H. Itoyama

p–p′ System with B field, branes at angles and noncommutative geometry

Abstract We study the generic p – p ′ system in the presence of constant NS 2-form B ij field. We derive properties concerning with the noncommutativity of D-brane worldvolume, the Green functions and the spectrum of this system. In the zero slope limit, a large number of light states appear as the lowest excitations in appropriate cases. We are able to relate the energies of the lowest states after the GSO projection with the configurations of branes at angles. Through analytic continuation, the system is compared with the branes with relative motion.

USp(2k) Matrix Model: F Theory Connection

We present a zero-dimensional matrix model based on USp(2k) with supermultiplets in symmetric, antisymmetric and fundamental representations. The four-dimensional comxad pactification of this model naturally captures the exact results of Sen 1) in F theory. Eight dynamical and eight kinematical supercharges are found, as required for critical string interxad pretation. The classical vacuum has ten coordinates and is equipped with orbifold structure. We clarify the issue of spacetime dimensions which F theory represented by this matrix model produces.

Worldsheet and spacetime properties of p–p′ system with B field and noncommutative geometry

We study worldsheet and spacetime properties of the p–p′ (p<p′) open string system with constant Bij field viewed from the Dp′-brane. The description of this system in terms of the CFT with spin and twist fields leads us to consider the renormal ordering procedure from the SL(2,R) invariant vacuum to the oscillator vacuum. We compute the attendant two distinct superspace two-point functions as well as their difference (the subtracted two-point function). These bring us an integral (Koba–Nielsen) representation for the multiparticle tree scattering amplitudes consisting of N−2 vectors and two tachyons. We evaluate them explicitly for the N=3,4 cases. Several novel features are observed which include a momentum dependent multiplicative factor to each external vector leg and the emergence of a symplectic tensor multiplying the polarization vectors. In the zero slope limit, the principal parts of the amplitudes translate into a noncommutative field theory in p′+1 dimensions in which a scalar field decaying exponentially in (p′−p) dimensions and a noncommutative U(1) gauge field interact via the minimal coupling and a new interaction. A large number of nearly massless states noted before are shown to propagate in the t-channel.

Correspondence between Noncommutative Soliton and Open String/D-Brane System via Gaussian Damping Factor

The gaussian damping factor (g.d.f.) and the new interaction vertex with the symplectic tensor are the characteristic properties of the N -point scalar-vector scattering amplitudes of the p − p′(p < p′) open string system which realizes noncommutative geometry. The g.d.f. is here interpreted as a form factor of the Dp-brane by noncommutative U(1) current. Observing that the g.d.f. is in fact equal to the Fourier transform of the noncommutative projector soliton introduced by Gopakumar, Minwalla and Strominger, we further identify the Dp-brane in the zero slope limit with the noncommutative soliton state. It is shown that the g.d.f. depends only on the total momentum of N − 2 incoming/outgoing photons in the zero slope limit. In the description of the low-energy effective action (LEEA) proposed before, this is shown to follow from the delta function propagator and the form of the initial/final wave functions in the soliton sector which resides in the x (m = p+1 · · · p′) dependent part of the scalar field Φ(x, x). The three and four point amplitudes computed from LEEA agree with string calculation. We discuss related issues which are resummation/lifting of infinite degeneracy and conservation of momentum transverse to the Dp-brane.

NON-ABELIAN BERRY PHASE, YANG–MILLS INSTANTON AND USp(2k) MATRIX MODEL

The non-Abelian Berry phase is computed in the T dualized quantum mechanics obtained from the USp(2k) matrix model. Integrating the fermions, we find that each of the space–time points is equipped with a pair of su(2) Lie algebra valued pointlike singularities located at a distance m(f) from the orientifold surface. On a four-dimensional paraboloid embedded in the five-dimensional Euclidean space, these singularities are recognized as the BPST instantons.

