Open Heterotic Strings

We classify potential cosmic strings according to the topological charge measurable outside the string core. We conjecture that in string theory it is this charge that governs the stability of long strings. This would imply that the SO(32) heterotic string can have endpoints, but not the E8 × E8 heterotic string. We give various arguments in support of this conclusion. 1 Stability of cosmic strings Compactifications of string theory give rise to many potential cosmic strings, including the fundamental strings themselves, D-strings and wrapped D-branes, solitonic strings and branes in ten dimensions, and magnetic and electric flux tubes in the four-dimensional effective theory. The small value of the cosmological constant suggests that the compactified dimensions in our vacuum have great topological complexity [1]; consequently there may be of order 10 cosmic string candidates, plus the bound states of these! However, the only strings that are cosmologically relevant are those those actually produced, and moreover it is necessary that some take the form of infinite random walks in order to seed the later string network [2]. Thus it is the much smaller number of phase breaking transitions after inflation that is relevant. Even if some infinite strings are produced, there is the possibility that they will decay too soon to be observed [3, 4]. In this paper we consider the stability of long strings. We propose a topological classification, based on the topological charge observable outside the string core, and we conjecture that all decays allowed by this classification actually occur in string theory. The rate might be slow on cosmological time scales; we are concerned here only with absolute stability. We distinguish four kinds of macroscopic string, in three noncompact spatial dimensions: • Local strings have no topological charge that can be detected by any measurement outside the core of the string. • Global strings have a topological charge that is visible in local measurements, the gradient of a scalar field that winds around the string. • Aharonov-Bohm strings [5] have no topological charge that can be detected by local measurements, but have an Aharonov-Bohm phase with respect to at least one particle that is neutral under all massless low energy gauge groups. • Quasi-Aharonov-Bohm strings have an Aharonov-Bohm phase, but only with respect to particles that are charged under the low energy gauge group. Note that this classification is along a different axis from the list in the first paragraph above, and applies to all strings in that list; it is independent of their internal structure. In particular the earlier description changes under duality, and in the middle of moduli space the distinctions disappear, while the topological classification is duality-invariant. The topological classification, which is a refinement of earlier discussions, determines the potential instabilities of the string: