Equivalent String Networks and Uniqueness of BPS States

TL;DR

This paper introduces a complex parameter to classify string networks in 7-brane backgrounds, demonstrating how to compute BPS masses without specific network details and exploring the conditions for their BPS stability.

Contribution

It proposes a new complex parameter for classifying string networks and analyzes the conditions under which equivalent networks are BPS, enhancing understanding of BPS state uniqueness.

Findings

The parameter M characterizes network equivalence classes and their BPS mass.

Equivalent networks may not always be BPS simultaneously, indicating constraints for consistency.

The method allows calculation of BPS mass without detailed network knowledge.

Abstract

We analyze string networks in 7-brane configurations in IIB string theory. We introduce a complex parameter M characterizing equivalence classes of networks on a fixed 7-brane background and specifying the BPS mass of the network as M_{BPS} = | M |. We show that M can be calculated without knowing the particular representative of the BPS state. Based on detailed examination of backgrounds with three and four 7-branes we argue that equivalent networks may not be simultaneously BPS, an essential requirement of consistency.