## Final Activity Report Summary - F.I.S.S. (Fundamental interactions and the structure of space-time)

The objective of the present project was to investigate the relationship of the two main tools in the study of fundamental interactions: gauge theories and gravity. The Standard model of fundamental interactions supplemented with the classical theory of gravity constitutes the best theory we have. It describes physics over distance scales that differ by more than forty orders of magnitude, ranging from the ends of the observable universe today to a fraction of the distances inside a nucleus. Its two main ingredients are gravity on one hand and gauge theories describing the three other interactions (weak, strong and electromagnetic).

In the past years string theory provided initially a new viewpoint on theories of quantum gravity. An unexpected breakthrough occurred in 1997, when it was realized that gauge theories and gravity are more intimately connected than scientists originally thought. The first version of this connection known as AdS / CFT correspondence presented a concrete example of a duality between a strongly coupled large-N gauge theory and string theory in the ten-dimensional AdS5 x S5 background. This duality is holographic as it maps a lower dimensional gauge theory to a higher dimensional string theory.

Since then, three directions started at being explored, namely (O1) understanding better and generalising the correspondence (O2) using it to crack the secrets of strongly coupled gauge theories and in particular QCD using weakly coupled gravity duals and (O3) Use the robustness of gauge theories to define string / gravity theories beyond perturbation theory and give a new picture of spacetime as an emergent concept.

(O1-O3) comprised the three objectives of the present project. These three directions were actively pursued in the present project with the following results:

(O1) Non-critical holography was developed and studied. In order to avoid typical problems of ten dimensional critical string theory, non-critical string theory was explored. In one direction, several non-critical solutions were found and their physics was analysed. This direction provided insights into the holographic duals of theories that are closer to QCD. A particular direction that was also developed was that of unquenched flavour. So far flavour degrees of freedom in holographic gauge theories were treated perturbatively (an approximation known as the 'quenched' approximation. Although for some purposes this is an acceptable approximation for others it is not. In the course of this project, many holographic solutions were found where flavour is unsuppressed. It is an exaggeration to say that the present team is the world leader in this direction.

(O2) The work performed in O1 led to an advancement in the knowledge needed in order to find hologreaphic theories that are close in terms of their dynamical behaviour to real world QCD. In particular, it was proposed that Einstein-dilation gravity in five-dimensions with a suitable dilation potential can describe very closely many properties of real world QCD including asymptotic freedom, confinement the mass gap and the glueball spectrum. This was developed in a series of works that subsequently have shown that the finite temperature behaviour of the model is very close to that of QCD as it emerges from lattice calculations with minimal tuning. This model has the best chance of providing transport coefficients like bulk viscosity, jet quenching parameters etc, that are currently needed in order to interpret data coming from the RHIC and in the future from LHC experiments.

(O3) In trying to understand the subtleties and instabilities of gravity, especially in its screened incarnations, needed to interpret recent cosmic acceleration data. We have applied the holographic technology in order to produce gravitational theories that on one hand are massive and on the other have a controllable dual description in terms of suitable gauge theories. This comparison made clear that instabilities inherent in massive gravity are generic and encoded into the RG landscape of associated gauge theories casting doubt into attempts to modify gravity in the IR.

In the past years string theory provided initially a new viewpoint on theories of quantum gravity. An unexpected breakthrough occurred in 1997, when it was realized that gauge theories and gravity are more intimately connected than scientists originally thought. The first version of this connection known as AdS / CFT correspondence presented a concrete example of a duality between a strongly coupled large-N gauge theory and string theory in the ten-dimensional AdS5 x S5 background. This duality is holographic as it maps a lower dimensional gauge theory to a higher dimensional string theory.

Since then, three directions started at being explored, namely (O1) understanding better and generalising the correspondence (O2) using it to crack the secrets of strongly coupled gauge theories and in particular QCD using weakly coupled gravity duals and (O3) Use the robustness of gauge theories to define string / gravity theories beyond perturbation theory and give a new picture of spacetime as an emergent concept.

(O1-O3) comprised the three objectives of the present project. These three directions were actively pursued in the present project with the following results:

(O1) Non-critical holography was developed and studied. In order to avoid typical problems of ten dimensional critical string theory, non-critical string theory was explored. In one direction, several non-critical solutions were found and their physics was analysed. This direction provided insights into the holographic duals of theories that are closer to QCD. A particular direction that was also developed was that of unquenched flavour. So far flavour degrees of freedom in holographic gauge theories were treated perturbatively (an approximation known as the 'quenched' approximation. Although for some purposes this is an acceptable approximation for others it is not. In the course of this project, many holographic solutions were found where flavour is unsuppressed. It is an exaggeration to say that the present team is the world leader in this direction.

(O2) The work performed in O1 led to an advancement in the knowledge needed in order to find hologreaphic theories that are close in terms of their dynamical behaviour to real world QCD. In particular, it was proposed that Einstein-dilation gravity in five-dimensions with a suitable dilation potential can describe very closely many properties of real world QCD including asymptotic freedom, confinement the mass gap and the glueball spectrum. This was developed in a series of works that subsequently have shown that the finite temperature behaviour of the model is very close to that of QCD as it emerges from lattice calculations with minimal tuning. This model has the best chance of providing transport coefficients like bulk viscosity, jet quenching parameters etc, that are currently needed in order to interpret data coming from the RHIC and in the future from LHC experiments.

(O3) In trying to understand the subtleties and instabilities of gravity, especially in its screened incarnations, needed to interpret recent cosmic acceleration data. We have applied the holographic technology in order to produce gravitational theories that on one hand are massive and on the other have a controllable dual description in terms of suitable gauge theories. This comparison made clear that instabilities inherent in massive gravity are generic and encoded into the RG landscape of associated gauge theories casting doubt into attempts to modify gravity in the IR.