  We report observations of dense molecular gas in the star-forming galaxy EGS
13004291 (z=1.197) using the Plateau de Bure Interferometer. We tentatively
detect HCN and HNC (J=2-1) emission when stacked together at ~4sigma
significance, yielding line luminosities of L_HCN (J=2-1) =(9 +/- 3) x 10^9 K
km s^-1 pc^2 and L_HNC (J=2-1)= (5 +/-2) x 10^9 K km s^-1 pc^2 respectively. We
also set 3sigma upper limits of < 7-8 x 10^9 K km s^-1 pc^2 on the HCO+, H2O
(3_13-2_20) and HC3N (J=20-19) line luminosities. We serendipitously detect CO
emission from two sources at z~1.8 and z~3.2 in the same field of view. We also
detect CO(J=2-1) emission in EGS 13004291, showing that the excitation in the
previously detected CO(J=3-2) line is subthermal (r_32=0.65 +/- 0.15). We find
a line luminosity ratio of L_HCN/L_CO=0.17 +/- 0.07 , as an indicator of the
dense gas fraction. This is consistent with the median ratio observed in z>1
galaxies (L_HCN/L_CO=0.16 +/- 0.07) and nearby ULIRGs (L_HCN/L_CO=0.13 +/-
0.03), but higher than in local spirals (L_HCN/L_CO=0.04 +/- 0.02). Although
EGS 13004291 lies significantly above the galaxy main sequence at z~1, we do
not find an elevated star formation efficiency (traced by L_FIR/L_CO) as in
local starbursts, but a value consistent with main-sequence galaxies. The
enhanced dense gas fraction, the subthermal gas excitation, and the lower than
expected star formation efficiency of the dense molecular gas in EGS 13004291
suggest that different star formation properties may prevail in high-z
starbursts. Thus, using L_FIR/L_CO as a simple recipe to measure the star
formation efficiency may be insufficient to describe the underlying mechanisms
in dense star-forming environments inside the large gas reservoirs.
