There is currently substantial interest in the application of holography to study conformal field theories of interest for condensed matter physics. Nice reviews of this activity are in [1]. In condensed matter, conformal theories emerge as effective descriptions of physics near a critical point in the phase diagram of a material. The underlying lattice model is not Lorentz-invariant, so the resulting field theory can be non-relativistic, and have an anisotropic scaling symmetry, which treats time and space differently.
I have been studying the construction of spacetime duals for these non-relativistic theories. This is an interesting challenge for holography; despite the very different spacetime structure of the field theories, it turns out to be possible to construct dual geometries in the context of ordinary relativistic gravity - Einstein's general relativity and supergravity theories. In [2,3], we studied the finite-temperature and hydrodynamic behaviour of one model, called the Schrodinger spacetime. In [4,5,6], we have begun systematically investigating the dictionary for another simpler model called the Lifshitz spacetime.
Lifshitz is a relatively simple deformation of anti-de Sitter space, and in [5] I have shown that there is a holographic dictionary relating the asymptotic behaviour of the spacetimes to observables in the field theory which closely parallels the AdS/CFT dictionary. This is the primary area where I have projects to work on; there are some further issues to be understood in this dictionary, and a number of interesting directions to apply it in.
[1] S. Hartnoll, "Lectures on holographic methods for condensed matter physics", arXiv:0903.3246; J. McGreevy, "Holographic duality with a view toward many-body physics", arXiv:0909.0518.
[2] C.P. Herzog, M. Rangamani and S. F. Ross, "Heating up Galilean holography", JHEP 0811 (2008) 080,
e-Print: arXiv:0807.1099.
[3] M. Rangamani, S. F. Ross, D. T. Son and E. Thompson, "Conformal non-relativistic hydrodynamics from gravity", JHEP 0901 (2009) 075,
e-Print: arXiv:0811.2049.
[4] S. F. Ross and O. Saremi, "Holographic stress tensor for non-relativistic theories", JHEP 0909 (2009) 009,
e-Print: arXiv:0907.1846.
[5] S. F. Ross, "Holography for asymptotically locally Lifshitz spacetimes", e-Print: arXiv:1107.4451.
[6] H. Braviner, R. Gregory and S. F. Ross, "Flows involving Lifshitz solutions", e-Print: arXiv:1108.3067.
I welcome enquiries about opportunities for PhD supervision. For practical information on the admissions process in Durham, you should see the CPT's Graduate studies webpages. At the moment, I have active opportunities for students to work on non-relativistic holography, specifically the Lifshitz spacetimes, but there may be other opportunities broadly on aspects of spacetime in string theory. You may also want to have a look at the webpages of other people in the CPT; there are a number of faculty here with similar interests.
Last modified on 5 October 2011