Four-manifold geography and superconformal symmetry

TL;DR

This paper introduces the concept of superconformal simple type for 4-manifolds, showing all known examples satisfy this property and exploring its implications through invariants and theoretical predictions from superconformal quantum field theories.

Contribution

It defines superconformal simple type for 4-manifolds, proves all known cases satisfy this, and connects the invariants to superconformal field theory predictions.

Findings

All known 4-manifolds with $b_2^+>1$ are of superconformal simple type.

Invariants of superconformal simple type 4-manifolds satisfy a generalized Noether inequality.

The phenomena are predicted by superconformal quantum field theories.

Abstract

A compact oriented 4-manifold is defined to be of ``superconformal simple type'' if certain polynomials in the basic classes (constructed using the Seiberg-Witten invariants) vanish identically. We show that all known 4-manifolds of $b_2^+>1$ are of superconformal simple type, and that the numerical invariants of 4-manifolds of superconformal simple type satisfy a generalization of the Noether inequality. We sketch how these phenomena are predicted by the existence of certain four-dimensional superconformal quantum field theories.