Instantons, Fermions and Chern-Simons Terms

Abstract

In five spacetime dimensions, instantons are finite energy, solitonic particles. We describe the dynamics of these objects in the presence of a Chern-Simons interaction. For U(N) instantons, we show that the 5d Chern-Simons term induces a corresponding Chern-Simons term in the ADHM quantum mechanics. For SU(N) instantons, we provide a description in terms of geodesic motion on the instanton moduli space, modified by the presence of a magnetic field. We show that this magnetic field is equal to the first Chern character of an index bundle. All of these results are derived by a simple method which follows the fate of zero modes as fermions are introduced, made heavy, and subsequently integrated out.

12 pages. v2: factor of 2 corrected

Cited by in corpus (15)

• 5-dim Superconformal Index with Enhanced En Global Symmetry
• Transverse Momentum Dependent Parton Distribution/Fragmentation Functions at an Electron-Ion Collider
• A Matrix Model for Baryons and Nuclear Forces
• Long-distance properties of baryons in the Sakai-Sugimoto model
• A 5d/3d duality from relativistic integrable system
• Dynamics of Strings between Walls
• The Dynamics of Chern-Simons Vortices
• Rigid limit for hypermultiplets and five-dimensional gauge theories
• A model for gauged skyrmions with low binding energies
• Supersymmetric Rényi Entropy and Defect Operators
• Condensates and instanton - torus knot duality. Hidden Physics at UV scale
• ADHM and the 4d Quantum Hall Effect
• Baryon as dyonic instanton
• Quantum Geometry and $\theta$-Angle in Five-Dimensional Super Yang-Mills
• A note on D0-branes and instantons in 5d supersymmetric gauge theories