Talks

The validity of a local AdS supergravity description of SYM at strong coupling requires the existence of a parametrically large gap in the spectrum of dimensions of the local operators, separating the low dimension operators dual to supergravity fields from the others. We shall give evidence that the reverse is also true: a large gap in the spectrum of dimensions implies a local bulk dual.

Using this limit we can extract the scattering amplitudes of the bulk theory in flat space from the correlation functions of the dual CFT. This gives a non-perturbative definition of flat space string theory scattering amplitudes as a limit of the correlation functions of SYM.

Dualities appear in nearly all disciplines of physics and play a central role in statistical mechanics and field theory. I will discuss in a pedagogical way our recent findings motivated by a quest for a simple unifying framework for the detection and treatment of dualities. I will explain how classical and quantum dualities, as well as duality relations that appear only in a sector of certain theories (i.e. emergent dualities), can be unveiled, and systematically established. Our method relies on the use of morphisms of the "bond algebra" of a quantum Hamiltonian. Dualities are characterized as unitary mappings implementing such morphisms, whose even powers become symmetries of the quantum problem. Dual variables (non-local mappings between the elementary degrees of freedom of the theory) which were guessed in the past can be derived in our formalism. New self-dualities for four-dimensional Abelian gauge field theories will be discussed.