  The Cosmic Microwave Background (CMB) bispectrum of the temperature
anisotropies induced by a network of cosmic strings is derived for small
angular scales, under the assumption that the principal cause of temperature
fluctuations is the Gott-Kaiser-Stebbins (GKS) effect. We provide analytical
expressions for all isosceles triangle configurations in Fourier space. Their
overall amplitude is amplified as the inverse cube of the angle and diverges
for flat triangles. The isosceles configurations generically lead to a negative
bispectrum with a power law decay l^(-6) for large multipole l. However,
collapsed triangles are found to be associated with a positive bispectrum
whereas the squeezed triangles still exhibit negative values. We then compare
our analytical estimates to a direct computation of the bispectrum from a set
of 300 statistically independent temperature maps obtained from Nambu-Goto
cosmic string simulations in a Friedmann-Lemaitre-Robertson-Walker (FLRW)
universe. We find good agreement for the overall amplitude, the power law
behaviour and angle dependency of the various triangle configurations. At l~500
the cosmic string GKS effect contributes approximately the same equilateral CMB
bispectrum amplitude as an inflationary model with |fNL|~10^3, if the strings
contribute about 10% of the temperature power spectrum at l=10. Current bounds
on fNL are not derived using cosmic string bispectrum templates, and so our fNL
estimate cannot be used to derive bounds on strings. However it does suggest
that string bispectrum templates should be included in the search of CMB
non-Gaussianities.
