String Theory and M-theory
One focus of our work has been AdS/CFT duality, which relates string theories in curved backgrounds to gauge theories. We have developed the semiclassical approach to AdS/CFT duality in the sector of string states with large quantum numbers. We used the coherent state effective action approach to prove that the same 2d sigma model effective actions of Landau-Lifshitz type appear from the AdS5 × S5 string theory and from the integrable spin chain Hamiltonian representing the N=4 super Yang-Mills dilatation operator in the corresponding limits of fast-moving strings and "long" SYM operators. The remarkable equivalence between the two actions implies the matching between stringenergies and anomalous dimensions of the corresponding Super-Yang-Mills operators, as well as a match between microscopic degrees of freedom of the two theories, providing a highly non-trivial check of the AdS/CFT duality. This matching does not depend on the symmetries of the dual theories and in this way goes beyond most previous tests. We also established a map between the profile of the leading order semiclassical string solution and the structure of the corresponding "locally BPS" Super-Yang-Mills scalar operator andwe have computed leading-order quantum superstring correction to the large spin limit of the string energies. These results are important because the semiclassical spinning strings provide a way to study the structure of the string spectrum in AdS5 × S5 beyond the supergravity limit and may eventually suggest methods (e.g., based on integrability) to prove the large N duality explicitly and to generalize it to more "realistic" (i.e. less supersymmetric) cases. We have also been working on generalizing the Penrose limit. The ordinary Penrose limit leads to a great simplification of the correspondence by focusing on the dynamics of states that are 1/2 BPS. We are trying to obtain similar simplifications by focusing on states that are 1/4 and 1/8 BPS.
We have worked on relating the recent work of Lin, Lunin and Maldacena to Mathur's conjecture that each of the microstates of black holes admits a classical supergravity description in terms of horizon-free and singularityfree geometries, and on the recent proposal for the quantum mechanical system that is holographically dual to the string theory in AdS2.
Much work on string theory has been in the regime in which supergravity gives a good low-energy effective description. We have initiated a program to analyse regimes which are truly ‘stringy' in which the background does not have a conventional spacetime description. We introduced a generalisation of the notion of spacetime manifold to allow duality transition functions, and have found a formulation in which this is embedded in a larger "doubled" space including all dual configurations.
We have studied global aspects of Scherk-Schwarz compactifications with flux, finding the conditions necessary for it to be possible to promote these from supergravity solutions to full string compactifications, and have investigated the duality and symmetry structure.
A major ongoing research effort in the group has been the systematic analysis of general supersymmetric string and M-theory backgrounds, including all possible low-energy fields. This line of work has a number of important implications including finding new dual AdS-CFT geometries, analysing flux compactifications for string phenomenology, generalising mirror symmetry conjectures and finding new black hole geometries. The program we initiated uses the mathematical notion of G-structure and intrinsic torsion which have proved to be very powerful tools.
We carried out a classification of the most general kinds of supersymmetric solutions in D=11 supergravity that contain five-dimensional anti-de-Sitter space. This constitutes the most general way of obtaining D=4 superconformal field theories in M-theory. We also found a rich class of explicit solutions. Using a sublcass of these solutions we discovered an infinite new class of D=5 Sasaki-Einstein manifolds which are dual to new superconformal field theories via type IIB supergravity. This latter work has led to much interest in the physics community since the dual conformal field theories can be explicitly determined. It has also prompted much interest in the mathematics community, not least since the construction contains the very first examples of irregular Sasaki-Einstein manifolds, and in addition the construction generalises to all odd dimensions.
The study of black holes in string theory continues to be an important area of our work. Another highlight of our work is the surprising discovery of supersymmetric black ring solutions in D=5. These black holes have horizons with topology S1× S2 instead of the usual spherical topology S3. We constructed surprising solutions that violate black hole uniqueness i.e. the black ring solutions are not uniquely specified by the conserved charges in contrast to black holes in D = 4. We have also constructed a rich class of concentric rings with a black hole sitting at the common centre. Understanding the features of these black rings from a microscopic string theory point of view is an important current area of research in the subject.
We are also trying to understand the entropy of the 3-charge BPS black holes. The counting for the 2-charge ones can be reproduced by simply counting the BPS configurations of 2-charge supertubes. The counting in the 3-charge case requires an understanding of the corresponding brane configuration. We are trying to show that such configuration corresponds to supertubes which suffer a further expansion due to a phenomenon analogous to the Myers effect.
An ongoing program on string corrections to compactifying spaces was extended to spacetimes of G2 and Spin 7 holonomy, and these also in the context of M-theory. The main result is that although supersymmetric spaces with special holonomy lose their special holonomy as a result of string corrections, they still remain special in a generalized holonomy that in cludes generators with higher products of gamma matrices, and that supersymme try remains unbroken. An important class of compactifications from string and M-theory proposed by Horava and Witten involves singular spacetimes in which one dimension corresponds to a finite line element. This has given rise to significant concerns about stability, owing to the fact that the brane sources at the ends of this interval must be of opposite sign, so negative tension objects are involved. Nonetheless, we have managed to prove a positive energy theorem that establishes that such braneworld spaces are in fact stable against localised perturbations on the brane worldsheet; this happens as consequence of unbroken supersymmetry of the static brane configuration.
