Fermionic backgrounds and condensation of supergravity fields in the type IIB matrix model

Abstract

In a previous paper [1] we constructed wave functions of a D-instanton and vertex operators in type IIB matrix model by expanding supersymmetric Wilson line operators. They describe couplings of a Dinstanton and type IIB matrix model to the massless closed string fields, respectively, and form a multiplet of D 10 N 2 supersymmetries. In this paper we consider fermionic backgrounds and condensation of supergravity fields in IIB matrix model by using these wave functions. We start from the type IIB matrix model in a flat background whose matrix size is N 1 N 1, or equivalently the effective action for N 1 D-instantons. We then calculate an effective action for N D-instantons by integrating out 1 Dinstanton (which we call a mean-field D-instanton) with an appropriate wave function and show that various terms can be induced corresponding to the choice of the wave functions. In particular, a ChernSimons-like term is induced when the mean-field D-instanton has a wave function of the antisymmetric tensor field. A fuzzy sphere becomes a classical solution to the equation of motion for the effective action. We also give an interpretation of the above wave functions in the superstring theory side as overlaps of the D-instanton boundary state with the closed string massless states in the Green-Schwarz formalism.

Progress toward the determination of complete vertex operators for the IIB matrix model

“…Thus the supersymmetric Wilson loop realizes the relation (2.3), and the coefficient of each wave function can be identified as the corresponding vertex operator. The fermionic variable λ may be regarded as an isolated eigenvalue of the matrix ψ representing the effect of the background as a "mean field" [4,8]. Indeed the SUSY transformations for such a single eigenvalue are generated by (2.10)(2.11) if the off-diagonal interactions are neglected.…”

Vertex operators of type IIB matrix model via calculation of disk amplitudes

“…In comparison to the previous investigations using supersymmetric transformation in IIB matrix model [3,4,5], we can check that the resultant formulae give the consistent form of the vertex operators for the IIB matrix model up to the 4-th rank antisymmetric tensor completely. This paper is organized as follows.…”

“…Subsequently a systematic procedure is developed through the construction of the supersymmetric Wilson loop operator. In this way, the vertex operator is determined completely up to the 4-th rank antisymmetric tensor [3,4]. Recently there was a further progress in determining the precise form of vertex operators for the matrix model [5].…”

Little type IIB matrix model

“…The parameter λ i may be thought of as an isolated eigenvalue of the matrix ψ i representing the whole effect of the background as a mean field [15] (See also [17]. ); k µ is the Fourier transform of the similarly isolated eigenvalue of A µ .…”