New $ \mathcal{N} $ =1 dualities

New Perspectives in String Phenomenology from Dualities 1

After a review of some topics concerning the phenomenological applications of perturbative string theory, I discuss to what extent all of it is affected by the recent developements in string dualities. To appear in the proceedings of the Workshop on Phenomenological Applications of String Theory (PAST), ICTP, Trieste (Italy), October 1997.

Dualities in population genetics: a fresh look with new dualities

We apply our general method of duality, introduced in [10], to models of population dynamics. The classical dualities between forward and ancestral processes can be viewed as a change of representation in the classical creation and annihilation operators, both for diffusions dual to coalescents of Kingman’s type, as well as for models with finite population size. Next, using SU(1, 1) raising an...

Two new homomorphism dualities and lattice operations

The study of constraint satisfaction problems definable in various fragments of Datalog has recently gained considerable importance. We consider constraint satisfaction problems that are definable in the smallest natural recursive fragment of Datalog monadic linear Datalog with at most one EDB per rule, and also in the smallest non-linear extension of this fragment. We give combinatorial and al...

Supersymmetry and Dualities in Various Dimensions 1

Sicilian gauge theories and N = 1 dualities

In theories without known Lagrangian descriptions, knowledge of the global symmetries is often one of the few pieces of information we have at our disposal. Gauging (part of) such global symmetries can then lead to interesting new theories, which are usually still quite mysterious. In this work, we describe a set of tools that can be used to explore the superconformal phases of these theories. ...