3,401 research outputs found
Long String Scattering in c = 1 String Theory
We study the scattering of long strings in c = 1 string theory, both in the
worldsheet description and in the non-singlet sector of the dual matrix quantum
mechanics. From the worldsheet perspective, the scattering amplitudes of long
strings are obtained from a decoupling limit of open strings amplitudes on FZZT
branes, which we compute by integrating Virasoro conformal blocks along with
structure constants of boundary Liouville theory. In particular, we study the
tree level amplitudes of (1) a long string decaying by emitting a closed
string, and (2) the scattering of a pair of long strings. We show that they are
indeed well defined as limits of open string amplitudes, and that our results
are in striking numerical agreement with computations in the adjoint and
bi-adjoint sectors of the dual matrix model (based on proposals of Maldacena
and solutions due to Fidkowski), thereby providing strong evidence of the
duality.Comment: 42 pages, 18 figure
The c=1 String Theory S-Matrix Revisited
We revisit the perturbative S-matrix of c=1 string theory from the worldsheet
perspective. We clarify the origin of the leg pole factors, the non-analyticity
of the string amplitudes, and the validity as well as limitations of earlier
computations based on resonance momenta. We compute the tree level 4-point
amplitude and the genus one 2-point reflection amplitude by numerically
integrating Virasoro conformal blocks with DOZZ structure constants on the
sphere and on the torus, with sufficiently generic complex Liouville momenta,
and find agreement with known answers from the c=1 matrix model.Comment: 32 pages, 7 figures; footnote and references added, typos correcte
A Two-Dimensional String Cosmology
We study two-dimensional string theory on a time-dependent background, whose
worldsheet description consists of Liouville theory at central charge c = 1 and
Liouville theory at central charge c = 25, together with the conformal ghosts.
We compute the tree-level three-point and four-point cosmological wavefunctions
in string perturbation theory. The latter is evaluated numerically by
decomposing the Liouville four-point correlation functions into Virasoro
conformal blocks and three-point function coefficients and integrating over the
moduli space of the four-punctured sphere string diagram. This computation
numerically confirms a surprisingly simple conjectural result for the
four-point wavefunction whose physical interpretation remains to be clarified.Comment: 24 pages, 7 figures, 1 .nb Mathematica notebook attachmen
The Torus One-Point Diagram in Two-Dimensional String Cosmology
We calculate numerically the torus one-point string diagram in the
two-dimensional string cosmology background by decomposing the one-point
functions in and Liouville CFT into torus one-point Virasoro
conformal blocks and integrating over the fundamental domain of the torus
moduli space. We find a remarkably simple result as a function of the outgoing
closed string energy. This torus one-point diagram is expected to contribute to
the one-point cosmological wavefunction at order , and to the four-point
cosmological wavefunction at order through the disconnected product of
the torus one-point diagram and the sphere three-point diagram.Comment: 13 pages, 2 figures, 1 .nb Mathematica notebook attachmen
The S-Matrix of 2D Type 0B String Theory Part 2: D-Instanton Effects
We study the effect of D-instantons on closed string scattering amplitudes in
the two-dimensional type 0B string theory from the worldsheet perspective. We
find that the contribution from a pair of D-instanton and anti-D-instanton to
the closed string reflection amplitude, with a suitable contour prescription
for the integration over the D-instanton moduli space, agrees with the
corresponding leading non-perturbative corrections in the proposed dual matrix
quantum mechanics. This analysis is further extended to thermal observables
defined at finite temperature. The infrared divergence in charged processes is
understood through the measure factor for charged D-instantons, and can be
treated with spacetime dimensional regularization.Comment: 30 pages, 3 figures, 1 tabl
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Inversores como nuevos agentes del cambio ambiental de las empresas, Los
Como su propio nombre indica, el objetivo del trabajo de investigación que se presenta en este documento ha sido profundizar sobre la influencia que los inversores han tenido, están teniendo y van a tener en el comportamiento medioambiental de las empresas. A través del análisis del fenómeno de los fondos de inversión «verdes», en este trabajo vemos cómo ética y negocio no han de constituir un «juego de suma cero», sino que, por el contrario, las empresas pueden favorecer su capacidad de crear valor considerando de forma simultánea los aspectos de negocio y su impacto en el medio ambiente y en la sociedad en general.cambio ambiental empresas; medioambiente;
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