  Global polarizations ($P$) of $\Lambda$ ($\bar{\Lambda}$) hyperons have been
observed in non-central heavy-ion collisions. The strong magnetic field
primarily created by the spectator protons in such collisions would split the
$\Lambda$ and $\bar{\Lambda}$ global polarizations ($\Delta P = P_{\Lambda} -
P_{\bar{\Lambda}} < 0$). Additionally, quantum chromodynamics (QCD) predicts
topological charge fluctuations in vacuum, resulting in a chirality imbalance
or parity violation in a local domain. This would give rise to an imbalance
($\Delta n = \frac{N_{\text{L}} - N_{\text{R}}}{\langle N_{\text{L}} +
N_{\text{R}} \rangle} \neq 0$) between left- and right-handed $\Lambda$
($\bar{\Lambda}$) as well as a charge separation along the magnetic field,
referred to as the chiral magnetic effect (CME). This charge separation can be
characterized by the parity-even azimuthal correlator ($\Delta\gamma$) and
parity-odd azimuthal harmonic observable ($\Delta a_{1}$). Measurements of
$\Delta P$, $\Delta\gamma$, and $\Delta a_{1}$ have not led to definitive
conclusions concerning the CME or the magnetic field, and $\Delta n$ has not
been measured previously. Correlations among these observables may reveal new
insights. This paper reports measurements of correlation between $\Delta n$ and
$\Delta a_{1}$, which is sensitive to chirality fluctuations, and correlation
between $\Delta P$ and $\Delta\gamma$ sensitive to magnetic field in Au+Au
collisions at 27 GeV. For both measurements, no correlations have been observed
beyond statistical fluctuations.
