  In this work, we study a class of higher derivative couplings in the string
effective action arising at the junction of topological string theory and
supersymmetric gauge theories in the $\Omega$-background. They generalise a
series of gravitational couplings involving gravitons and graviphotons, which
reproduces the topological string theory partition function. The latter
reduces, in the field theory limit, to the partition function of the gauge
theory in the $\Omega$-background when one if its parameters, say $\epsilon_+$,
is set to zero. This suggests the existence of a one-parameter extension called
the refined topological string. The couplings considered in this work involve
an additional vector multiplet and are evaluated, perturbatively and
non-perturbatively, at the string level. In the field theory limit, they
correctly reproduce the partition function of the gauge theory in a general
$\Omega$-background. Hence, these couplings provide new perspectives toward a
worldsheet definition of the refined topological string.
