Six-Dimensional Tensionless Strings In The Large N Limit

TL;DR

The work explores six-dimensional tensionless strings arising in M-theory and type-IIB/K3 constructions, proposing a surface-based generalization of Yang-Mills dynamics via Wilson-surfaces and Makeenko-Migdal–type equations. It develops an operator formalism and abelian/non-abelian surface equations to capture interactions between tensionless strings and anti-self-dual two-forms, and discusses supersymmetry and potential worldsheet CFTs. In the large $N$ limit, adiabatic duality arguments suggest an emergent extra dimension and a continuous spectrum, with concrete checks in Type-IIB on $A_{N-1}$ and the CHS symmetric five-brane setup; some channels (e.g., Type-IIA on $A_{N-1}$) do not produce the extra dimension. The results point to a possible independent 6D framework for tensionless-string theories and a bridge to M-theory via emergent dimensions at large $N$.

Abstract

When $N$ five-branes of M-theory coincide the world-volume theory contains tensionless strings, according to Strominger's construction. This suggests a large $N$ limit of tensionless string theories. For the small $E_8$ instanton theories, the definition would be a large instanton number. An adiabatic argument suggests that in the large $N$ limit an effective extra uncompactified dimension might be observed. We also propose ``surface-equations'', which are an analog of Makeenko-Migdal loop-equations, and might describe correlators in the tensionless string theories. In these equations, the anti-self-dual two forms of 6D and the tensionless strings enter on an equal footing. Addition of strings with CFTs on their world-sheet is analogous to addition of matter in 4D QCD.