Andrew K. Waldron
AMS Math Reviews
Web Page: http://www.math.ucdavis.edu/~wally/
Office: MSB 3138
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 [1, 3].
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 goemetric topology.
- The Matrix Theory S-matrix (with J. C. Plefka and M. Serone),
Phys. Rev. Lett. 81 (1998), 2866-2869, arXiv:hep-th/9806081.
- An index theorem for non-standard Dirac operators
(with J.-W. van Holten and K. Peeters),
Class. Quant. Grav. 16 (1999), 2537-2544, arXiv:hep-th/9901163.
- Three graviton scattering in M-Theory
(with R. Helling, J. Plefka, and M. Serone),
Nucl. Phys. B559 (1999), 184-204, arXiv:hep-th/9905183.
- R^4 couplings, the fundamental membrane and exceptional
theta correspondences (with B. Pioline, H. Nicolai, and J. Plefka),
JHEP 0103 (2001), 036, arXiv:hep-th/0102123.
- Null propagation of partially massless higher spins in (A)dS and
cosmological constant speculations (with S. Deser), arXiv:hep-th/0105181.
Last updated: 0000-00-00