## Final Report Summary - HWTC (Holographic Walking Technicolor)

Quantum chromodynamics (QCD) is the theory which governs one of the fundamental interactions in nature, namely the strong interactions. It is also a building block of the standard model, which is the complete theory of particle physics. But while there is overwhelming evidence that QCD is the correct theory of strong interactions, computations using this theory are extremely complicated due to the strength of the interactions. Consequently QCD is still an active field of research even decades after its discovery. The elementary particles of QCD are quarks, which form the matter, and gluons, which mediate the strong force. Therefore most of the matter seen in nature is made of composite systems of quarks, bound together by gluons.

The standard model also involves another possible example of a strongly interacting sector. The model contains the unified theory of electromagnetic and weak interactions, which is based on the so called electroweak symmetry. This symmetry is, however, broken in nature, as seen from the finite and large masses of the Z and W bosons which are the mediators of the weak force. The breaking of the symmetry can be seen to be due to the Higgs boson, which has been observed directly at the Large Hadron Collider (LHC) recently. It is possible that this breaking is triggered by an underlying strongly interacting theory, somewhat similar to QCD, in which case the Higgs boson is not an elementary particle but a composite system of two fermions. Such an underlying theory has been coined technicolor.

One generic tool which helps to solve strongly interacting theories is gauge-gravity duality. It is a relation between a "gravitational theory" in more than four dimensions, and a four dimensional "gauge field theory" (like QCD) which lives on the boundary of the higher-dimensional space of the gravitational theory. In this relation, a strongly coupled field theory is mapped to a weakly coupled high-dimensional gravitation which can be solved exactly. For QCD, however, an exact gauge-gravity duality has not been constructed. Also no exact dualities for viable candidates of technicolor are known.

This project marks a significant step toward holographic understanding of QCD and technicolor theories. We use an approach were we explore a large class of five-dimensional gravitational theories in order to find ones that reproduce physics similar to QCD or possible candidate technicolor theories. A novel ingredient in this work is the "backreaction", which means that the dynamics of both the quarks and the gluons is fully modeled (whereas in many earlier models an approximation for the dynamics of the quarks was used). This allows as to do a reliable exploration of the generalizations of QCD where the amount of quarks is large with respect to amount of gluons, and may also improve the holographic modeling of "ordinary" QCD.

The main result is the phase structure of the resulting holographic model, in particular the so-called "conformal transition". This transition takes place between the phase with dynamics similar to ordinary QCD and a conformal phase. In the QCD-like phase the spectrum of the bound states of quarks is discrete whereas in the conformal phase it is continuous. We also uncovered the extension of the phase diagram from zero to finite temperatures, and to finite chemical potential of the quarks, and computed observables relevant for technicolor studying in detail the regime near the transition, where viable technicolor candidates are expected to lie.

This project combined the expertise of the researcher obtained earlier at the center of excellence CP3-Origins in Odense, Denmark, with the expertise of the Crete Center for Theoretical Physics. The results were presented in some of the most important European conferences in holography and string theory. Collaboration with several Universities and research institutes also emerged as a part of the implementation of the project, strengthening the ties between these institutes.

The project website is http://hep.physics.uoc.gr/hwtc.shtml

The standard model also involves another possible example of a strongly interacting sector. The model contains the unified theory of electromagnetic and weak interactions, which is based on the so called electroweak symmetry. This symmetry is, however, broken in nature, as seen from the finite and large masses of the Z and W bosons which are the mediators of the weak force. The breaking of the symmetry can be seen to be due to the Higgs boson, which has been observed directly at the Large Hadron Collider (LHC) recently. It is possible that this breaking is triggered by an underlying strongly interacting theory, somewhat similar to QCD, in which case the Higgs boson is not an elementary particle but a composite system of two fermions. Such an underlying theory has been coined technicolor.

One generic tool which helps to solve strongly interacting theories is gauge-gravity duality. It is a relation between a "gravitational theory" in more than four dimensions, and a four dimensional "gauge field theory" (like QCD) which lives on the boundary of the higher-dimensional space of the gravitational theory. In this relation, a strongly coupled field theory is mapped to a weakly coupled high-dimensional gravitation which can be solved exactly. For QCD, however, an exact gauge-gravity duality has not been constructed. Also no exact dualities for viable candidates of technicolor are known.

This project marks a significant step toward holographic understanding of QCD and technicolor theories. We use an approach were we explore a large class of five-dimensional gravitational theories in order to find ones that reproduce physics similar to QCD or possible candidate technicolor theories. A novel ingredient in this work is the "backreaction", which means that the dynamics of both the quarks and the gluons is fully modeled (whereas in many earlier models an approximation for the dynamics of the quarks was used). This allows as to do a reliable exploration of the generalizations of QCD where the amount of quarks is large with respect to amount of gluons, and may also improve the holographic modeling of "ordinary" QCD.

The main result is the phase structure of the resulting holographic model, in particular the so-called "conformal transition". This transition takes place between the phase with dynamics similar to ordinary QCD and a conformal phase. In the QCD-like phase the spectrum of the bound states of quarks is discrete whereas in the conformal phase it is continuous. We also uncovered the extension of the phase diagram from zero to finite temperatures, and to finite chemical potential of the quarks, and computed observables relevant for technicolor studying in detail the regime near the transition, where viable technicolor candidates are expected to lie.

This project combined the expertise of the researcher obtained earlier at the center of excellence CP3-Origins in Odense, Denmark, with the expertise of the Crete Center for Theoretical Physics. The results were presented in some of the most important European conferences in holography and string theory. Collaboration with several Universities and research institutes also emerged as a part of the implementation of the project, strengthening the ties between these institutes.

The project website is http://hep.physics.uoc.gr/hwtc.shtml