Ghost story. III. Back to ghost number zero

After having defined a 3-strings midpoint-inserted vertex for the bc system, we analyze the relation between gh=0 states (wedge states) and gh=3 midpoint duals. We find explicit and regular relations connecting the two objects. In the case of wedge states this allows us to write down a spectral decomposition for the gh=0 Neumann matrices, despite the fact that they are not commuting with the matrix representation of K1. We thus trace back the origin of this noncommutativity to be a consequence of the imaginary poles of the wedge eigenvalues in the complex k-plane. With explicit reconstruction formulas at hand for both gh=0 and gh=3, we can finally show how the midpoint vertex avoids this intrinsic noncommutativity at gh=0, making everything as simple as the zero momentum matter sector.Comment: 40 pages. v2: typos and minor corrections, presentation improved in sect. 4.3, plots added in app. A.1, two refs added. To appear in JHE

Ghost story. II. The midpoint ghost vertex

We construct the ghost number 9 three strings vertex for OSFT in the natural normal ordering. We find two versions, one with a ghost insertion at z=i and a twist-conjugate one with insertion at z=-i. For this reason we call them midpoint vertices. We show that the relevant Neumann matrices commute among themselves and with the matrix $G$ representing the operator K1. We analyze the spectrum of the latter and find that beside a continuous spectrum there is a (so far ignored) discrete one. We are able to write spectral formulas for all the Neumann matrices involved and clarify the important role of the integration contour over the continuous spectrum. We then pass to examine the (ghost) wedge states. We compute the discrete and continuous eigenvalues of the corresponding Neumann matrices and show that they satisfy the appropriate recursion relations. Using these results we show that the formulas for our vertices correctly define the star product in that, starting from the data of two ghost number 0 wedge states, they allow us to reconstruct a ghost number 3 state which is the expected wedge state with the ghost insertion at the midpoint, according to the star recursion relation.Comment: 60 pages. v2: typos and minor improvements, ref added. To appear in JHE

The off-shell Veneziano amplitude in Schnabl gauge

We give a careful definition of the open string propagator in Schnabl gauge and present its worldsheet interpretation. The propagator requires two Schwinger parameters and contains the BRST operator. It builds surfaces by gluing strips of variable width to the left and to the right of off-shell states with contracted or expanded local frames. We evaluate explicitly the four-point amplitude of off-shell tachyons. The computation involves a subtle boundary term, crucial to enforce the correct exchange symmetries. Interestingly, the familiar on-shell physics emerges even though string diagrams produce Riemann surfaces more than once. Off-shell, the amplitudes do not factorize over intermediate on-shell states.Comment: 48 pages, 10 figures. v2:acknowledgments adde

Fluctuations around the Tachyon Vacuum in Open String Field Theory

We consider quadratic fluctuations around the tachyon vacuum numerically in open string field theory. We work on a space ${\cal H}_N^{{\rm vac}}$ spanned by basis string states used in the Schnabl's vacuum solution. We show that the truncated form of the Schnabl's vacuum solution on ${\cal H}_N^{{\rm vac}}$ is well-behaved in numerical work. The orthogonal basis for the new BRST operator $\tilde Q$ on ${\cal H}_N^{{\rm vac}}$ and the quadratic forms of potentials for independent fields around the vacuum are obtained. Our numerical results support that the Schnabl's vacuum solution represents the minimum energy solution for arbitrary fluctuations also in open string field theory.Comment: 16 pages, 2 figures, some comments and one table added, version to appear in JHE

Solving Open String Field Theory with Special Projectors

Schnabl recently found an analytic expression for the string field tachyon condensate using a gauge condition adapted to the conformal frame of the sliver projector. We propose that this construction is more general. The sliver is an example of a special projector, a projector such that the Virasoro operator \L_0 and its BPZ adjoint \L*_0 obey the algebra [\L_0, \L*_0] = s (\L_0 + \L*_0), with s a positive real constant. All special projectors provide abelian subalgebras of string fields, closed under both the *-product and the action of \L_0. This structure guarantees exact solvability of a ghost number zero string field equation. We recast this infinite recursive set of equations as an ordinary differential equation that is easily solved. The classification of special projectors is reduced to a version of the Riemann-Hilbert problem, with piecewise constant data on the boundary of a disk.Comment: 64 pages, 6 figure

