Open Access
January 2010 Five-Branes in M-Theory and a Two-Dimensional Geometric Langlands Duality
Meng-Chwan Tan
Adv. Theor. Math. Phys. 14(1): 179-224 (January 2010).


A recent attempt to extend the geometric Langlands duality to affine Kac–Moody groups has led Braverman and Finkelberg to conjecture a mathematical relation between the intersection cohomology of the moduli space of G-bundles on certain singular complex surfaces, and the integrable representations of the Langlands dual of an associated affine G-algebra, where G is any simply-connected semisimple group. For the AN−1 groups, where the conjecture has been mathematically verified to a large extent, we show that the relation has a natural physical interpretation in terms of six-dimensional compactifications of M-theory with coincident five-branes wrapping certain hyperkähler four-manifolds; in particular, it can be understood as an expected invariance in the resulting spacetime BPS spectrum under string dualities. By replacing the singular complex surface with a smooth multi-Taub-NUT manifold, we find agreement with a closely related result demonstrated earlier via purely field-theoretic considerations by Witten. By adding OM five-planes to the original analysis, we argue that an analogous relation involving the non-simply-connected DN groups ought to hold as well. This is the first example of a string-theoretic interpretation of such a two-dimensional extension to complex surfaces of the geometric Langlands duality for the A–D groups.


Download Citation

Meng-Chwan Tan. "Five-Branes in M-Theory and a Two-Dimensional Geometric Langlands Duality." Adv. Theor. Math. Phys. 14 (1) 179 - 224, January 2010.


Published: January 2010
First available in Project Euclid: 31 August 2010

zbMATH: 1201.81095
MathSciNet: MR2684980

Rights: Copyright © 2010 International Press of Boston

Vol.14 • No. 1 • January 2010
Back to Top