Non-perturbative Aspects Of Gauge Theories And String
Aree / Gruppi di ricerca
Partecipanti al progetto
Descrizione del progetto
The purpose of this project is to promote the study of (supersymmetric) gauge theories and of string theory with particular emphasis on their non-perturbative aspects.
String theory provides an elegant framework in which gravity and the other fundamental interactions that are present in Nature are unified in a consistent (and presumably finite) quantum theory. Although very peculiar, string theory is not at all incompatible with other common models for elementary particles or for gravitational theories. Indeed, it has deep connections with both gauge theories and general relativity, which arise in the low-energy limit when the string length becomes negligible.
Over the years string theory has offered many efficient tools to describe quantum field theories (in particular gauge theories) within various contexts. The central role is played by the so-called D-branes, which are solitonic supergravity configurations whose low-energy dynamics is described by quantum gauge theories. Therefore D-branes represent the natural tool to study gauge theories within string theory; moreover, their dual role as supergravity solitons has led to a deep relation between gauge and gravity theories. This gauge/gravity correspondence, whose prototype is the famous AdS/CFT duality between N=4 super Yang-Mills theory in four dimensions and the IIB string in the AdS_5 x S_5 background, allows one to study the strong coupling limit of gauge theories by means of the geometric properties of classical supergravity solutions or, more generally, of strings propagating in non-trivial backgrounds.
The exploration of the strong coupling regime where perturbation theory is not valid has been the focal point of interest of many researchers for many years. In the context of quantum field theories it has been understood since a long time that non-perturbative physics is often associated to topologically non-trivial field configurations, such as instantons in gauge theories. On the other hand, in the context of string theory the development of D-brane techniques has opened a completely new perspective in the study of the non-perturbative dynamics. In particular, the observation that instantons can be described in terms of D-branes within D-branes has led to a very intuitive picture of instantons and to the discovery of new "exotic" non-perturbative effects with interesting phenomenological applications since their strength is not linked to the gauge theory scale, a feature that is very welcome in the search of semi-realistic string scenarios for physics beyond the Standard Model.
Studies of the strong coupling behaviour of gauge theories have been recently boosted thanks to the application of localization techniques that have allowed numerous exact results in supersymmetric gauge theories to be found and the multi-instanton calculus to be developed far beyond what was known in the past. Certain non-perturbative phenomena, which only a few years ago seemed to be out of reach of a proper mathematical treatment, are now put in a framework where well-known methods of analysis can be applied.
The primary challenge of this project is to establish a more solid and predictive connection among the various aspects of this research field, exploring in particular the following topics:
A) Study of novel non-perturbative features of supersymmetric gauge theories and string theory by means of extensions and applications of localization techniques;
B) Applications of holography to understand supersymmetric gauge theories on curved backgrounds and supersymmetry breaking dynamics;
C) Analysis of Instanton Effects in Gauge and String Theories and their potential phenomenological applications.
Progress on these subjects may open up new lines of research in high-energy theoretical physics as well as in other more applicative fields.
The participants in this project have significantly contributed to the development of these topics and their publications provide an extremely solid scientific base for this research program.