## Final Activity Report Summary - GRACE TO SOPHYA (Gravity, Chern-Simons extensions, topology and solid-state physics applications)

'Gravity, Chern-Simons extensions, topology and solid-state physics applications' (GRACE TO SOPHYA) was a heavily research-oriented project that addressed many theoretical and phenomenological issues related to gravitational physics, Chern-Simons terms, topology and unexpected applications of black holes, e.g. in solid state physics or particle physics. The results were published in 20 peer reviewed papers and disseminated in 21 scientific meetings. Spin-offs include follow-up projects with a total volume over EUR 1 million, long-term collaborations with the Massachusetts Institute of Technology (MIT) and outreach activities in Austria. Here is a brief description of the scientific results of GRACE TO SOPHYA.

Topology is a branch of mathematics that began with Euler's paper on 'Seven bridges in Königsberg' in 1736. From a topological point of view a doughnut and a cup of coffee are the same: both have two-dimensional surfaces with one hole. The number of holes in a surface is an example of a topological invariant. An important topological invariant in physics is the so-called Chern-Simons term. In theories of gravity the consideration of a gravitational Chern-Simons term has a profound impact on the theory and on the phenomenology. For instance, mass and angular momentum of stars or black holes change in the presence of a gravitational Chern-Simons term and gravity waves propagate with different amplitudes, as shown by Roman Jackiw (MIT) and So-Young Pi (Boston U.). In three dimensions (two spatial and one time) it may even be the case that the theory exists only in the presence of a gravitational Chern-Simons term.

One puzzling question concerns the rotation of black holes in Chern-Simons modified gravity. With Nicolas Yunes (Princeton University) we addressed the question 'How do black holes spin in Chern-Simons modified gravity?' in a comprehensive paper and provided precise answers. The techniques employed in that work were useful for some spin-off projects, e.g. an Ariadna study for the European Space Agency on 'Rotating gravitationally bound systems' or an astrophysics work with Ana-Maria Piso (MIT) where we found for the first time an exact solution for a fully relativistic viscous accretion disk surrounding the black hole GRS1915+105 in the constellation Aquila.

Quantum gravity is sometimes called the 'holy grail of theoretical physics'. In 2007, Edward Witten (IAS) proposed a new way to construct quantum gravity in three dimensions by appealing to the holographic principle. In a nutshell the holographic principle (technically known as 'AdS/CFT correspondence' or 'gauge / gravity duality') relates two apparently different theories in two different dimensions, one of which contains gravity and one of which does not contain gravity. Thus, with certain technical caveats, quantum gravity can be mapped to an ordinary quantum theory without gravity. The latter kind of theory is well-understood since the 1930ies, but with Niklas Johansson (Uppsala University) we found an unexpected novel feature in 2008: if the gravitational theory contains a Chern-Simons term the non-gravitational theory is not unitary, but rather a so-called 'logarithmic conformal field theory'. Theories of this type are used in condensed matter physics applications e.g. to describe turbulence. We have therefore uncovered a novel potential relation between gravitational physics and condensed matter physics.

The principal investigator, Daniel Grumiller, has recently received the Austrian START prize and is in the process of building a black hole research group at the Vienna University of Technology. In collaboration with Anton Rebhan (scientist in charge of GRACE TO SOPHYA), with the MIT group and with other international collaborators the focus will be on further unexpected applications of gravitational and black hole physics in condensed matter and elementary particle physics.

Topology is a branch of mathematics that began with Euler's paper on 'Seven bridges in Königsberg' in 1736. From a topological point of view a doughnut and a cup of coffee are the same: both have two-dimensional surfaces with one hole. The number of holes in a surface is an example of a topological invariant. An important topological invariant in physics is the so-called Chern-Simons term. In theories of gravity the consideration of a gravitational Chern-Simons term has a profound impact on the theory and on the phenomenology. For instance, mass and angular momentum of stars or black holes change in the presence of a gravitational Chern-Simons term and gravity waves propagate with different amplitudes, as shown by Roman Jackiw (MIT) and So-Young Pi (Boston U.). In three dimensions (two spatial and one time) it may even be the case that the theory exists only in the presence of a gravitational Chern-Simons term.

One puzzling question concerns the rotation of black holes in Chern-Simons modified gravity. With Nicolas Yunes (Princeton University) we addressed the question 'How do black holes spin in Chern-Simons modified gravity?' in a comprehensive paper and provided precise answers. The techniques employed in that work were useful for some spin-off projects, e.g. an Ariadna study for the European Space Agency on 'Rotating gravitationally bound systems' or an astrophysics work with Ana-Maria Piso (MIT) where we found for the first time an exact solution for a fully relativistic viscous accretion disk surrounding the black hole GRS1915+105 in the constellation Aquila.

Quantum gravity is sometimes called the 'holy grail of theoretical physics'. In 2007, Edward Witten (IAS) proposed a new way to construct quantum gravity in three dimensions by appealing to the holographic principle. In a nutshell the holographic principle (technically known as 'AdS/CFT correspondence' or 'gauge / gravity duality') relates two apparently different theories in two different dimensions, one of which contains gravity and one of which does not contain gravity. Thus, with certain technical caveats, quantum gravity can be mapped to an ordinary quantum theory without gravity. The latter kind of theory is well-understood since the 1930ies, but with Niklas Johansson (Uppsala University) we found an unexpected novel feature in 2008: if the gravitational theory contains a Chern-Simons term the non-gravitational theory is not unitary, but rather a so-called 'logarithmic conformal field theory'. Theories of this type are used in condensed matter physics applications e.g. to describe turbulence. We have therefore uncovered a novel potential relation between gravitational physics and condensed matter physics.

The principal investigator, Daniel Grumiller, has recently received the Austrian START prize and is in the process of building a black hole research group at the Vienna University of Technology. In collaboration with Anton Rebhan (scientist in charge of GRACE TO SOPHYA), with the MIT group and with other international collaborators the focus will be on further unexpected applications of gravitational and black hole physics in condensed matter and elementary particle physics.