Fermionic Backgrounds and Condensation of Supergravity Fields in IIB Matrix Model

TL;DR

This paper explores fermionic backgrounds and supergravity field condensation in the IIB matrix model, demonstrating how wave functions induce various terms in the effective action and identifying fuzzy spheres as classical solutions.

Contribution

It introduces a method to incorporate fermionic backgrounds into the IIB matrix model using wave functions, leading to new induced terms and classical solutions like fuzzy spheres.

Findings

Induction of Chern-Simons-like terms from specific wave functions.

Fuzzy sphere solutions emerge as classical solutions.

Wave functions interpreted as overlaps with closed string states.

Abstract

In a previous paper hep-th/0410182 we constructed wave functions and vertex operators for massless supergravity fields in type IIB matrix model by expanding supersymmetric Wilson line operators. 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 $(N+1) \times (N+1)$, or equivalently the effective action for $(N+1)$ D-instantons. We then calculate an effective action for $N$ D-instantons by integrating out one D-instanton (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 Chern-Simons-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 from the string theory side as overlaps of the D-instanton boundary state with closed string massless states in the Green-Schwarz formalism.