Compactification of Tensionless String Theories

TL;DR

The paper investigates how the 6D tensionless N=2 S-theory behaves under compactification on complex two-folds to yield 2D conformal field theories, exploiting a topological twist to connect to Vafa–Witten twisted N=4 Yang–Mills partition functions. It analyzes the IR left-moving sector, derives the central-charge difference via anomaly matching, and calculates the free-field spectrum and the potential impact of instantons from strings wrapping 2-cycles. A key result is the condition for nontrivial instanton contributions, D·D = -1, which cannot be satisfied on K3 for analytic cycles, suggesting no instanton corrections in that case, though blow-ups may alter this conclusion. The work highlights modularity and gauge-bundle issues in matching to RCFT data, and outlines future directions for S-theory variants and further duality-based interpretations.

Abstract

We study compactifications of the $N=2$ 6D tensionless string on various complex two-folds down to two-dimensions. In the IR limit they become non-trivial conformal field theories in 2D. Using results of Vafa and Witten on the partition functions of twisted Super-Yang-Mills theories, we can study the resulting CFT. We also discuss the contribution of instantons made by wrapping strings on 2-cycles of the complex two-fold.