Research

String theory and gauge/gravity duality

String theory is a consistent theory of quantum gravity - the only one known so far. However, so far we only have a non-perturbative formulation of this theory on a limited class of space-times which have specific types of boundaries, using the gauge/gravity duality and its generalizations. And even this duality has not yet been derived (though there is substantial evidence that it is true). Can we generalize the gauge/gravity duality to more general situations, for instance to weakly coupled field theories which should be dual to backgrounds with light high-spin fields ("high-spin gravities") ? Can this help us to derive the gauge/gravity duality, namely construct the mapping between the field theory degrees of freedom and those of the gravitational theory (such as string theory) ? Can we find a non-perturbative formulation for string theory on more general backgrounds, such as flat space or de Sitter space ?

Dualities in quantum field theory

Quantum field theories can easily be studied in perturbation theory when they are weakly coupled, but very little is known about them when they are strongly coupled, even though many interesting field theories (including quantum chromodynamics at low energies) are strongly coupled. For some quantum field theories, it has been found that the strongly coupled theory has an alternative description in terms of some different quantum field theory, that is sometimes weakly coupled. In two space-time dimensions this phenomenon has been known for a long time and is reasonably well-understood. In higher dimensions we have a list of examples of this phenomenon, mostly in supersymmetric field theories, but no general understanding of when and how it happens. Can we find dual descriptions for more strongly coupled field theories in three and four space-time dimensions, in particular for more non-supersymmetric theories ? Can we relate the dualities of different theories (including theories in different space-time dimensions) ? Can we understand duality mappings in general, and obtain rules that will tell us when some theory has a dual description, and what it is ?

Quantum field theories in higher dimensions

Weakly coupled interacting quantum field theories exist only in four or less space-time dimensions. However, there are arguments that consistent quantum field theories exist also in five and six space-time dimensions. In particular there are indirect arguments for the existence of local superconformal field theories in five and six dimensions, and of non-local field theories (called "little string theories") in six dimensions. Can we provide direct constructions of these higher dimensional theories, and understand their properties ? What can we learn about lower dimensional field theories by compactifying these theories on various manifolds ? Are there any consistent field theories above six space-time dimensions, and are there any consistent non-supersymmetric field theories above four space-time dimensions ? What are the rules for dealing with non-local (but non-gravitational) theories like "little string theories" ?

Supersymmetry

Supersymmetry is a symmetry that maintains Bose-Fermi degeneracy, so the spectrum of bosons and fermions has to be identical. Supersymmetry also imposes severe constraints on the allowed interactions between the various particle species. These models are special, and lead to powerful tools that are applicable even for strongly coupled theories. Traditionally, the power of supersymmetry was mostly limited to studying the vacuum structure (more precisely, the chiral ring). Recently, it was realized that supersymmetry leads to remarkable simplifications also on curved spaces, and it allows to extract information that extends well beyond the chiral ring of the theory. These recent developments can also be used to evaluate the expectation values of non-local observables, such as the entanglement entropy of the vacuum. These observables are of exceeding interest in particle physics and also in condensed matter physics. Which additional quantities can be evaluated non-perturbatively in supersymmetric field theories? What can we learn about general aspects of quantum field theory such as dualities and anomalies? What do we learn about the vacuum of quantumfield theory? What is the mathematical interpretation of supersymmetric theories on curved spaces?