Scattering of massive open strings in pure spinor

In Park (2008) [4], it was proposed that the D-brane geometry could be produced by open string quantum effects. In an effort to verify the proposal, we consider scattering amplitudes involving massive open superstrings. The main goal of this paper is to set the ground for two-loop “renormalization” of an oriented open superstring on a D-brane and to strengthen our skill in the pure spinor formulation of a superstring, an effective tool for multi-loop string diagrams. We start by reviewing scattering amplitudes of massless states in the 2D component method of the NSR formulation. A few examples of massive string scattering are worked out. The NSR results are then reproduced in the pure spinor formulation. We compute the amplitudes using the unintegrated form of the massive vertex operator constructed by Berkovits and Chandia (2002) [15]. We point out that it may be possible to discover new Riemann type identities involving Jacobi ?-functions by comparing a NSR computation and the corresponding pure spinor computation.     

Radiative widths of neutral kaon excitations

We observe 147 events of the axial vector pairK ₁(1270)–K ₁(1400) produced in the Coulomb field of a Pb target and measure the radiative widths Γ(K ₁(1400)→K ⁰ + γ) = 280.8 ±23.2(stat.) ±40.4(syst.) keV and Γ(K ₁(1270) →K ⁰ + γ) = 73.2 ±6.1(stat.) ±28.3(syst.) keV. These first measurements are lower than the quark-model predictions. We also place upper limits on the radiative widths forK*(1410) andK ₂ ^* (1430) and find that the latter is very small in accord withSU(3)invariance in the naive quark model.     

A theory of dual massive strings

A theory of relativistic strings with non-vanishing mechanical mass is developed. The theory involves the usual massless strings, and the main features of the massless theory are retained so that the system is dual and ghost-free. Some new features appear especially in the mass spectrum of the pomeron sector. The mode with Neveu-Schwarz spin is also considered.     

Holomorphic factorization and open strings

It is established that, apart from a function of the period matrix of the double of the surface, the open bosonic string integrand at an arbitrary order of string perturbation theory is the modulus squared of a necessarily complex function of real moduli coordinates and that no surface terms contribute to any obstruction to this factorization. This function is related to the modulus of the holomorphic function in the moduli space of the double of the surface guaranteed to exist by the previously established result of holomorphic factorization for closed strings.     

The geometry of open bosonic strings

The coordinate conditions usually used to describe the open string and its boundary conditions are intrinsically singular at the boundary. As a result, the boundary conditions are difficult to understand or interpret geometrically. The physical requirement that the variation of the string at the boundary yield a vanishing contribution to the variation of the action may be accomplished by the requirement that the induced metric, in non-singular coordinates, have signature (0, — 1) at the boundary and that the metric be C¹ on the boundary. These geometrically simple by analytically somewhat complicated requirements are equivalent to the usual boundary conditions. Lastly it is shown that the open string is, in a strict sense, a special case of the closed string. Some of the peculiar behavior of characteristic curves on the open string becomes clear in this context.     

Radial and Regge excitations in unified,grand unified and subconstituent models

Necessary group theoretic conditions for all elementary gauge bosons and fermions of an arbitrary renormalizable gauge theory to lie on Regge trajectories are reviewed. It is then argued that in properly unified gauge theories all particles of a given spin lie on Regge trajectories. This then implied that a properly unified gauge theory has no local U(1) factor groups, and no massive fermion singlets. A consideration of the general pattern of Regge and radial recurrences to be expected in quantum field theories suggests that the presence or absence of spin $\text{3}\text{2}$ quarks and/or leptons in the TeV region will provide crucial clues to enable one to distinguish between various classes of unified, grand unified, and subconstituent models. The correct interpretation of such excited fermions will require correlation with the Higgs boson mass and possible radial and Regge excitations of the weak vector bosons.     

Minimal area problems and quantum open strings

We discuss minimal area problems for surfaces with boundaries and both open and closed string punctures. We define open-closed string diagrams to be surfaces with metrics of minimal area under the condition that any nontrivial Jordan open curve be longer or equal to and any nontrivial Jordan closed curve be longer or equal to 2. It is proven that the double of an open-closed string diagram is a closed string diagram of covariant closed string field theory.Supported in part by funds provided by the U.S. Department of Energy (D.O.E.) under contract #DE-AC02-76ER03069     

Supersymmetry breaking,open strings and M-theory

We study supersymmetry breaking by Scherk-Schwarz compactifications in type I string theory. While in the gravitational sector all mass splittings are proportional to a (large) compactification radius, supersymmetry remains unbroken for the massless excitations of D-branes orthogonal to the large dimension. In this sector, supersymmetry breaking can then be mediated by gravitational interactions alone, that are expected to be suppressed by powers of the Planck mass. The mechanism is non-perturbative from the heterotic viewpoint and requires a compactification radius at intermediate energies of order 10¹²−10¹⁴ GeV This can also explain the value of Newton's constant if the string scale is close to the unification scale, of order 10¹⁶ GeV.     

Decay of electronic excitations in bulk metals and at surfaces

We present a brief survey of the contemporary state of theoretical study of quasiparticles (excited electrons and holes) dynamics in bulk metals and at metal surfaces. Quasiparticle decay mechanisms are discussed in terms of electron-electron (e-e) and electron-phonon (e-ph) interactions. The e-ph decay channel is shown to be important for all materials considered. It is especially important for systems with the thickness of one monolayer. In the e-e decay channel the quasiparticle decay can be realized via one-electron transfer processes, via creation of electron-hole pairs, and via plasmon excitation. In ferromagnetic systems the electron (hole) decay via the Stoner pair excitation or/and magnon excitation is made possible.     

Statistical properties of resonance widths for open quantum graphs

We connect quantum compact graphs with infinite leads, and turn them into scattering systems. We derive an exact expression for the scattering matrix, and explain how it is related to the spectrum of the corresponding closed graph. The resulting expressions allow us to get a clear understanding of the phenomenon of resonance trapping due to over-critical coupling with the leads. Finally, we analyse the statistical properties of the resonance widths and compare our results with the predictions of random matrix theory. Deviations appearing due to the dynamical nature of the system are pointed out and explained.     

Statistical properties of resonance widths for open quantum graphs

We connect quantum compact graphs with infinite leads, and turn them into scattering systems. We derive an exact expression for the scattering matrix, and explain how it is related to the spectrum of the corresponding closed graph. The resulting expressions allow us to get a clear understanding of the phenomenon of resonance trapping due to over-critical coupling with the leads. Finally, we analyse the statistical properties of the resonance widths and compare our results with the predictions of random matrix theory. Deviations appearing due to the dynamical nature of the system are pointed out and explained.     

Decay of high-frequency acoustic excitations in chain-type lattices and weak localization

The attenuation of high-frequency sound in disordered quasi-one-dimensional semiconducting and dielectric crystals, which is associated with three-phonon decay and elastic scattering by structure defects is considered theoretically. It is shown that specific interference processes occurring in the regime of weak localization of acoustic vibrational excitations considerably affect the propagation of sound. This mechanism of sound attenuation can be observed experimentally from the anomalies in the frequency dependence of the reciprocal attenuation length of sound.     

A geometrical approach for open and closed strings

We show that a candidate for the open string lagrangian proposed earlier has a large tangent space invariance group, in addition to being invariant under extended reparametrization transformations. We also simplify the underlying differential geometry and extend it to the closed string. In the latter case, the well known constraint relating the number of the right and left movers emerges naturally.