Murat Gunaydin

Research Interests:

M/Superstring theory, supergravity, AdS/CFT dualities, exceptional groups and related algebraic and geometric structures, representations of noncompact groups and supergroups and their applications, algebraic foundations of Quantum Mechanics, generalized spacetimes defined by Jordan algebras, double-copy constructions of the amplitudes of supergravity theories in terms of gauge theory amplitudes, higher spin theories, the classification of higher spin algebras in various dimensions and their unitary realizations.

I have done extensive work on the construction and classification of novel supergravity theories and their gaugings in various dimensions and AdS/CFT dualities. Of particular interest from physics point of view are gauged supergravity theories that describe the low energy effective theories of flux compactifications from M/Superstring theory that are relevant for AdS/CFT dualities in M/Superstring theory.
Another focus of my research has been on the problem of understanding how the spectra of various superstring theories or M-theory are related to the unitary representations of their non-perturbative symmetry groups or supergroups. Towards this goal I have done extensive work on the unitary representations of continuous U-duality groups of supergravity theories, some of which arise as low energy effective theories of compactified M-theory or superstring theories. I have also been studying the unitary representations of spectrum generating symmetry groups in five and four dimensional supergravity theories and their applications to the BPS black hole spectra. More recently I have been trying to extend these results to discrete arithmetic subgroups of U-duality groups which lead to some fascinating connections with number theory.

U-duality groups of five dimensional supergravity theories with homogeneous scalar manifolds admit extensions to spectrum generating generalized conformal groups. Similarly, U-duality groups of corresponding four dimensional theories admit extensions to spectrum generating quasiconformal groups. Quasiconformal realization of the spectrum generating symmetry group E8(8) of the maximal supergravity in four dimensions, constructed in 2000, was the first known geometric realization of E8. Quasiconformal realizations exist for different real forms of all Lie groups and they leave invariant a generalized light-cone defined by a quartic distance function. The quantization of geometric quasiconformal realization of a noncompact group leads directly to its minimal unitary representation.

More recent work on quasiconformal realizations of noncompact groups have established a one-to-one correspondence between massless conformal fields in all spacetime dimensions and their minimal unitary representations and their deformations. This correspondence extends also to conformal superalgebras that exist in space-time dimensions six or less. The enveloping algebras of the minimal unitary representation and its deformations describe the higher spin algebras and their deformations in the respective dimensions.

My current research focuses on the construction of the scattering amplitudes of matter coupled supergravity theories as double copies of gauge theory amplitudes using BCJ relations. Another area of my current research focuses on the deep connections between discrete arithmetic U-duality groups and number theory.

Publications: See my papers listed in Spires:
http://inspirehep.net/search?p=find+a+gunaydin,+m.