Nonabelian monopoles from matrices

Abstract We study the expectation value of (the product) of the one-particle projector(s) in the reduced matrix model and matrix quantum mechanics in general. This quantity is given by the nonabelian Berry phase: we discuss the relevance of this with regard to the spacetime structure. The case of the USp matrix model is examined from this respect. Generalizing our previous work, we carry out the complete computation of this quantity which takes into account both the nature of the degeneracy of the fermions and the presence of the spacetime points belonging to the antisymmetric representation. We find the singularities as those of the SU(2) Yang monopole connection as well as the pointlike singularities in 9+1 dimensions coming from its SU(8) generalization. The former type of singularities, which extend to four of the directions lying in the antisymmetric representations, may be regarded as seeds of our four-dimensional spacetime structure and is not shared by the IIB matrix model. From a mathematical viewpoint, these connections can be generalizable to arbitrary odd space dimensions due to the nontrivial nature of the eigenbundle and the Clifford module structure.

USp(2k) Matrix Model

We review the construction and theoretical implications of the USp(2k) matrix model in zero dimension introduced in ref. cite{IT1,IT2}. It is argued that the model provides a constructive approach to Type I superstrings and is at the same time dynamical theory of spacetime points. Three subjects are discussed : semiclassical pictures and series of degenerate perturbative vacua associated with the worldvolume representation of the model, the formation of extended (D-)objects from the fermionic integrations via the (non-)abelian Berry phase, and the Schwinger-Dyson/loop equations which exhibit the joining-splitting interactions required. Lectures presented at the 13th Nishinomiya-Yukawa Memorial Symposium ``Dynamics of Fields and Strings (November 12-13,1998) and at the YITP workshop (November 16-18, 1998).

Berry's connection and USp(2k) matrix model

Abstract Berrys connection is computed in the USp (2 k ) matrix model. In T dualized quantum mechanics, the Berry phase exhibits a residual interaction taking place at a distance m ( f ) from the orientifold surface via the integration of the fermions in the fundamental representation. This is interpreted as a coupling of the magnetic D 2 with the electric D 4 branes. We make a comment on the Berry phase associated with the 6 D nonabelian gauge anomaly whose cancellation selects the number of flavours n f =16.

USp(2k) Matrix Model— Schwinger-Dyson Equations and Closed-Open String Interactions —

We derive the Schwinger-Dyson/loop equations for the USp(2k) matrix model which close among the closed and open Wilson loop variables. These loop equations exhibit a complete set of the joining and splitting interactions required for the nonorientable Type I superstrings. The open loops realize the SO(2n_f) Chan-Paton factor and their linearized loop equations derive the mixed Dirichlet/Neumann boundary conditions.

Extension of boundary string field theory on disc and RP 2 worldsheet geometries

We present a construction of open-closed string field theory based on disc and RP 2 geometries. Finding an appropriate BRS operator in the case of the RP 2 geometry, we generalize the background independent open string field theory (or boundary string field theory) of Witten on a unit disc. The coupling constant flow at the closed string side is driven by the scalar operator inserted at the nontrivial loop of RP 2 . We discuss the off-shell extension of the boundary/crosscap states. Our construction provides an interpolation of orientifold planes of various dimensions as well as that of D-branes.I review progress related to the calculation of QCD jet cross sections at the NLO accuracy. After a short introduction into the theory of NLO calculations, I discuss two recent developments: the calculation of twoand three-jet leptoproduction at the NLO accuracy and the extension of the dipole subtraction method for computing NLO corrections for processes involving massive partons. Jet cross sections at the NLO accuracy consist of the first two terms of the perturbative expansion in the strong coupling, σ = σ + σ = ∫ m dσ + σ . (1) The leading order cross section is the integral of the fully exclusive Born matrix element of m final-state partons over the available phase space. The NLO correction is a sum of two terms: the real correction is the integral of the Born matrix element of m + 1 finalstate partons and the virtual correction is the integral of the interference term between the Born-level and one-loop amplitudes of m final state partons, σ = ∫