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 $c=1$ and $c=25$ 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 $g_s$, and to the four-point cosmological wavefunction at order $g_s^2$ 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

Rights declaration in Linked Data

Linked Data is not always published with a license. Sometimes a wrong license type is used, like a license for software, or it is not expressed in a standard, machine readable manner. Yet, Linked Data resources may be subject to intellectual property and database laws, may contain personal data subject to privacy restrictions or may even contain important trade secrets. The proper declaration of which rights are held, waived or licensed is a must for the lawful use of Linked Data at its different granularity levels, from the simple RDF statement to a dataset or a mapping. After comparing the current practice with the actual needs, six research questions are posed

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;