Professor Andrew Waldron's research is devoted to a broad range of problems in theoretical and mathematical physics. In particular he has made an important contribution to the conjectured Banks-Fishler-Shenker-Susskind (BFSS) matrix model of string theory and M-theory. String theory is a proposed perturbative theory that would unify all of the fundamental forces of physics; in other words it is a “theory of everything”. Its non-perturbative counterpart is a hypothetical theory called M-theory. One part of the BFSS conjecture relates the scattering of bound states to scattering of supergravitons. (Eleven-dimensional supergravity is a known low-energy limit of M-theory.) This relation has been verified in many cases; the strongest results in this direction belong to Professor Waldron.
Professor Waldron has also studied other problems arising in M-theory and in supergravity. In particular, he analyzed higher spin fields on a special model universe called anti-de-Sitter space. These results are relevant to the AdS/CFT conjecture in M-theory, which asserts that supergravity on anti-de-Sitter space is equivalent to conformal field theory on its boundary. Several other articles by Professor Waldron are devoted to the theory of spinors and of operators acting on spinor fields. For example, he calculated the index of non-standard Dirac operators. This result in the vein of the celebrated Atiyah-Singer index theorem, which was one of the first connections between quantum field theory and geometric topology.