SUSYin silico: Numerical D-brane bound state spectroscopy
Abstract
We numerically construct the supersymmetric and non-supersymmetric wave functions of an $\mathcal{N}=4$ quiver quantum mechanics with two Abelian nodes and a single arrow. This model captures the dynamics of a pair of wrapped D-branes interacting via a single light string mode. A dimensionless parameter $\ensuremath{\nu}$, which is inversely proportional to the Fayet-Iliopoulos parameter, controls whether the bulk of the wave functions are supported on the Higgs branch or the Coulomb branch. We demonstrate how the supersymmetric and excited states morph as $\ensuremath{\nu}$ is tuned. We also numerically compute the energy gap between the ground state and the first excited states as a function of $\ensuremath{\nu}$. An expression for the gap, computed on the Coulomb branch, matches nicely with our numerics at large $\ensuremath{\nu}$ but deviates at small $\ensuremath{\nu}$ where the Higgs branch becomes the relevant description of the physics. In the appendix, we provide the Schr\"odinger equations fully reduced via symmetries which, in principle, allow for the numerical determination of the entire spectrum at any point in moduli space. For the ground states, this numerical determination of the spectrum can be thought of as the first in silico check of various Witten index calculations.
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