We construct a consistent Kaluza–Klein reduction of D = 11 supergravity
on Σ2 × S4
, where Σ2 = S2, R2 or H2
, 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) × SE(3) ⊂ SO(5, 3) subgroup of the SO(1, 1) × SO(5, 3) global
symmetry group of the ungauged theory. For Σ2 = H2, the D = 5 theory
has a maximally supersymmetric AdS5 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 Σ2 = S2
, we find two AdS5 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) × SO(1, 1), and a single hypermultiplet, with quaternionic
Kähler manifold SU(2, 1)/S[U(2) × U(1)] and gauging associated with an
SO(2) × R ⊂ SU(2, 1) subgroup.