The zero-form and one-form global symmetries of the Aharony-Bergman-Jafferis (ABJ) related theories, with at least $\mathcal{N}=6$ supersymmetry in three dimensions, are examined detail. Starting from well-known dualities between theories orthogonal symplectic gauge groups those unitary groups, we their or subgroups obtain new dualities. One side latter involves special other groups; there is a...

We derive the fivebrane instanton corrections to the hypermultiplet moduli space MH of Calabi-Yau string vacua using S-duality symmetry of the type IIB formulation. The result is given in terms of a set of holomorphic functions on the twistor space of MH . It contains not only all orders of the instanton expansion, but also takes into account the presence of D1-D(-1)-brane instantons. Furthermo...

Traditionally in natural duality theory the algebras carry no topology and the objects on the dual side are structured Boolean spaces. Given a duality, one may ask when the topology can be swapped to the other side to yield a partner duality (or, better, a dual equivalence) between a category of topological algebras and a category of structures. A prototype for this procedure is provided by the...

Duality transformations with respect to rotational isometries relate supersymmetric with non-supersymmetric backgrounds in string theory. We find that non-local world-sheet effects have to be taken into account in order to restore supersymmetry at the string level. The underlying superconformal algebra remains the same, but in this case T-duality relates local with non-local realizations of the...

The effective action for type II string theory compactified on a six torus is N = 8 supergravity, which is known to have an E 7 duality symmetry. We show that this is broken by quantum effects to a discrete subgroup, E 7 (Z), which contains both the T-duality group O(6, 6; Z) and the S-duality group SL(2; Z). We present evidence for the conjecture that E 7 (Z) is an exact 'U-duality' symmetry o...

Given an algebra M we may adjoin an isolated zero to form an algebra M∞ satisfying all identities u ≈ v true in M for which u and v contain the same variables. Drawing on the structure theory of P lonka sums, we show that if M is a finite, dualisable algebra which is strongly irregular, then M∞ is also dualisable. Turning the construction of M∞ upside-down for the two-element left-zero band, we...

We argue that all conjectured dualities involving various string, Mand F theory compactifications can be ‘derived’ from the conjectured duality between type I and SO(32) heterotic string theory, T-dualities, and the definition of Mand F theories. (Based on a talk given at the conference on ‘Advanced Quantum Field Theory’, Le Londe-les-Maures, France, Aug.31-Sept.5, 1996, in memory of Claude Itz...

255 Samenvatting (in Dutch) 257

I describeour understanding of physics near the planck length, in particular the great progress of the last four years in string theory. Superstring theory, and a recent extension called M theory, are leading candidates for a quantum theory that unifies gravity with the other forces. As such, they are certainly not ordinary quantum field theories. However, recent duality conjectures suggest tha...

In the fruitful interplay between gauge fields and strings and in many conjectured M-theory dualities, open strings play a prominent role. We review the construction of open-string descendants (un-orientifolds) of closed-string theories admitting a generalized orientation reversal involution. We then specialize the construction to some classes of non-supersymmetric models in D = 10 that have be...