Four-dimensional N=4 SYM theory and the swampland.

We consider supergravity theories with 16 supercharges in Minkowski space with dimensions d>3. We argue that there is an upper bound on the number of massless modes in such theories depending on d. In particular, we show that the rank of the gauge symmetry group G in d dimensions is bounded by rG≤26-d. This in particular demonstrates that four-dimensional N=4 SYM theories with rank bigger than 22, despite being consistent and indeed finite before coupling to gravity, cannot be consistently coupled to N=4 supergravity in Minkowski space and belong to the swampland. Our argument is based on the swampland conditions of completeness of spectrum of defects as well as a strong form of the distance conjecture and relies on unitarity as well as supersymmetry of the world sheet theory of BPS strings. The results are compatible with known string constructions and provide further evidence for the string lamppost principle: that string theory lamppost seems to capture all consistent quantum gravitational theories. [ABSTRACT FROM AUTHOR]