12,398 research outputs found
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 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 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 is
well-behaved in numerical work. The orthogonal basis for the new BRST operator
on 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 , gets reduced by the symmetry breaking term,
defined by the Hamiltonian For this I
define two symmetry loop algebras , by
choosing the `basic generators' differently. These
can be mapped isomorphically onto subalgebras of , of
codimension 2 or 3, revealing the reduction of symmetry. Both factor algebras
, relative to the corresponding
energy-dependent ideals , are isomorphic to
and for , respectively, just as for the
pure Kepler case. However, they yield two different non-standard contractions
as , namely to the Heisenberg-Weyl algebra or to an abelian Lie algebra, instead of the Euclidean algebra
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
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