Swampland conjectures for an almost topological gravity theory

We analyze AdS and dS swampland conjectures in a three-dimensional higher spin theory with self-interacting matter, which contains conformal gravity is almost topological. A of similar type was proposed as the effective high energy phase non-critical M-theory 3D. With some details differing from usual string story, it found that resulting theory, namely topologically massive gravity, fits well into web conjectures. Supporting recent proposal, particular we find this 3D gives rise to quantum break time scales like tQ∼H−1.