Self-Dual Strings of Six-Dimensional SCFTs

Abstract

In this thesis we aim to characterize the self-dual strings of six-dimensional superconformal field theories (SCFTs) and develop a variety of techniques to compute their elliptic genera, which provide information about their spectra. All known N = (1, 0) supersymmetric SCFTs in 6d can be obtained by compactifying F-theory on an elliptic Calabi-Yau threefold with singular, noncompact base B. Resolving the singularity in B and wrapping D3 branes on the exceptional curves leads to strings on the tensor branch of the SCFT. The strings become tensionless at the superconformal fixed point and appear to play an important role in the dynamics of the SCFT. For a number of SCFTs we identify two-dimensional N = (0, 4) quiver gauge theories describing bound states of self-dual strings and obtain their elliptic genera by localization. We achieve this for 6d SCFTs describing M5 or D5 branes at a singularity, as well as n M5 branes probing an M9 plane (corresponding to n small E8 instantons). More generally, we relate the elliptic genera of strings of 6d SCFTs to the counting of supersymmetric (BPS) particles that arise upon compactification to 5d. This enables us to compute elliptic genera by topological string techniques. Following this approach we obtain information about the strings associated to SCFTs with a single tensor multiplet and minimal gauge group. Additionally, for SCFTs whose strings arise from M2 branes suspended between M5 or M9 branes we find a quantum mechanical picture in which M5 branes or M9 planes are represented by domain wall operators or states; in this context, elliptic genera are expressed in terms of suitable correlators which we compute. Finally, we find a non-perturbative completion of the topological string partition function that can be employed to compute five-sphere partition functions of 5d SCFTs and superconformal indices of 6d SCFTs. In the latter case, we argue that the superconformal index can be written in terms of elliptic genera of the self-dual strings, providing further evidence of the important role these strings play in the dynamics of 6d SCFTs.