry • Four-dimensional wall-crossing • Three-manifolds and equivalence relations between these. The first item concerns the physics of extended solitonic strings rather than point-like particles. By strings we do not mean the fundamental objects of string theory here but string excitations of ordinary field theory. The string we are concerned with is the so called "magnetic string" and carries magnetic charge. The magnetic string can be seen as the uplift of the point-like topological defect known as the magnetic monopole in four-dimensions to five-dimensions. In further work we develop a more detailed understanding of these strings, their microscopic degeneracies and their embedding into M-theory. We address questions related to the last three items in the above list. We realize threedimensional quantum field theories as domain-walls in four-dimensional ones and thus deduce mirror symmetry from four-dimensional wall-crossing. Furthermore we embed all these theories into M-theory by wrapping an M5 brane on a three-cycle in a Calabi-Yau and map the equivalences between three dimensional physical theories to equivalences between these three-manifolds. Regarding F-theory and elliptic Calabi-Yau manifolds the research provides fundamental new insights into the following topics: • Six-dimensional (2,0) superconformal theories • M-theory on elliptic Calabi-Yau manifolds and type IIB duals • Nekrasov partition function • Two-dimensional (4,0) supersymmetric quiver gauge theories. We study deformations of (2,0) superconformal theories on flat space and in the presence of AN singularities. We proceed by engineering the theory in terms of M-theory on a Calabi-Yau threefold and its dual type IIB description. This provides us with a new method to compute the Nekrasov partition function in terms of elliptic genera of two-dimensional (4,0) theories. Last but not least we arrive at new identities for two-dimensional elliptic genera.
Publications
- M-Strings
B. Haghighat, A. Iqbal, C. Kozcaz, G. Lockhart and C. Vafa
- On orbifolds of M-Strings
B. Haghighat, C. Kozcaz, G. Lockhart and C. Vafa
- Tangles, Generalized Reidemeister Moves, and Three- Dimensional Mirror Symmetry
C. Cordova, S. Espahbodi, B. Haghighat, A. Rastogi and C. Vafa
- "A 5d/2d/4d correspondence," JHEP 1303, 157 (2013)
B. Haghighat, J. Manschot and S. Vandoren
