  Correlated orientations of quasar optical and radio polarisation, and of
radio jets, have been reported on Gpc scales, possibly arising from intrinsic
alignment of spin axes. Optical quasar polarisation appears to be
preferentially either aligned or orthogonal to the host large-scale structure,
specifically large quasar groups (LQGs). Using a sample of 71 LQGs at redshifts
$1.0 \leq z \leq 1.8$, we investigate whether LQGs themselves exhibit
correlated orientation. We find that LQG position angles (PAs) are unlikely to
be drawn from a uniform distribution ($p$-values $0.008 \lesssim p \lesssim
0.07$). The LQG PA distribution is bimodal, with median modes at
$\bar{\theta}\sim45\pm2^{\circ}, 136\pm2^{\circ}$, remarkably close to the mean
angles of quasar radio polarisation reported in two regions coincident with our
LQG sample. We quantify the degree of alignment in the PA data, and find that
LQGs are aligned and orthogonal across very large scales. The maximum
significance is $\simeq 0.8\%$ ($2.4\sigma$) at typical angular (proper)
separations of $\sim 30^{\circ}$ (1.6 Gpc). If the LQG orientation correlation
is real, it represents large-scale structure alignment over scales larger than
those predicted by cosmological simulations and at least an order of magnitude
larger than any so far observed, with the exception of quasar-polarisation /
radio-jet alignment. We conclude that LQG alignment helps explain
quasar-polarisation / radio-jet alignment, but raises challenging questions
about the origin of the LQG correlation and the assumptions of the concordance
cosmological model.
