Workshop on Large-N at Swansea

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In 1974 't Hooft proposed to approximate QCD by an SU(N) gauge theory, where the number of colours, N, is taken to infinity. 't Hooft showed that in this limit the dynamics of the gauge theory is controlled by planar graphs. This idea is known as the ``'t Hooft large-N limit''. 't Hooft also proposed that in this limit the gauge theory may have a description in terms of a tree level string theory. The 't Hooft large-N limit has led to several phenomenological successes, among them an explanation of the Zweig rule and the Witten-Veneziano formula for the eta' mass. In 1998 Maldacena conjectured that large-N N=4 SYM has a dual description in terms of type IIB supergravity on the space AdS5 x S5 , giving a concrete realization of 't Hooft's idea in a four-dimensional setup. This connection is known as the AdS/CFT duality. Thanks to this duality, a completely new class of strongly coupled field theories with non-trivial dynamics became accessible to analytical methods, by applying a set of controllable deformations to the weakly-coupled dual description.This example illustrates how powerful a tool the classification of solvable field theories and of their properties is, by allowing to explore new large classes of models which cannot be studied with standard perturbative techniques. Since the original work by Maldacena, string-gauge duality has evolved to include examples of theories of immediate relevance for QCD and Beyond the Standard Model phenomenology and theories that describe condensed matter system. Besides, the intense theoretical activity on gauge-string duality has stimulated the formation of a community dedicated to studies of theories in the large-N limit with lattice techniques, which provide first-principle results enabling us to connect theories at large-N and models at finite N.We propose to organize a four day workshop at Swansea about various aspects of large-N gauge theories: formal, phenomenological and lattice simulations. The focus of this conference is twofold. On the formal side, we want to stress the importance of searching for non-trivial systems that can be fully solved and understood in a satisfactory and rigorous way. On the application side, we want to summarise the progress that this program made possible towards the understanding of dynamical systems exhibiting non-trivial features such as conformal fixed points and phase transitions, both analytically and with numerical lattice studies. Special attention will be given also to the phenomenological implications such as the study of QCD, of large-N gauge theories with generic representations of the Lie algebra of the underlying symmetries and of Dynamical Electro-Weak Symmetry Breaking.