Supercharges, Killing Spinors and Intersecting Gauge Five-branes

TL;DR

This paper constructs new heterotic string solutions involving intersecting gauge 5-branes with strings and pp-waves, analyzing supersymmetry and clarifying misconceptions about zero eigenvalues and supersymmetry enhancement.

Contribution

It provides explicit solutions for intersecting gauge 5-branes with detailed supersymmetry analysis, clarifying the nature of zero eigenvalues in supersymmetry counting.

Findings

Solutions involve string and pp-wave in intersecting gauge 5-branes

Supersymmetry analysis shows zero eigenvalues are spurious

Clarifies supersymmetry enhancement misconceptions

Abstract

We obtain new solutions where a string and a pp-wave lie in the common worldvolume directions of the non-standard intersection of two gauge 5-branes in the heterotic string. The two 5-branes are supported by independent SU(2) Yang-Mills instantons in their respective (non-overlapping) transverse spaces. We present a detailed study of the unbroken supersymmetry, focusing especially on a comparison between a direct construction of Killing spinors and a counting of zero eigenvalues in the annticommutator of supercharges. The results are in agreement with some previous arguments, to the effect that additional zero eigenvalues resulting from a ``fine-tuning'' between positive-energy and negative-energy contributions from different components in an intersection are spurious, and should not be taken as an indication of supersymmetry enhancements. These observations have a general applicability that goes beyond the specific example we study in this paper.