Abstract
We study tree level scattering amplitudes of four massless states in the double scaled little string theory, and compare them to perturbative loop amplitudes in six-dimensional super-Yang-Mills theory. The little string amplitudes are computed from correlators in the cigar coset CFT and in N=2 minimal models. The results are expressed in terms of integrals of conformal blocks and evaluated numerically in the alpha' expansion. We find striking agreements with up to 2-loop scattering amplitudes of massless gluons in 6D SU(k) SYM at a Z_k invariant point on the Coulomb branch. We comment on the issue of UV divergence at higher loop orders in the gauge theory and discuss the implication of our results.
Highlights
There are two interesting maximally supersymmetric quantum field theories in six dimensions: the (2, 0) superconformal field theory and the (1, 1) super-Yang-Mills theory
We study tree level scattering amplitudes of four massless states in the double scaled little string theory, and compare them to perturbative loop amplitudes in sixdimensional super-Yang-Mills theory
The interactions of massless modes of little string theories (LST) are expected to be described by an effective theory that is 6D SYM deformed by higher dimensional operators. α will be mapped to the 6D Yang-Mills coupling via the relation
Summary
There are two interesting maximally supersymmetric quantum field theories in six dimensions: the (2, 0) superconformal field theory and the (1, 1) super-Yang-Mills theory. We find agreement between up to two-loop amplitudes of the massless gluons on the Coulomb branch of the 6D SYM, expanded to leading order in 1/m2W , and the tree level amplitude of the corresponding massless string modes in DSLST, expanded up to second order in α This is achieved through explicit computation of amplitudes in the SU(k) SYM, based on previously known two-loop results derived from unitarity cut methods [10,11,12,13,14,15], and in the DSLST by a worldsheet computation that involves expressing SL(2)/U(1) coset CFT correlators in terms of Liouville correlators, which are expressed as integrals of Virasoro conformal blocks. Details on the numerical integration of conformal blocks, based on Zamolodchikov’s recursion relations [19, 20], are described in appendix C
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