1. Vertex Operators and Effective Action of IIB Matrix Model
Yoshihisa Kitazawa
KEK and Sokendai
March

2. 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

3. IIB matrix model

4. 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

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

6. Supersymmetric Wilson Loop
Let us consider Hamada
It satsifies

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

8. N=2 SUSY Transformations

9. Explicit Form of Vertex Operators

12. Mizoguchi, Saito, Kitazawa

13. Block diagonal backgrounds

14. One loop effective action
Supergravity description

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

16. Vertex operators for diagonal backgrounds
We also have the phase:

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

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

19. 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.

20. 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.

21. 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