We measure the fraction of Luminous Red Galaxies (LRGs) in dynamically close pairs (with projected separation less than 20 $h^{-1}$ kpc and velocity difference less than 500 km s$^{-1}$) to estimate the dry merger rate for galaxies with $-23 < M(r)_{k+e,z=0.2} +5 log h < -21.5$ and $0.45 < z < 0.65$ in the 2dF-SDSS LRG and QSO (2SLAQ) redshift survey. For galaxies with a luminosity ratio of $1:4$ or greater we determine a $5sigma$ upper limit to the merger fraction of 1.0% and a merger rate of $< 0.8 times 10^{-5}$ Mpc$^{-3}$ Gyr$^{-1}$ (assuming that all pairs merge on the shortest possible timescale set by dynamical friction). This is significantly smaller than predicted by theoretical models and suggests that major dry mergers do not contribute to the formation of the red sequence at $z < 0.7$.
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