Quantum field theory, String theory, Conformal field theory, Affine Lie algebra, Matrix theory, orbifold theory, and the large N limit.
For the past few years, we have been constructing the theory of the general current-algebraic orbifold, which had previously been studied only at the level of examples. The general construction also allows us to see more deeply into orbifold theory, and we are presently working out new twisted KZ equations for various classes of orbifolds. Extensions of this program including open WZW strings and twisted open WZW strings are also being studied in our group.
J. de Boer, J. Evslin, M. B. Halpern, and J. E. Wang, “New duality transformations in orbifold theory,” Int. J. Mod. Phys A15, 1297 (2000).
M. B. Halpern and J. E. Wang, “More about all current-algebraic orbifolds,” Int. J. Mod. Phys A16, 97 (2001).
S. Giusto and M. B. Halpern, “Hamiltonian formulation of open WZW strings,” hep-th/0101220.
J. de Boer, M. B. Halpern, and N. A. Obers, “The operator algebra and twisted KZ equations of WZW orbifolds,” hep-th/0105305.