Strings in Singular Time-Dependent Backgrounds

We review the construction of time-dependent backgrounds with space-like singularities. We mainly consider exact CFT backgrounds. The algebraic and geometric aspects of these backgrounds are discussed. Physical issues, results and difficulties associated with such systems are reviewed. Finally, we present some new results: a two dimensional cosmology in the presence of an Abelian gauge field described within a family of (SL(2)xU(1))/(U(1)xZ) quotient CFTs.Comment: 22 pages, 4 figures, Contribution to the proceedings of Symposium Ahrenshoop, August 200

On Least Action D-Branes

We discuss the effect of relevant boundary terms on the nature of branes. This is done for toroidal and orbifold compactifications of the bosonic string. Using the relative minimalization of the boundary entropy as a guiding principle, we uncover the more stable boundary conditions at different regions of moduli space. In some cases, Neumann boundary conditions dominate for small radii while Dirichlet boundary conditions dominate for large radii. The c=1 and c=2 moduli spaces are studied in some detail. The antisymmetric background field B is found to have a more limited role in the case of Dirichlet boundary conditions. This is due to some topological considerations. The results are subjected to T-duality tests and the special role of the points in moduli space fixed under T-duality is explained from least-action considerations.Comment: Latex, 20 pages, 2 figures, references adde

Geometry And Quantum Noise

We study the fine structure of long-time quantum noise in correlation functions of AdS/CFT systems. Under standard assumptions of quantum chaos for the dynamics and the observables, we estimate the size of exponentially small oscillations and trace them back to geometrical features of the bulk system. The noise level is highly suppressed by the amount of dynamical chaos and the amount of quantum impurity in the states. This implies that, despite their missing on the details of Poincare recurrences, `virtual' thermal AdS phases do control the overall noise amplitude even at high temperatures where the thermal ensemble is dominated by large AdS black holes. We also study EPR correlations and find that, in contrast to the behavior of large correlation peaks, their noise level is the same in TFD states and in more general highly entangled states.Comment: 30 pages. 4 figure

Self-Duality and New TQFTs for Forms

We discuss theories containing higher-order forms in various dimensions. We explain how Chern--Simons-type theories of forms can be defined from TQFTs in one less dimension. We also exhibit new TQFTs with interacting Yang--Mills fields and higher--order forms. They are obtained by the dimensional reduction of TQFTs whose gauge functions are free self-duality equations. Interactions are due to the gauging of global internal symmetries after dimensional reduction. We list possible symmetries and give a brief discussion on the possible relation of such systems to interacting field theories.Comment: teX-fil

Conformal Complementarity Maps

We study quantum cosmological models for certain classes of bang/crunch singularities, using the duality between expanding bubbles in AdS with a FRW interior cosmology and perturbed CFTs on de Sitter space-time. It is pointed out that horizon complementarity in the AdS bulk geometries is realized as a conformal transformation in the dual deformed CFT. The quantum version of this map is described in full detail in a toy model involving conformal quantum mechanics. In this system the complementarity map acts as an exact duality between eternal and apocalyptic Hamiltonian evolutions. We calculate the commutation relation between the Hamiltonians corresponding to the different frames. It vanishes only on scale invariant states.Comment: 38 pages, 9 figure

Induced Boundary Flow on the c = 1 Orbifold Moduli Space

Boundary flow in the $c=1$ 2d CFT of a $\mathbb{Z}_2$ orbifold of a free boson on a circle is considered. Adding a bulk marginal operator to the $c=1$ orbifold branch induces a boundary flow. We show that this flow is consistent for any bulk marginal operator and known initial given boundary condition. The supersymmetric $c=3/2$ case is also mentioned. The supersymmetric $c=3/2$ case is also mentioned. For the circle branch of the moduli space this has been shown in arXiv:hep-th/0609034v2. The ground state multiplicity ($g_b$) is calculated and it is shown that it does indeed decrease

Time-dependent stabilization in AdS/CFT

We consider theories with time-dependent Hamiltonians which alternate between being bounded and unbounded from below. For appropriate frequencies dynamical stabilization can occur rendering the effective potential of the system stable. We first study a free field theory on a torus with a time-dependent mass term, finding that the stability regions are described in terms of the phase diagram of the Mathieu equation. Using number theory we have found a compactification scheme such as to avoid resonances for all momentum modes in the theory. We further consider the gravity dual of a conformal field theory on a sphere in three spacetime dimensions, deformed by a doubletrace operator. The gravity dual of the theory with a constant unbounded potential develops big crunch singularities; we study when such singularities can be cured by dynamical stabilization. We numerically solve the Einstein-scalar equations of motion in the case of a time-dependent doubletrace deformation and find that for sufficiently high frequencies the theory is dynamically stabilized and big crunches get screened by black hole horizons.Comment: LaTeX, 38 pages, 13 figures. V2: appendix C added, references added and typos correcte