There are good reasons for thinking that a quantum theory of gravity may necessitate abandoning the notion that the basic constituents of matter are point particles. Using extended objects such as strings instead avoids a number of mathematical pitfalls. Other possibilities that have been studied include two-dimensional membranes and higher-dimensional objects which have come to be known as p-branes. The most attractive theories, such as superstring theory, involve also the concept of supersymmetry, a symmetry that connects particles with different spin and statistics. Often the theories are self-consistent only in space-times with more than the conventional four dimensions (three space and one time); the assumption is that all except four are 'compactified' - curled up into a very small size.
The last decade have witnessed a sharp surge of activity in string theory and related fields, stimulated by the ``duality revolution'' and, in particular, by gravity/gauge theory dualities. One of the basic problems that bedevilled the field was that there seemed to be too many consistent string theories. Five distinct theories were known, in 10 or 11 dimensions. The discovery of 'duality' relations between these showed that these theories were in fact equivlaent. For example, in some cases one of the theories in the strong coupling regime can be shown to be equivalent to another in weak coupling.
The most far-reaching examples of dualities are so-called holographic dualities between gravitational theories and dual gauge theories (with no gravity). These include the famous conjecture by Maldacena that string theory in the background of an anti-de Sitter (AdS) spacetime in (d+1)-dimensions is dual to a conformal field theory in d-dimensions.
Such holographic dualities represent a complete paradigm shift: on the one hand the duality implies that spacetime can be reconstructed from gauge theory data, and in the other direction the duality implies that one can study strong coupling dynamics in gauge theories using gravity!
My research is centred around exploring the implications of holography: how is spacetime reconstructed? what do gravity/gauge theory dualities imply for black hole physics? can we find useful holographic models for QCD? can we quantify what features of QCD these models capture?
My area of research is string theory, in particular exploring whether and how holography is realized. The famous AdS/CFT correspondence, relating string theory in a negative curvature background to a field theory on the boundary, is one example of a conjectured gravity/gauge theory duality. Other examples of holographic dualities are also known, but it is far from clear whether string theory is always holographic and whether the physics of interesting cosmological spacetimes, such as de Sitter space, can be described holographically by a non-gravitational theory. Going in the other direction, from field theory to geometry, one would like to construct geometric duals of phenomenologically interesting field theories.
A primary goal in understanding these dualities is to develop precise holographic dictionaries between gravity and gauge theory quantities. Such a holographic dictionary must operate in both directions: one must show both how field theory data, such as correlation functions and expectation values of Wilson loops, can be extracted from the geometry and in reverse how this field theory data reconstructs the geometry, in particular global features such as horizons.
Substantial progress has been made on these issues in the context of AdS/CFT; indeed in recent work Skenderis and I have shown how the field theory data of all chiral primary operators is encoded in general asymptotically anti-de Sitter dual geometries. However many key questions remain and these are one focus of my current research. For example, little progress has been made on how global spacetime structure is captured by the field theory. Promising directions which may shed light on this include developing the connection between bulk singularity theorems and RG flows in the field theory. In the short term one would hope to understand timelike singularities in this way, but the long term goal would be to shed light on the resolution and holographic description of cosmological singularities also.
Applying the holographic dictionary in the other direction field theory data is extracted from dual bulk gravitational physics. Currently I and collaborators (Kanitscheider, Skenderis) are developing tools to extract precise field theory data from geometries which are not related to anti-de Sitter but nonetheless have conjectured field theory duals, such as $Dp$-brane backgrounds with $p \neq 3$. With these computational tools one can develop precision holography in D-brane models for QCD such as the Witten-Sakai-Sugimoto model.
Gravity/gauge theory dualities potentially have very significant implications for phenomenology, since typically the weakly coupled gravitational background gives information about strong coupling behavior in the gauge theory. Although there is currently no known candidate geometric dual for QCD, nor any other asymptotically free theory, remarkably the strong coupling data extracted from known geometric duals for UV conformal theories agrees (in some instances) with thermal QCD. This is surprising, since QCD and conformal theories are in a completely different universality class, and understanding why and when strong coupling behavior is universal for such different theories could be important in understanding QCD.
In an attempt to shed light on these questions, we are exploring whether it is possible to construct consistent holographic models for asymptotically free four-dimensional gauge theories. The idea is to use five-dimensional domain wall geometries, with the warp factor of the domain wall tuned to capture the beta function of the dual theory. Clearly when the beta function vanishes one should have an AdS geometry, but the question is whether one can change the boundary asymptotics (whilst retaining small curvature) to capture theories which are not UV conformal. To address this question one needs to set up a precise bulk/boundary dictionary, and check for what beta functions this setup is self-consistent and well-defined. If indeed one can show that QCD can be consistently described by such a domain wall this would be significant progress. Moreover once one understands such geometric setups one should also see why some strong coupling behavior is universal, and what features of QCD are well modeled by holographic duals.
Gravity/gauge theory dualities are also profoundly important in understanding black hole physics. The key result of microscopic counting of black hole entropy due to Strominger and Vafa is in fact an immediate corollary of the AdS/CFT correspondence. More recently, AdS/CFT has led to an interesting proposal for black hole physics, the so-called fuzzball proposal. According to this proposal of Mathur, for each microstate of the black hole there is a horizon-free, non-singular geometry which approaches the black hole geometry at large distances but differs in the interior. The black hole geometry emerges upon coarse-graining over these geometries.
This interesting proposal has the potential to resolve long standing black hole issues, such as the information loss paradox. AdS/CFT provides evidence for the proposal, since according to the general framework pure states in the CFT should have a geometric dual with no horizon, whilst mixed states should be dual to geometries with horizons. In a recent series of papers, Skenderis and I have provided detailed evidence for this picture, by matching data extracted from fuzzball geometries with CFT data, for certain supersymmetric black hole systems. We are considering how to extend this work to other supersymmetric black holes, and moreover showing how other black objects such as black rings emerge with different choices of coarse-graining. We are also currently writing an invited Physics Report summarizing the status of this proposal.
Apart from these specific directions, my research interests include string theory, supersymmetric field theory and more generally beyond the standard model physics. Indeed one can envisage holographic results being important in supersymmetric phenomenology and even in understanding QCD amplitudes. To give an example, Alday and Maldacena have recently discovered how to obtain gluon scattering amplitudes from the bulk; their results are likely in the short term to lead to new understanding of the proposed integrability of N=4 SYM but longer term may lead to qualitative progress in efficient computation of scattering amplitudes.
As another example, an important open question is the UV completion of phenomenologically interesting models with metastable supersymmetry breaking vacua, such as generalized O'Raifeartaigh models. Various avenues are being explored, including trying to find field theories which give rise to such models in the IR and embedding into string theory via brane constructions. Holography is also an important avenue: ultimately one would hope to construct holographic duals for such models, which could address otherwise inaccessible strong coupling questions.
With LHC soon approaching, I also increasingly follow phenomenology. Whether LHC finds supersymmetry, or discovers something entirely unexpected, I would anticipate becoming involved with the theoretical interpretation of its discoveries.