Contraction of broken symmetries via Kac-Moody formalism

I investigate contractions via Kac-Moody formalism. In particular, I show how the symmetry algebra of the standard 2-D Kepler system, which was identified by Daboul and Slodowy as an infinite-dimensional Kac-Moody loop algebra, and was denoted by ${\mathbb H}_2$, gets reduced by the symmetry breaking term, defined by the Hamiltonian $$H(\beta)= \frac 1 {2m} (p_1^2+p_2^2)- \frac \alpha r - \beta r^{-1/2} \cos ((\phi-\gamma)/2).$$ For this $H (\beta)$ I define two symmetry loop algebras ${\mathfrak L}_{i}(\beta), i=1,2$, by choosing the `basic generators' differently. These ${\mathfrak L}_{i}(\beta)$ can be mapped isomorphically onto subalgebras of ${\mathbb H}_2$, of codimension 2 or 3, revealing the reduction of symmetry. Both factor algebras ${\mathfrak L}_i(\beta)/I_i(E,\beta)$, relative to the corresponding energy-dependent ideals $I_i(E,\beta)$, are isomorphic to ${\mathfrak so}(3)$ and ${\mathfrak so}(2,1)$ for $E0$, respectively, just as for the pure Kepler case. However, they yield two different non-standard contractions as $E \to 0$, namely to the Heisenberg-Weyl algebra ${\mathfrak h}_3={\mathfrak w}_1$ or to an abelian Lie algebra, instead of the Euclidean algebra ${\mathfrak e}(2)$ for the pure Kepler case. The above example suggests a general procedure for defining generalized contractions, and also illustrates the {\em `deformation contraction hysteresis'}, where contraction which involve two contraction parameters can yield different contracted algebras, if the limits are carried out in different order.Comment: 21 pages, 1 figur

Descent Relations in Cubic Superstring Field Theory

The descent relations between string field theory (SFT) vertices are characteristic relations of the operator formulation of SFT and they provide self-consistency of this theory. The descent relations and in the NS fermionic string field theory in the kappa and discrete bases are established. Different regularizations and schemes of calculations are considered and relations between them are discussed.Comment: Replaced to JHEP styl

GW band structure of InAs and GaAs in the wurtzite phase

We report the first quasiparticle calculations of the newly observed wurtzite polymorph of InAs and GaAs. The calculations are performed in the GW approximation using plane waves and pseudopotentials. For comparison we also report the study of the zinc-blende phase within the same approximations. In the InAs compound the In 4d electrons play a very important role: whether they are frozen in the core or not, leads either to a correct or a wrong band ordering (negative gap) within the Local Density Appproximation (LDA). We have calculated the GW band structure in both cases. In the first approach, we have estimated the correction to the pd repulsion calculated within the LDA and included this effect in the calculation of the GW corrections to the LDA spectrum. In the second case, we circumvent the negative gap problem by first using the screened exchange approximation and then calculating the GW corrections starting from the so obtained eigenvalues and eigenfunctions. This approach leads to a more realistic band-structure and was also used for GaAs. For both InAs and GaAs in the wurtzite phase we predict an increase of the quasiparticle gap with respect to the zinc-blende polytype.Comment: 9 pages, 6 figures, 3 table

Exact marginality in open string field theory: a general framework

We construct analytic solutions of open bosonic string field theory for any exactly marginal deformation in any boundary conformal field theory when properly renormalized operator products of the marginal operator are given. We explicitly provide such renormalized operator products for a class of marginal deformations which include the deformations of flat D-branes in flat backgrounds by constant massless modes of the gauge field and of the scalar fields on the D-branes, the cosine potential for a space-like coordinate, and the hyperbolic cosine potential for the time-like coordinate. In our construction we use integrated vertex operators, which are closely related to finite deformations in boundary conformal field theory, while previous analytic solutions were based on unintegrated vertex operators. We also introduce a modified star product to formulate string field theory around the deformed background.Comment: 63 pages, 10 figures, LaTeX2

Superstring field theory equivalence: Ramond sector

We prove that the finite gauge transformation of the Ramond sector of the modified cubic superstring field theory is ill-defined due to collisions of picture changing operators. Despite this problem we study to what extent could a bijective classical correspondence between this theory and the (presumably consistent) non-polynomial theory exist. We find that the classical equivalence between these two theories can almost be extended to the Ramond sector: We construct mappings between the string fields (NS and Ramond, including Chan-Paton factors and the various GSO sectors) of the two theories that send solutions to solutions in a way that respects the linearized gauge symmetries in both sides and keeps the action of the solutions invariant. The perturbative spectrum around equivalent solutions is also isomorphic. The problem with the cubic theory implies that the correspondence of the linearized gauge symmetries cannot be extended to a correspondence of the finite gauge symmetries. Hence, our equivalence is only formal, since it relates a consistent theory to an inconsistent one. Nonetheless, we believe that the fact that the equivalence formally works suggests that a consistent modification of the cubic theory exists. We construct a theory that can be considered as a first step towards a consistent RNS cubic theory.Comment: v1: 24 pages. v2: 27 pages, significant modifications of the presentation, new section, typos corrected, references adde