  In this work, we found the solution for the field equations of
eleven-dimensional supergravity with a BPS conical topological defect
configuration. We chose the solutions that corresponded to a M2-brane where the
space-time presents the co-dimension two. The source of the topological defect
is a sigma model where the brane tension is connected with the angular deficit.
We analyzed the Killing spinor equations, a 3-form gauge potential and
Einstein's equations, proving that it is possible to find a full solution for
the system. We analyzed the near-horizon limit proving that it is possible to
obtain an $AdS_4 \times S^1 \times \mathbb{E}^6 $ geometry for certain values
of the brane tension. We also discussed some applications in the strong
coupling theory for condensed matter systems.
