## Final Activity Report Summary - SUPERCFT (Conformal field theories with Lie superalgebra symmetry and string backgrounds with fluxes)

The project was concerned with fundamental aspects of string theory. This theory is widely believed to provide the long sought marriage of quantum theory with Einstein's theory of gravity. At the same time it naturally includes the physics of elementary particles which can be thought of as different vibration modes of the string. Furthermore, scientists hope to be able to extract cosmological models from string theory which are capable of explaining the evolution of our universe after the big bang and the formation of the cosmic structure. Many of the physical phenomena we see every day are due to the interaction of electrons with electric or magnetic fields. Similarly, generalisations of electro-magnetic fields are of equal important in string theory. In fact, for all concrete physical predictions it is inevitable to understand how strings behave in the presence of fluxes. Progress in this direction was hindered for a long time, since the mathematical foundations have not been understood.

In this project a systematic analysis of these problems was provided and a variety of methods has been developed to overcome these difficulties. The starting point was a toy model which already exhibited a vast number of the specific features that are present in the general case. In this case a complete solution was possible due to the large amount of symmetry. At the same time, invaluable insights about the mathematical structure of the underlying theory could be obtained. In a second step, deformations of the toy model have been studied in order to make contact with real string theoretic setups. As a result it was possible to derive the energy of open strings as a function of the deformation parameter.

In the second half of the project, an important step towards a treatment of the celebrated AdS/CFT correspondence has been taken. The latter states that a specific setup of string theory - involving the presence of certain flux configurations - is actually completely equivalent to a theory which normally appears in pure particle physics. The most astonishing fact about this correspondence is that it relates a theory with gravity to one without, and many important insights have already been deduced.

The present work treated examples whose structure is very similar to that of the string theory setup mentioned before. As a consequence an unexpected equivalence between two theories was discovered, one being of geometric origin, the other having no relation to geometry. Although not directly relevant to the AdS/CFT correspondence, it nevertheless led to important insights which might turn out to be useful in an eventual proof of the latter. Indeed, even though the AdS/CFT correspondence already found numerous applications and passed many non-trivial checks, it still has the status of a conjecture.

Based on the achievements outlined above, physicists can now start to develop concrete string theory scenarios which allow explaining new experimental results which are soon to be expected from the particle collider LHC at CERN or from astronomical observations. Other applications concern the study of exotic materials exposed to strong magnetic fields. These materials exhibit transitions between phases where the charge carriers are localised and others where they are delocalised. It is an amazing fact that this phenomenon can be described by very similar theories.

In this project a systematic analysis of these problems was provided and a variety of methods has been developed to overcome these difficulties. The starting point was a toy model which already exhibited a vast number of the specific features that are present in the general case. In this case a complete solution was possible due to the large amount of symmetry. At the same time, invaluable insights about the mathematical structure of the underlying theory could be obtained. In a second step, deformations of the toy model have been studied in order to make contact with real string theoretic setups. As a result it was possible to derive the energy of open strings as a function of the deformation parameter.

In the second half of the project, an important step towards a treatment of the celebrated AdS/CFT correspondence has been taken. The latter states that a specific setup of string theory - involving the presence of certain flux configurations - is actually completely equivalent to a theory which normally appears in pure particle physics. The most astonishing fact about this correspondence is that it relates a theory with gravity to one without, and many important insights have already been deduced.

The present work treated examples whose structure is very similar to that of the string theory setup mentioned before. As a consequence an unexpected equivalence between two theories was discovered, one being of geometric origin, the other having no relation to geometry. Although not directly relevant to the AdS/CFT correspondence, it nevertheless led to important insights which might turn out to be useful in an eventual proof of the latter. Indeed, even though the AdS/CFT correspondence already found numerous applications and passed many non-trivial checks, it still has the status of a conjecture.

Based on the achievements outlined above, physicists can now start to develop concrete string theory scenarios which allow explaining new experimental results which are soon to be expected from the particle collider LHC at CERN or from astronomical observations. Other applications concern the study of exotic materials exposed to strong magnetic fields. These materials exhibit transitions between phases where the charge carriers are localised and others where they are delocalised. It is an amazing fact that this phenomenon can be described by very similar theories.