The Marie Curie project AdSCFT Munich as part of FP7-MC-IEF has now completed its planned two-year period with important new results on applying the AdS/CFT correspondence, a new development in theoretical physics originating from string theory, to systems of relevance in heavy-ion and condensed matter physics. The fellow Dr. Jonathan Shock has worked at the Max Planck Institute for Physics in Munich within the research group of Dr. Johanna Erdmenger. He has published four papers in the Journal of High Energy Physics (JHEP), the leading journal in this research area, on the subjects outlined in the formal proposal, thus achieving the proposed milestones. He has also spent time in many other research institutes and universities within the EU and in China, disseminating these results, gaining new expertise and bringing it back to Munich. He has also taken part in outreach programs both within the EU and outside and this has allowed him to get strong ties with teaching institutions around the world. These will continue to impact his career development for the foreseeable future. During the two years the fellow has also expanded his areas of interest thanks to the career advancement opportunities of the Marie Curie fellowship. This has resulted in him winning a faculty position as a lecturer in the department of Mathematics and Applied Mathematics at the University of Cape Town in South Africa. It is certainly in large part thanks to the Marie Curie fellowship that the fellow was awarded this prestigious position.

The research undertaken has encompassed formal aspects of the AdS/CFT correspondence, as well as applications to heavy-ion physics (in particular early states close to thermalisation) and condensed matter physics (in particular superconductivity). The four published articles are outlined below:

The open string membrane paradigm with external electromagnetic fieldsKeun-Young Kim, Jonathan Shock, Javier Tarrio - JHEP 06 (2011) 017

In this paper the fellow and collaborators were able to develop an entirely new paradigm for understanding regions of D-branes in the presence of electric fields which previously had not been understood. By developing an open string membrane paradigm the fellow was able to show that an effective horizon develops on a D-brane when large electric fields are present. Using this new membrane paradigm it is possible to find, in a very simple manner, transport properties of gauge theories when electric and magnetic fields are turned on. Such behaviour is extremely important now as this can be applied both to the heavy ion collision physics at the LHC as well as to lower dimensional condensed matter systems which are being studied in great detail via the holographic correspondence.

Critical phase transitions and quantum critical points of the D3/D7(D5) systems with mutually perpendicular E and B fields at finite temperature and densityNick Evans, Keun-Young Kim, Jonathan Shock - JHEP 1109 (2011) 021

In this work the fellow and collaborators extended greatly the known phase space for N=4 Super Yang Mills in the presence of fundamental matter, both in 3+1 dimensions as well as the 2+1 dimensional defect theory. They were able to classify the nature of all phase transitions in this three dimensional phase space, including first order, second order and novel all-order (BKT)

phase transitions which are not of mean field type but which have essentially an infinite critical exponent - leading to an exponential behaviour in the order parameter. The phase diagram for such theories is vital for our ability to model novel behaviours of materials being developed in condensed matter contexts.

On Stability and Transport of Cold Holographic MatterMartin Ammon, Johanna Erdmenger, Shu Lin, Steffen Müller, Andy O’Bannon, Jonathan Shock - JHEP 1109 (2011) 030

This was the first ever full perturbative study of a bosonic probe brane system at finite baryon density. Various hints suggested that such a system may be perturbatively unstable which would be extremely important as these systems are studied in many different contexts related to heavy ion physics and condensed matter physics, and an inherent instability would be very damaging to several years of results. The fellow and his collaborators were able to show, through complex use of analytic and numerical computation that in fact this system is perturbatively stable, thus ensuring that all previous studies are validated within the probe limit.

Magnetic field induced lattice ground states from holographyYan-Yan Bu, Johanna Erdmenger, Jonathan Shock, Migael Strydom - submitted to JHEP

In this paper the fellow and collaborators were able to find the ground state of a QCD-like system at very large magnetic field strength. Such a system was known to transition to a superconductor, but no calculation within AdS/CFT had ever found the form of the ground state. In this paper it was shown that the ground state breaks translational invariance by forming a triangular lattice. This result agrees with the results of Chernodub et al, which had been found in the context of an effective theory of QCD. The results from this study have consequences both for heavy ion collision experiments, currently underway at CERN as well as for our further understanding of unconventional superconductors which remain at the forefront of applied AdS/CFT research within the EU.

In this figure, the ground state condensate for a QCD-like theory at large magnetic field is shown as obtained in the paper described. The condensate breaks translational invariance and gives rise to superconductivity.

In summary, the project has paved the way for further applications of generalizations of the AdS/CFT correspondence from string theory to strongly coupled systems of relevance in heavy-ion and in condensed matter physics, thus providing new description methods and calculation tools for these systems which are inherently difficult to describe by standard methods.

Moreover, the project has allowed for a large amount of intellectual exchange and growth within research institutions of EU member states. The fellow himself has brought a new level of understanding of symbolic programming languages to the host institution, introducing use of the Mathematica programming package at a far higher level than previously. Through research visits of the fellow, links have also been created or enhanced between the Max Planck Institute for Physics in Munich and the Henri Poincaré Institute in Paris, the Abdus Salam Centre for Theoretical Physics in Trieste, as well as Universities in Belgium, Spain, Portugal, the UK, Ireland and the Netherlands.

Through public outreach activities including public lectures and debates, the fellow has also publicized his research results to an audience of several hundred people, including school children, university students and members of the general public.