Interpolating the Coulomb Phase of Little String Theory

Abstract

We study up to 8-derivative terms in the Coulomb branch effective action of (1,1) little string theory, by collecting results of 4-gluon scattering amplitudes from both perturbative 6D super-Yang-Mills theory up to 4-loop order, and tree-level double scaled little string theory (DSLST). In previous work we have matched the 6-derivative term from the 6D gauge theory to DSLST, indicating that this term is protected on the entire Coulomb branch. The 8-derivative term, on the other hand, is unprotected. In this paper we compute the 8-derivative term by interpolating from the two limits, near the origin and near the infinity on the Coulomb branch, numerically from SU(k) SYM and DSLST respectively, for k=2,3,4,5. We discuss the implication of this result on the UV completion of 6D SYM as well as the strong coupling completion of DSLST. We also comment on analogous interpolating functions in the Coulomb phase of circle-compactified (2,0) little string theory.

39 pages, 4 figures, 4 tables

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• On Higher Derivative Couplings in Theories with Sixteen Supersymmetries
• Supervertices and Non-renormalization Conditions in Maximal Supergravity Theories
• An Index for Ray Operators in 5d $E_n$ SCFTs
• The ABCDEFG of Little Strings
• Recursive Representations of Arbitrary Virasoro Conformal Blocks
• Little String Defects and Bala-Carter Theory
• On the component structure of one-loop effective actions in $6D$, $\mathcal{N}=(1,0)$ and $\mathcal{N}=(1,1)$ supersymmetric gauge theories
• Low-energy $6D$, $\mathcal{N}=(1,1)$ SYM effective action beyond the leading approximation
• Instanton corrections to the effective action of N=4 SYM