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Register a new userVertex Operators in IIB Matrix Model
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Authors
Y. Kitazawa
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The vertex operators for the supergravity multiplet can be constructed through the Wilson lines in IIB matrix model. We investigate the structure of the vertex operators and the symmetry of their correlation functions. For this purpose, we perturb the theory by the Wilson lines dual to the supergravity multiplet. The structure of the Wilson lines can be determined by requiring $cal{N}$=2 SUSY under the low energy approximation. We argue that the generating functional of the correlators is invariant under local SUSY transformations of IIB supergravity.
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We review our proposal for a constructive definition of superstring, type IIB matrix model. The IIB matrix model is a manifestly covariant model for space-time and matter which possesses N=2 supersymmetry in ten dimensions. We refine our arguments to reproduce string perturbation theory based on the loop equations. We emphasize that the space-time is dynamically determined from the eigenvalue distributions of the matrices. We also explain how matter, gauge fields and gravitation appear as fluctuations around dynamically determined space-time.
We show that twisted reduced models can be interpreted as noncommutative Yang-Mills theory. Based upon this correspondence, we obtain noncommutative Yang-Mills theory with D-brane backgrounds in IIB matrix model. We propose that IIB matrix model with D-brane backgrounds serve as a concrete definition of noncommutative Yang-Mills. We investigate D-instanton solutions as local excitations on D3-branes. When instantons overlap, their interaction can be well described in gauge theory and AdS/CFT correspondence. We show that IIB matrix model gives us the consistent potential with IIB supergravity when they are well separated.
We review recent developments in the type IIB matrix model, which was conjectured to be a nonperturbative formulation of superstring theory. In the first part we review the recent results for the Euclidean model, which suggest that SO(10) symmetry is spontaneously broken. In the second part we review the recent results for the Lorentzian model. In particular, we discuss Monte Carlo results, which suggest that (3+1)-dimensional expanding universe emerges dynamically. We also discuss some results suggesting the emergence of exponential expansion and the power-law expansion at later times. The behaviors at much later times are studied by the classical equation of motion. We discuss a solution representing 3d expanding space, which suggests a possible solution to the cosmological constant problem.
Assuming that the large-$N$ master field of the Lorentzian IIB matrix model has been obtained, we go through the procedure of how the coordinates of emerging spacetime points can be extracted. Explicit calculations with test master fields suggest that the genuine IIB-matrix-model master field may have a fine-structure that is essential for producing the spacetime points of an expanding universe.
The large-$N$ master field of the Lorentzian IIB matrix model can, in principle, give rise to a particular degenerate metric relevant to a regularized big bang. The length parameter of this degenerate metric is then calculated in terms of the IIB-matrix-model length scale.
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