On the Twisted (2,0) and Little-String Theories

TL;DR

This paper investigates the compactification of (2,0) and little-string theories with R-symmetry twists, revealing connections to moduli spaces, phase transitions, and conjectures involving non-commutative geometry.

Contribution

It introduces a novel analysis of twisted compactifications of (2,0) and little-string theories, linking them to known moduli spaces and proposing new conjectures involving instantons on non-commutative tori.

Findings

Same moduli spaces as (1,0) with E8 Wilson lines

Reproduction of SU(2) moduli space with massive hypermultiplet

Observation of a phase transition with string condensation

Abstract

We study the compactification of the $(2,0)$ and type-II little-string theories on $S^1$, $T^2$ and $T^3$ with an R-symmetry twist that preserves half the supersymmetry. We argue that it produces the same moduli spaces of vacua as compactification of the $(1,0)$ theory with $E_8$ Wilson lines given by a maximal embedding of SU(2). In certain limits, this reproduces the moduli space of SU(2) with a massive adjoint hyper-multiplet. In the type-II little-string theory case, we observe a peculiar phase transition where the strings condense. We conjecture a generalization to more than two 5-branes which involves instantons on non-commutative $T^4$. We conclude with open questions.