Little strings and T-duality

TL;DR

The authors construct and compare UV 2d gauge theories for IIA and IIB little strings on NS5-branes, introducing a new N=(0,4) description for IIA to enable protected observable computations. They compute the elliptic genera on both sides and demonstrate precise T-duality mappings between the IIA and IIB spectra, after properly removing extra contributions from the D6/FI sector via a Z_{extra} factor. The work also uncovers rich modular properties and trialities of the elliptic genus, revealing SL(2,Z) invariances in multiple fugacities and clarifying how complex structure and K2hler parameters interchange under dualities. These results provide a concrete, calculable check of little-string T-duality and offer robust tools for exploring related 6d theories and dualities in string theory.

Abstract

We study the 2d N = 4 gauge theory descriptions of little strings on type II NS5- branes. The IIB strings on N NS5-branes are described by the N = (4,4) gauge theories, whose Higgs branch CFTs on U(N) instanton moduli spaces are relevant. The IIA strings are described by N = (4,4) circular A_{N-1} quiver theories, whose Coulomb branch CFTs are relevant. We study new N = (0,4) quiver gauge theories for the IIA strings, which make it easier to study some infrared observables. In particular, we show that the elliptic genera of the IIA / IIB strings precisely map to each other by T-duality.

Figures (5)

• Figure 1: M-theory brane uplift of the IIA little strings
• Figure 2: $\hat{A}_{N-1}$ quiver diagram of the 2d $\mathcal{N}=(0,4)$ gauge theory for the IIA strings. Solid lines denote the hypermultiplets, thin dashed lines denote the Fermi multiplets, and thick dashed lines denote the twisted hyper multiplets.
• Figure 3:
• Figure 4: a) $(p,q)$ fivebranes web dual to rank 1 little string theory. b) Triality between three Kähler parameters, $\hat{q}=qy^{-1}$, $\hat{w}=wy^{-1}$, and $y$.
• Figure 5: $(p,q)$ fivebranes web dual to rank 2 little string theory