Measurements of the Absolute Branching Fraction of the Semileptonic Decay ${\mathbf{\Xi }}^{-}\to \mathbf{\Lambda }{\mathbf{e}}^{-}{\bar{\mathbf{\nu }}}_{\mathbf{e}}$ and the Axial Charge of the ${\mathbf{\Xi }}^{-}$

Using $(10087\pm 44)\times {10}^6$ $J\mathrm{/}\psi$ events collected with the BESIII detector, we study the semileptonic decay ${\mathrm{\Xi }}^{-}\to \mathrm{\Lambda }{e}^{-}{\bar{\nu }}_e$ for the first time at an electron-positron collider. The absolute branching fraction is determined for the first time to be $(3.60\pm {0.40}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}}\pm {0.10}_{\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}})\times {10}^{-4}$, which is 3.9 standard deviations below the world average. In addition, using an 11-dimensional angular analysis, the axial-vector to vector coupling $g_{av}$ is determined to be $0.18\pm {0.07}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}}\pm {0.02}_{\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}}$. These results are used to test various SU(3)-flavour effective models. Under the SU(3)-flavour symmetry limit, the axial charge is found to be $g_A^H=0.22\pm {0.08}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}}\pm {0.02}_{\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}}$. Despite using only 5% of the statistics of previous experiments, this analysis achieves a comparable precision for the axial charge.