1,349 research outputs found
The Appell Function and Regge String Scattering Amplitudes
We show that each 26D open bosonic Regge string scattering amplitude (RSSA)
can be expressed in terms of one single Appell function in the Regge
limit. This result enables us to derive infinite number of recurrence relations
among RSSA at arbitrary mass levels, which are conjectured to be related to the
known SL(5,C) dynamical symmetry of . In addition, we show that these
recurrence relations in the Regge limit can be systematically solved so that
all RSSA can be expressed in terms of one amplitude. All these results are dual
to high energy symmetries of fixed angle string scattering amplitudes
discovered previously [4-8].Comment: 12 pages,no figur
The SL(K+3,C) Symmetry of the Bosonic String Scattering Amplitudes
We discover that the exact string scattering amplitudes (SSA) of three
tachyons and one arbitrary string state, or the Lauricella SSA (LSSA), in the
26D open bosonic string theory can be expressed in terms of the basis functions
in the infinite dimensional representation space of the SL(K+3,C) group. In
addition, we find that the K+2 recurrence relations among the LSSA discovered
by the present authors previously can be used to reproduce the Cartan
subalgebra and simple root system of the SL(K+3,C) group with rank K+2. As a
result, the SL(K+3,C) group can be used to solve all the LSSA and express them
in terms of one amplitude. As an application in the hard scattering limit, the
SL(K+3,C) group can be used to directly prove Gross conjecture [1-3], which was
previously corrected and proved by the method of decoupling of zero norm states
[4-10].Comment: 19 pages, no figure. v2: 20 pages, typos corrected and Eqs. added.
v3: 24 pages, Examples in sec. II added,"Discussion" added, to be published
in Nucl.Phys.
Solving Lauricella String Scattering Amplitudes through Recurrence Relations
We show that there exist infinite number of recurrence relations valid for
all energies among the open bosonic string scattering amplitudes (SSA) of three
tachyons and one arbitrary string state, or the Lauricella SSA. Moreover, these
infinite number of recurrence relations can be used to solve all the Lauricella
SSA and express them in terms of one single four tachyon amplitude. These
results extend the solvability of SSA at the high energy, fixed angle
scattering limit and those at the Regge scattering limit discovered previously.Comment: 19 pages. v2: Fig.1 adde
String Scattering Amplitudes and Deformed Cubic String Field Theory
We study string scattering amplitudes by using the deformed cubic string
field theory which is equivalent to the string field theory in the proper-time
gauge. The four-string scattering amplitudes with three tachyons and an
arbitrary string state are calculated. The string field theory yields the
string scattering amplitudes evaluated on the world sheet of string scattering
whereas the coventional method, based on the first quantized theory brings us
the string scattering amplitudes defined on the upper half plane. For the
highest spin states, generated by the primary operators, both calculations are
in perfect agreement. In this case, the string scattering amplitudes are
invariant under the conformal transformation, which maps the string world sheet
onto the upper half plane. If the external string states are general massive
states, generated by non-primary field operators, we need to take into account
carefully the conformal transformation between the world sheet and the upper
half plane. We show by an explicit calculation that the string scattering
amplitudes calculated by using the deformed cubic string field theory transform
into those of the first quantized theory on the upper half plane by the
conformal transformation, generated by the Schwarz-Christoffel mapping.Comment: 12 pages, 2 figures, references adde
Anatomy of Zero-norm States in String Theory
We calculate and identify the counterparts of zero-norm states in the old
covariant first quantised (OCFQ) spectrum of open bosonic string in two other
quantization schemes of string theory, namely the light-cone DDF zero-norm
states and the off-shell BRST zero-norm states (with ghost) in the Witten
string field theory (WSFT). In particular, special attention is paid to the
inter-particle zero-norm states in all quantization schemes. For the case of
the off-shell BRST zero-norm states, we impose the no ghost conditions and
recover exactly two types of on-shell zero-norm states in the OCFQ string
spectrum for the first few low-lying mass levels. We then show that off-shell
gauge transformations of WSFT are identical to the on-shell stringy gauge
symmetries generated by two types of zero-norm states in the generalized
massive sigma-model approach of string theory. The high energy limit of these
stringy gauge symmetries was recently used to calculate the proportionality
constants, conjectured by Gross, among high energy scattering amplitudes of
different string states. Based on these zero-norm state calculations, we have
thus related gauge symmetry of WSFT to the high-energy stringy symmetry of
Gross.Comment: 30 page
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