Searching for anisotropic cosmic birefringence with polarization data from SPTpol

We present a search for anisotropic cosmic birefringence in 500 deg(2) of southern sky observed at 150 GHz with the SPTpol camera on the South Pole Telescope. We reconstruct a map of cosmic polarization rotation anisotropies using higher-order correlations between the observed cosmic microwave background (CMB) E and B fields. We then measure the angular power spectrum of this map, which is found to be consistent with zero. The nondetection is translated into an upper limit on the amplitude of the scale-invariant cosmic rotation power spectrum, L(L + 1)C-L(alpha alpha)/2 pi < 0.10 x 10(-4) rad(2) (0.033 deg(2), 95% C.L.). This upper limit can be used to place constraints on the strength of primordial magnetic fields, B-1 Mpc < 17 nG (95% C.L.), and on the coupling constant of the Chern-Simons electromagnetic term g(alpha gamma) < 4.0 x 10(-2)/H-I (95% C.L.), where H-I is the inflationary Hubble scale. For the first time, we also cross-correlate the CMB temperature fluctuations with the reconstructed rotation angle map, a signal expected to be nonvanishing in certain theoretical scenarios, and find no detectable signal. We perform a suite of systematics and consistency checks and find no evidence for contamination.