Vertex Operators and Effective Action of IIB Matrix Model Yoshihisa Kitazawa KEK and Sokendai March 15 2007

Introduction Spacetime may emerge out of condensations of D-branes. 　Emergent spacetime Matrix Models are a promising approach to investigate such a possibility. Gravity is expected to arise through open/closed string duality. Fuzzy and generic curved spacetime (principle bundle) may be constructed

IIB matrix model

Role of SUSY Maximal SUSY plays an important role for IIB matrix model to contain gravity. Matrix models with the half SUSY may be relevant to little strings. 　　 　Mizoguchi　Saito Kitazawa Supergravity multiplet couple to the vertex operators whose structure is determined by N=2 SUSY. Kitazawa, 　Iso 　Terachi　 Umetsu

Vertex Operators Vertex operatoprs couple linearly to the fields in the supergravity multiplet Under N=2 SUSY trasformation, they transform as

Supersymmetric Wilson Loop Let us consider Hamada It satsifies

When k2=0, Wilson loop can be expanded in l up to the eighth order It indeed satisfies 　 Iso Terachi Umetsu

N=2 SUSY Transformations

Explicit Form of Vertex Operators

Mizoguchi, Saito, Kitazawa

Block diagonal backgrounds

One loop effective action Supergravity description

Low energy effective action For generic backgrounds, we postulate Let us recall diagonal backgrouds

Vertex operators for diagonal backgrounds We also have the phase:

Effective action between i-j blocks The supergravity multiplet exchanges are consistent with Aoki,Iso,Kawai,Kitazawa,Tada

Effective supergravity action Integration over fermionic zeromodes gives rise to higher dimensional operators:

Dynamical implications These operators give rise to network-like structures as The analysis of this kind of effective theory may be useful to understand the dynamics of IIB matrix model.

Conclusions and Discussions Low energy effective action of IIB matrix model is given by supergravity and the vertex operators. The vertex operators can be determined by N=2 SUSY and they are explicitly determined up to the 6-th descent order. Effective action of Aoki et.al. can be understood in such an interpretation.

Higher dimensional operators are induced in supergravity effective action after the integration over the fermionic zeromodes. Investigations of such an effective supergravity may be useful to elucidate the dynamics of IIB matrix model