This mini-course will review recent developments in our understanding of scattering amplitudes in gauge theories, particularly N=4 SYM in four dimensions. We will discuss a dual theory for these scattering amplitudes associated with contour integrals over Grassmannians, where the remarkable symmetries of the theory are manifest, but space-time and unitarity emerge as secondary concepts.
This mini-course will review recent developments in our understanding of scattering amplitudes in gauge theories, particularly N=4 SYM in four dimensions. We will discuss a dual theory for these scattering amplitudes associated with contour integrals over Grassmannians, where the remarkable symmetries of the theory are manifest, but space-time and unitarity emerge as secondary concepts.
False vacua in QFT are liable to undergo spontaneous decay. Slowness of quantum tunneling can however allow a long lifetime to the false vacuum state. In supersymmetric theories this is a crucial criterion for obtaining a long lived universe with spontaneously broken supersymmetry. We have explored false vacua which admit topological defects, including in a supersymmetric model with O'Rafeartaigh type supersymmetry breaking. We show that the presence of topological defects significantly alters the stability of the false vacuum. For some values of parameters, it also results in the putative false vacuum being rendered unstable. Finally I report a formula derived for instanton assisted tunneling applicable to metastable vacua with monopoles.