Exceptional properties of exceptional instantons

Michele Del Zotto

According to a recent classification of 6d (1, 0) theories within F-theory there are only six ``pure'' 6d gauge theories which flows in the UV to SCFTs. The corresponding gauge groups are SU(3), SO(8), F4, E6, E7, and E8. These exceptional models have BPS strings which are also instantons for the corresponding gauge groups. The ADHM construction, however, does not capture the corresponding worldsheets. For G simply-laced, we determine the 2d N = (0, 4) worldsheet theories of such BPS instanton strings by a simple geometric engineering argument. These are given by a twisted S2 compactification of the 4d N = 2 theories of type H2, D4, E6, E7 and E8 (and their higher rank generalizations), where the 6d instanton number is mapped to the rank of the corresponding 4d SCFT. This determines their anomaly polynomials and, via topological strings, establishes an interesting relation among the corresponding T2 × S2 partition functions and the Hilbert series for moduli spaces of G instantons. Such relations allows to ``bootstrap'' the corresponding elliptic genera by modularity. As an example of such procedure, the elliptic genera of the one-instanton strings are determined. As an aside, these results unveil a rather surprising relation with the Schur index of the corresponding 4d N = 2 models. Based on joint work with G. Lockhart.

http://scgp.stonybrook.edu/video_portal/video.php?id=2847

Simons- Physics Seminar