Present Research Efforts
The Coadjoint Representations: The coadjoint representation of the Virasoro algebra and Affine Lie algebras have provided insight into the nature of classical and quantum gravity in the absence of curvature especially in two and three space-time dimensions. We are using these ideas to understand a variety of problems. These include:
- Dark Energy and Dark Matter originating from representations of diffeomorphisms - the diffeomorphism field.
- Supersymmetric extensions of two and three dimensional quantum gravity for arbitrary numbers of supersymmetries.
- Cosmological implications of a diffeomorphism field interacting with electromagnetic radiation and in particular the microwave anisotropy.
- Short distance expansions of the fields in the coadjoint and adjoint representations using the algebraic properties.
- Developing geometric actions related to the Courant Bracket for geometric understanding of B-field interactions with D-Branes in string theories.
- Develop the AdS/CFT correspondence in three dimensions using coadjoint representations, geometric actions and transverse actions.
- Marrying Affine Lie algebras and Courant Bracket structures to see how one might find non-abelian extensions of B-field physics and to understand D-brane interactions with Yang-Mills fields and B-fields simultaneously.
- Relationship of certain adjoint fields that appear naturally in this formalism to Higgs fields and spontaneously broken symmetry.
AdS/CFT and Nuclear Physics: One of the most powerful ideas of the AdS/CFT correspondence is that physicists might have theoretical access to the non-perturbative regime of strongly coupled field theories. There are a class of strongly coupled field theories that can be related to weakly couple gravitational theories. Our focus is on configurations in particle physics that overlap with configurations that can be computed using lattice QCD, namely K-Strings. We study the tension and stability of K-string associated with specific supergravity backgrounds and their comparison with lattice gauge theory calculations.
AdS/CFT and Asymptotic Gravity: The AdS/CFT correspondence tells us that there is huge amounts of information about field theories that live on the boundaries. Interesting relations may exist between the physics near a black hole and its asymptotic properties such as angular momentum and energy. There are other extreme objects that might have similar data residing in their asymptotics. We are investigating how much information can be encoded in the two dimensional world on the boundary that can be related back to four-dimensional physics.