TL;DR
This paper demonstrates how quiver quantum mechanics bridges two descriptions of BPS states in string theory, enabling precise counting of ground states in complex multi-particle and gauge theory systems.
Contribution
It introduces a smooth interpolation via quiver quantum mechanics between particle and brane pictures, applying mathematical results to solve nontrivial ground state counting problems.
Findings
Solved ground state counting in multi-particle quantum mechanics
Counted dyon degeneracies in supersymmetric Yang-Mills theories
Applied to quantum Hall effect setups
Abstract
Two pictures of BPS bound states in Calabi-Yau compactifications of type II string theory exist, one as a set of particles at equilibrium separations from each other, the other as a fusion of D-branes at a single point of space. We show how quiver quantum mechanics smoothly interpolates between the two, and use this, together with recent mathematical results on the cohomology of quiver varieties, to solve some nontrivial ground state counting problems in multi-particle quantum mechanics, including one arising in the setup of the spherical quantum Hall effect, and to count ground state degeneracies of certain dyons in supersymmetric Yang-Mills theories. A crucial ingredient is a non-renormalization theorem in N=4 quantum mechanics for the first order part of the Lagrangian in an expansion in powers of velocity.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.