Research On Supersymmetric Gauge Theories Via Matrix Models : A New Approach

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1.We studied the gravitational corrections to the F-term in four-dimensional N=1 U(N) gauge theories with flavors, using the Dijkgraaf-Vafa theory. We derived a compact formula for the annulus contribution in terms of the prime form on the matrix model curve, and found that the full TrR^R correction was reproduced as a special momentum sector of a single c=1 CFT correlator.2.We have shown that Unitary 1-matrix models are exactly equivalent to hermitian 1-matrix models coupled to 2N vectors with appropriate potentials, to all orders in the 1/N expansion. This duality is useful, for example, for : (1) an explicit confirmation that the unitary matrix formulation of the N=2 pure SU(2) gauge theory correctly reproduces the genus-1 topological string amplitude (2) derivations of the special geometry relations in unitary as well as the Chern-Simons matrix models.3.We studied a one-dimensional sigma model associated with the hyperbolic Kac-Moody algebra G2H and its link to D=5, N=2 pure supergravity. The bosonic equations of motion and the Bianchi identity for D=5 pure supergravity match the equations of the level 3 truncation of the G2H sigma model up to higher level terms.4.We have obtained sets of infinite number of conserved nonlocal charges of strings in a flat space and pp-wave backgrounds.5.We showed that the lower-dimensional pure-spinor superstrings were cohomologically equivalent to the double-spinor superstrings in the same dimensions, and that the former were closely related to noncritical strings.6.We studied the zero-dimensional reduced model of D=6 pure super Yang-Mills theory and argued that the large N limit described the (2,0) Little String Theory. Also, we determined some so-far unknown vertex operators for the IIB matrix model and confirmed that they were consistent with the kinematical factor of a four-point graviton amplitude in a D-instanton background.