Interpolating the Coulomb Phase of Little String Theory

TL;DR

This paper investigates higher-derivative terms in the Coulomb branch effective action of (1,1) little string theory by interpolating between perturbative super-Yang-Mills and double scaled little string theory results, revealing insights into UV and strong coupling completions.

Contribution

It introduces a numerical interpolation method for 8-derivative terms in little string theory, bridging perturbative gauge theory and string theory limits.

Findings

Successfully interpolated 8-derivative terms for k=2,3,4,5.

Indicated the protected nature of 6-derivative terms across the Coulomb branch.

Provided implications for UV completion of 6D SYM and DSLST.

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.