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In this paper, we investigate the properties of a membrane in the M5-brane background. Through solving the classical equations of motion of the membrane, we can understand the classical dynamics of the membrane in this background.
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We study dimensional reduction of M5 branes on a circle bundle when the supersymmetry parameter is not constant along the circle. When the gauge group is Abelian and the fields appear quadratically in the Lagrangian, we can always obtain a supersymmetric five-dimensional theory by keeping fermionic nonzero modes that match with the corresponding nonzero modes of the supersymmetry parameter, and by keeping the zero modes for the bosonic fields as usual. But a supersymmetric non-Abelian generalization can be found only under special circumstances. One instance where we find a non-Abelian supersymmetric generalization is when we perform dimensional reduction along a null direction.
We construct supersymmetric $AdS_5times Sigma$ solutions of $D=7$ gauged supergravity, where $Sigma$ is a two-dimensional orbifold known as a spindle. These uplift on $S^4$ to solutions of $D=11$ supergravity which have orbifold singularites. We argue that the solutions are dual to $d=4$, $mathcal{N}=1$ SCFTs that arise from $N$ M5-branes wrapped on a spindle, embedded as a holomorphic curve inside a Calabi-Yau three-fold. In contrast to the usual topological twist solutions, the superconformal R-symmetry mixes with the isometry of the spindle in the IR, and we verify this via a field theory calculation, as well as reproducing the gravity formula for the central charge.
We show that charge-quantization of the M-theory C-field in J-twisted Cohomotopy implies emergence of a higher Sp(1)-gauge field on single heterotic M5-branes, which exhibits worldvolume twisted String structure.
We study three-dimensional superconformal field theories on wrapped M5-branes. Applying the gauge/gravity duality and the recently proposed 3d-3d relation, we deduce quantitative predictions for the perturbative free energy of a Chern-Simons theory on hyperbolic 3-space. Remarkably, the perturbative expansion is expected to terminate at two-loops in the large N limit. We check the correspondence numerically in a number of examples, and confirm the N^3 scaling with precise coefficients.
We construct a consistent Kaluza-Klein reduction of $D=11$ supergravity on $Sigma_2times S^4$, where $Sigma_2=S^2,mathbb{R}^2$ or $H^2$, or a quotient thereof, at the level of the bosonic fields. The result is a gauged $N=4$, $D=5$ supergravity theory coupled to three vector multiplets, with the gauging lying in an $SO(2)times SE(3)subset SO(5,3)$ subgroup of the $SO(1,1)times SO(5,3)$ global symmetry group of the ungauged theory. For $Sigma_2=H^2$, the $D=5$ theory has a maximally supersymmetric $AdS_5$ vacuum which uplifts to the known solution of $D=11$ supergravity corresponding to M5-branes wrapping a Riemann surface with genus greater than one and dual to an $N=2$ SCFT in $d=4$. For $Sigma_2=S^2$, we find two $AdS_5$ solutions, one of which is new, and both of which are unstable. There is an additional subtruncation to an $N=2$ gauged supergravity coupled to two vector multiplets, with very special real manifold $SO(1,1)times SO(1,1)$, and a single hypermultiplet, with quaternionic Kahler manifold $SU(2,1)/S[U(2)times U(1)]$ and gauging associated with an $SO(2)timesmathbb{R}subset SU(2,1)$ subgroup.
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