Invariance Theorems for Supersymmetric Yang-Mills Theories
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2017-06-01
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Abstract
We consider quantum mechanical Yang-Mills theories with eight supercharges and a $Spin(5) \times SU(2)_R$ flavor symmetry. We show that all normalizable ground states in these gauge theories are invariant under this flavor symmetry. This includes, as a special case, all bound states of D0-branes and D4-branes. As a consequence, all bound states of D0-branes are invariant under the $Spin(9)$ flavor symmetry. When combined with index results, this implies that the bound state of two D0-branes is unique.
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Scholars@Duke
Mark A. Stern
The focus of Professor Stern's research is the study of analytic problems arising in geometry and physics.
In recent and ongoing work, Professor Stern has studied analytical, geometric, and topological questions arising in Yang-Mills theory. These include analyzing the moduli space of Yang Mills instantons on gravitational instantons, analyzing the asymptotic structure of instantons (proving a nonlinear analog of the inverse square law of electromagnetism), and analyzing the structure of singularities of instantons and of harmonic maps.
In addition, Professor Stern has recently studied questions arising in the interplay between geometric group theory and Lp and L2 cohomology. This work includes finding new bounds on L2 betti numbers of negatively curved manifolds, and new growth,
stability, and vanishing results for Lp and L2 cohomology of symmetric and locally symmetric spaces.
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