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

Abstract

We report on progress in determining the complete form of vertex operators for the IIB matrix model. The exact expressions are obtained for those emitting massless IIB supergravity fields up to sixth order in the light-cone superfield, in which the conjugate gravitino and conjugate two-form vertex operators are newly determined. We also provide a consistency check by computing the kinematical factor of a four-point graviton amplitude in a D-instanton background. We conjecture that the low-energy effective action of the IIB matrix model at large N is given by tree-level supergravity coupled to the vertex operators.

Authors:
;  [1];  [2];  [1];  [2]
  1. High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki 305-0801 (Japan)
  2. (Japan)
Publication Date:
OSTI Identifier:
20933309
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. D, Particles Fields; Journal Volume: 75; Journal Issue: 10; Other Information: DOI: 10.1103/PhysRevD.75.106002; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ACTION INTEGRAL; INSTANTONS; LIGHT CONE; MATRICES; SUPERGRAVITY

Citation Formats

Kitazawa, Yoshihisa, Mizoguchi, Shun'ya, Department of Particle and Nuclear Physics, The Graduate University for Advanced Studies, Tsukuba, Ibaraki 305-0801, Saito, Osamu, and Institute for Cosmic Ray Research, University of Tokyo, Kashiwa 277-8582. Progress toward the determination of complete vertex operators for the IIB matrix model. United States: N. p., 2007. Web. doi:10.1103/PHYSREVD.75.106002.
Kitazawa, Yoshihisa, Mizoguchi, Shun'ya, Department of Particle and Nuclear Physics, The Graduate University for Advanced Studies, Tsukuba, Ibaraki 305-0801, Saito, Osamu, & Institute for Cosmic Ray Research, University of Tokyo, Kashiwa 277-8582. Progress toward the determination of complete vertex operators for the IIB matrix model. United States. doi:10.1103/PHYSREVD.75.106002.
Kitazawa, Yoshihisa, Mizoguchi, Shun'ya, Department of Particle and Nuclear Physics, The Graduate University for Advanced Studies, Tsukuba, Ibaraki 305-0801, Saito, Osamu, and Institute for Cosmic Ray Research, University of Tokyo, Kashiwa 277-8582. Tue . "Progress toward the determination of complete vertex operators for the IIB matrix model". United States. doi:10.1103/PHYSREVD.75.106002.
@article{osti_20933309,
title = {Progress toward the determination of complete vertex operators for the IIB matrix model},
author = {Kitazawa, Yoshihisa and Mizoguchi, Shun'ya and Department of Particle and Nuclear Physics, The Graduate University for Advanced Studies, Tsukuba, Ibaraki 305-0801 and Saito, Osamu and Institute for Cosmic Ray Research, University of Tokyo, Kashiwa 277-8582},
abstractNote = {We report on progress in determining the complete form of vertex operators for the IIB matrix model. The exact expressions are obtained for those emitting massless IIB supergravity fields up to sixth order in the light-cone superfield, in which the conjugate gravitino and conjugate two-form vertex operators are newly determined. We also provide a consistency check by computing the kinematical factor of a four-point graviton amplitude in a D-instanton background. We conjecture that the low-energy effective action of the IIB matrix model at large N is given by tree-level supergravity coupled to the vertex operators.},
doi = {10.1103/PHYSREVD.75.106002},
journal = {Physical Review. D, Particles Fields},
number = 10,
volume = 75,
place = {United States},
year = {Tue May 15 00:00:00 EDT 2007},
month = {Tue May 15 00:00:00 EDT 2007}
}
  • We clarify the relation between the vertex operators in type IIB matrix model and superstring. Green-Schwarz light-cone closed superstring theory is obtained from IIB matrix model on two-dimensional noncommutative backgrounds. Superstring vertex operators should be reproduced from those of IIB matrix model through this connection. Indeed, we confirm that supergravity vertex operators in IIB matrix model on the two-dimensional backgrounds reduce to those in superstring theory. Noncommutativity plays an important role in our identification. Through this correspondence, we can reproduce superstring scattering amplitudes from IIB matrix model.
  • We systematically construct wave functions and vertex operators in the type IIB (IKKT) matrix model by expanding a supersymmetric Wilson loop operator. They form a massless multiplet of the N=2 type IIB supergravity and automatically satisfy conservation laws.
  • We show that the supersymmetric Wilson loops in a type-IIB matrix model give a transition operator from reduced supersymmetric Yang-Mills theory to supersymmetric space-time theory. In comparison with Green-Schwarz superstring we identify the supersymmetric Wilson loops with the asymptotic states of a type-IIB superstring. It is pointed out that the supersymmetry transformation law of the Wilson loops is the inverse of that for the vertex operators of massless modes in the U(N) open superstring with a Dirichlet boundary condition. {copyright} {ital 1997} {ital The American Physical Society}
  • 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 D-instanton 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)x(N+1), or equivalently the effective action for (N+1) D-instantons. We thenmore » calculate an effective action for N D-instantons by integrating out 1 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 in the superstring theory side as overlaps of the D-instanton boundary state with the closed string massless states in the Green-Schwarz formalism.« less
  • A group of fuzzy spacetime with SU(3) isometry is studied at the two-loop level in a IIB matrix model. It consists of spacetime from four to six dimensions, namely, from CP{sup 2} to SU(3)/U(1)xU(1). The effective action scales in a universal manner in the large N limit as N and N{sup 4/3} on four- and six-dimensional manifolds, respectively. The four-dimensional spacetime CP{sup 2} possesses the smallest effective action in this class.