Wspólnotowy Serwis Informacyjny Badan i Rozwoju - CORDIS

Periodic Report Summary 1 - GT5LD2013 (Gauge theories in 5 and lower dimensions: string perspective, holographic avatars and exact results)

Quantum Field Theory (QFT) is an essential tool in our description of Nature. Over the recent past we have discovered many fascinating and unforeseen aspects of it, such as duality and the profound role of its non-perturbative aspects. Yet, we believe that this progress only scratches the surface of a deeply fascinating topic. Concentrating on supersymmetric theories as laboratory, the String Theory inspiration has taught us very recently that QFT should be regarded in a more abstract way regardless of lagrangians, including their dualities and often implicitly described through String/M Theory objects. In this context, very recently QFT's in dimensions higher than four have attracted a lot of interest, in part through their remarkable properties but also due to the fact that they play, in a certain sense, a role as building blocks of theories. With this on mind, in this project we set out to study QFT's with special interest on the case of 5d theories.

More precisely we have obtained interesting results concerning the structure of the spectrum and the instanton operators of 5d theories. To begin with, we have classified the backgrounds where they can be consistently defined. This result is very useful for further use of the latest analytic tools of supersymmetric localization. Moreover, it allowed us to study under what conditions relevant deformations into a standard gauge theory exist. As a consequence, this provided a novel way to regard instanton operators yielding a very interesting new interpretation. Moreover, we have discovered hints of the existence of a BPS-like quiver in 5d theories where instanton states play a very important role. We have also studied 4d gauge theories in generic toric Kahler backgrounds, including as well their instanton sector. The latter shows interesting properties which follow from an ADHM-like construction whose embedding into a physics context we introduced.

During the first half of the project we have produced 8 highly appreciated research papers, written in collaboration both with junior members of the local group as well as with renowned scientists from the best institutions worldwide. Moreover, we have engaged in a very active dissemination agenda, including lectures in adult programs, courses for advanced undergraduate students on modern physics as well as high school talks.

The CIG grant is being very important in the re-integration of the fellow to the University of Oviedo, both in providing funds to achieve the results but also in helping towards the promotion to a permanent position.

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