Small $E_8$ Instantons and Tensionless Non-critical Strings

TL;DR

The paper addresses the problem of small $E_8\times E_8$ instantons and the possibility that their zero-size limit hosts a tensionless non-critical string in six dimensions. It employs T-duality between $E_8\times E_8$ and $SO(32)$ heterotic strings and an M-theory (Horava–Witten) strong-coupling picture to propose a geometric brane construction in which tensionless strings arise from membranes connecting branes and their images or fixed points. The authors identify low-energy content including a chiral $E_8$ current algebra on intersections and a surviving $16$ of $SO(16)$ after compactification, and they describe how phase transitions in six dimensions can be mediated by tensionless strings, analogous to four-dimensional phenomena. The work links small instanton physics to tensionless-string dynamics and brane configurations, with implications for non-perturbative six-dimensional physics and duality connections across string theories.

Abstract

T-duality is used to extract information on an instanton of zero size in the $E_8\times E_8$ heterotic string. We discuss the possibility of the appearance of a tensionless anti-self-dual non-critical string through an implementation of the mechanism suggested by Strominger of two coincident 5-branes. It is argued that when an instanton shrinks to zero size a tensionless non-critical string appears at the core of the instanton. It is further conjectured that appearance of tensionless strings in the spectrum leads to new phase transitions in six dimensions in much the same way as massless particles do in four dimensions.