F-theory and the Classification of Little Strings

TL;DR

The paper provides a comprehensive, geometry-driven framework for classifying 6D little string theories via F-theory, showing that LSTs with multiple tensor multiplets arise as affine extensions of 6D SCFTs by a non-dynamical tensor multiplet. It constructs LST bases by augmenting SCFT bases, constrains possible base and fiber configurations through a tensor-decoupling criterion, and demonstrates that all SCFTs embed into LSTs. A central insight is that LSTs exhibit T-duality realized through double elliptic fibrations, linking geometric exchanges to circle compactifications. The work also outlines explicit classifications of bases and fibers, provides concrete low- and high-rank examples, and discusses outliers and non-geometric phases, setting the stage for future non-geometric realizations and RG-flow perspectives in LSTs.

Abstract

Little string theories (LSTs) are UV complete non-local 6D theories decoupled from gravity in which there is an intrinsic string scale. In this paper we present a systematic approach to the construction of supersymmetric LSTs via the geometric phases of F-theory. Our central result is that all LSTs with more than one tensor multiplet are obtained by a mild extension of 6D superconformal field theories (SCFTs) in which the theory is supplemented by an additional, non-dynamical tensor multiplet, analogous to adding an affine node to an ADE quiver, resulting in a negative semidefinite Dirac pairing. We also show that all 6D SCFTs naturally embed in an LST. Motivated by physical considerations, we show that in geometries where we can verify the presence of two elliptic fibrations, exchanging the roles of these fibrations amounts to T-duality in the 6D theory compactified on a circle.

Figures (7)

• Figure 1: Depiction of how to construct the base of an F-theory model for an LST. All LST bases are obtained by adding one additional curve to the base for a 6D SCFT. This additional curve can intersect either one or two curves of the SCFT base. Much as in the study of Lie algebras, LSTs should be viewed as an "affine extension" of SCFTs.
• Figure 2: Depiction of the tensor branch of the $\mathcal{N}=(2,0)$$\widehat{A}_{3}$ LST. In the top figure, we engineer this example using spacetime filling M5-branes probing the geometry $S_{\bot}^1 \times \mathbb{C}^2$. In the dual F-theory realization, we have four $-2$ curves in the base, which are arranged as the affine $\widehat{A}_3$ Dynkin diagram. The Kähler class of each $-2$ curve in the F-theory realization corresponds in the M-theory realization to the relative separation between the M5-branes.
• Figure 3: Top: Depiction of the LST realized by $k$ M5-branes in between the two Horava-Witten nine-brane walls of heterotic M-theory ($k=3$ above). This leads to an LST with an $E_8 \times E_8$ flavor symmetry Bottom: The Corresponding F-theory base given by the configuration of curves $[E_8],1,2,...,2,1,[E_8]$ for $k$ total compact curves. In this realization, the $E_8$ flavor symmetry is localized on two non-compact 7-branes, one intersecting each $-1$ curve.
• Figure 4: $F_4$
• Figure 5: $G_2$