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

Geometry of Conformal Manifolds and the Inversion Formula

Families of conformal field theories are naturally endowed with a Riemannian geometry which is locally encoded by correlation functions of exactly marginal operators. We show that the curvature of such conformal manifolds can be computed using Euclidean and Lorentzian inversion formulae, which combine the operator content of the conformal field theory into an analytic function. Analogously, operators of fixed dimension define bundles over the conformal manifold whose curvatures can also be computed using inversion formulae. These results relate curvatures to integrated four-point correlation functions which are sensitive only to the behavior of the theory at separated points. We apply these inversion formulae to derive convergent sum rules expressing the curvature in terms of the spectrum of local operators and their three-point function coefficients. We further show that the curvature can smoothly diverge only if a conserved current appears in the spectrum, or if the theory develops a continuum. We verify our results explicitly in $2d$ examples. In particular, for $2d$ (2,2) superconformal field theories we derive a lower bound on the scalar curvature, which is saturated by free theories when the central charge is a multiple of three.Comment: 48 page

On Time-Dependent Backgrounds In 1+1 Dimensional String Theory

In perturbative string theory, one is generally interested in asymptotic observables, such as the S-matrix in flat spacetime, and boundary correlation functions in anti-de Sitter spacetime. However, there are backgrounds in which such observables do not exist. We study examples of such backgrounds in 1+1 dimensional string theory. In these examples, the Liouville wall accelerates and can become spacelike in the past and/or future. When that happens, the corresponding null infinity, at which the standard scattering states are defined, is shielded by the Liouville wall. We compute scattering and particle production amplitudes in these backgrounds in the region in parameter space where the wall remains timelike, and discuss the continuation of this picture to the spacelike regime. We also discuss the physics from the point of view of the dynamics of free fermions in backgrounds with a time-dependent Fermi surface.Comment: 45+12 pages, 11 figure

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

Gentrificação, turismo e conflitos: análise comparada entre o Bonfim (Porto, Portugal) e Koukaki (Atenas, Grécia)

Dissertação de mestrado em Geografia (especialização em Turismo e Comunicação Territorial)Esta pesquisa teve como objetivo central fazer um estudo comparativo entre o processo de gentrificaçãoe a relação deste com o turismo na freguesia do Bonfim, na cidade do Porto, e no bairro de Koukaki, nacidade de Atenas. O caminho metodológico foi percorrido de duas formas: a utilização da metodologia andante em que foi realizada durante dois meses em cada cidade para escolha dos recortes espaciais que seriam analisados posteriormente, e entrevistas semiestruturadas com pessoas que moram ou que possuíam algum tipo de relação com os bairros estudados. Tendo em vista a aplicação destes esforços metodológicos, os resultados obtidos reforçam que os conflitos existentes não aparecem em termos de confronto, sendo muito mais silenciosos nesse sentido, mas que por outro lado, aparecem no aumento das rendas e na dificuldade de acessibilidade aos bairros em função do aumento do turismo e os crescimentos dos Alojamentos Locais e AIRBNBs nos dois bairros. No caso do Bonfim, a gentrificação é mais visível em função do crescimento dos Alojamentos Locais e das fileiras de casas reabilitadas que perderam habitantes. Em Koukaki, percebeu-se mais turistificação e menos gentrificação, pois o bairro ainda preserva uma quantidade significativa de moradores antigos que são de classe média.This research aimed to make a comparative study between the gentrification process and its relationship with tourism in the parish of Bonfim, in the city of Porto, and in the neighborhood of Koukaki, in the cityof Athens. The methodological path was followed in two ways: the use of the walking methodology in which it was carried out for two months in each city to choose the spatial clippings that would be analyzed later, and semi-structured interviews with people who live or had some kind of relationship with the studied neighborhoods. In view of the application of these methodological efforts, the results obtainedreinforce that the existing conflicts do not appear in terms of confrontation, being much more silent inthissense, but that, on the other hand, they appear in the increase in rents and in the difficulty of accessibility to neighborhoods in due to the increase in tourism and the growth of Local Accommodation and AIRBNBs in the two neighborhoods. In the case of Bonfim, gentrification is more visible due to the growth of Local Accommodation and the line of houses rehabilitated that have lost inhabitants. InKoukaki, there was more touristification and less gentrification, as the neighborhood still preserves a significant amount of old residents who are more middle class