Light-cone Superstring Field Theory, pp-wave background and integrability properties

We show that the three strings vertex coefficients in light--cone open string field theory satisfy the Hirota equations for the dispersionless Toda lattice hierarchy. We show that Hirota equations allow us to calculate the correlators of an associated quantum system where the Neumann coefficients represent the two--point functions. We consider next the three strings vertex coefficients of the light--cone string field theory on a maximally supersymmetric pp--wave background. Using the previous results we are able to show that these Neumann coefficients satisfy the Hirota equations for the full Toda lattice hierarchy at least up to second order in the 'string mass' $\mu$.Comment: 23 pages, 3 figures, footnote and references adde

Corrections to the Cardy-Verlinde formula from the generalized uncertainty principle

In this letter, we compute the corrections to the Cardy-Verlinde formula of $d-$dimensional Schwarzschild black hole. These corrections stem from the generalized uncertainty principle. Then we show, one can taking into account the generalized uncertainty principle corrections of the Cardy-Verlinde entropy formula by just redefining the Virasoro operator $L_0$ and the central charge $c$.Comment: 8 pages, no figure

Coupling a Point-Like Mass to Quantum Gravity with Causal Dynamical Triangulations

We present a possibility of coupling a point-like, non-singular, mass distribution to four-dimensional quantum gravity in the nonperturbative setting of causal dynamical triangulations (CDT). In order to provide a point of comparison for the classical limit of the matter-coupled CDT model, we derive the spatial volume profile of the Euclidean Schwarzschild-de Sitter space glued to an interior matter solution. The volume profile is calculated with respect to a specific proper-time foliation matching the global time slicing present in CDT. It deviates in a characteristic manner from that of the pure-gravity model. The appearance of coordinate caustics and the compactness of the mass distribution in lattice units put an upper bound on the total mass for which these calculations are expected to be valid. We also discuss some of the implementation details for numerically measuring the expectation value of the volume profiles in the framework of CDT when coupled appropriately to the matter source.Comment: 26 pages, 9 figures, updated published versio

On time-dependent AdS/CFT

We clarify aspects of the holographic AdS/CFT correspondence that are typical of Lorentzian signature, to lay the foundation for a treatment of time-dependent gravity and conformal field theory phenomena. We provide a derivation of bulk-to-boundary propagators associated to advanced, retarded and Feynman bulk propagators, and provide a better understanding of the boundary conditions satisfied by the bulk fields at the horizon. We interpret the subleading behavior of the wavefunctions in terms of specific vacuum expectation values, and compute two-point functions in our framework. We connect our bulk methods to the closed time path formalism in the boundary field theory.Comment: 19 pages, v2: added reference, JHEP versio

Unification of Residues and Grassmannian Dualities

The conjectured duality relating all-loop leading singularities of n-particle N^(k-2)MHV scattering amplitudes in N=4 SYM to a simple contour integral over the Grassmannian G(k,n) makes all the symmetries of the theory manifest. Every residue is individually Yangian invariant, but does not have a local space-time interpretation--only a special sum over residues gives physical amplitudes. In this paper we show that the sum over residues giving tree amplitudes can be unified into a single algebraic variety, which we explicitly construct for all NMHV and N^2MHV amplitudes. Remarkably, this allows the contour integral to have a "particle interpretation" in the Grassmannian, where higher-point amplitudes can be constructed from lower-point ones by adding one particle at a time, with soft limits manifest. We move on to show that the connected prescription for tree amplitudes in Witten's twistor string theory also admits a Grassmannian particle interpretation, where the integral over the Grassmannian localizes over the Veronese map from G(2,n) to G(k,n). These apparently very different theories are related by a natural deformation with a parameter t that smoothly interpolates between them. For NMHV amplitudes, we use a simple residue theorem to prove t-independence of the result, thus establishing a novel kind of duality between these theories.Comment: 56 pages, 11 figures; v2: typos corrected, minor improvement

Real time response on dS_3: the Topological AdS Black Hole and the Bubble

We study real time correlators in strongly coupled N=4 supersymmetric Yang-Mills theory on dS_3 x S^1, with antiperiodic boundary conditions for fermions on the circle. When the circle radius is larger than a critical value, the dual geometry is the so-called "topological AdS_5 black hole". Applying the Son- Starinets recipe in this background we compute retarded glueball propagators which exhibit an infinite set of poles yielding the quasinormal frequencies of the topological black hole. The imaginary parts of the propagators exhibit thermal effects associated with the Gibbons-Hawking temperature due to the cosmological horizon of the de Sitter boundary. We also obtain R-current correlators and find that after accounting for a small subtlety, the Son-Starinets prescription yields the retarded Green's functions. The correlators do not display diffusive behaviour at late times. Below the critical value of the circle radius, the topological black hole decays to the AdS_5 "bubble of nothing". Using a high frequency WKB approximation, we show that glueball correlators in this phase exhibit poles on the real axis. The tunnelling from the black hole to the bubble is interpreted as a hadronization transition.Comment: 52 pages, 11 figures, typos corrected, references adde

How Not to Construct an Asymptotically de Sitter Universe

Observational evidence suggests that our universe is currently evolving towards an asymptotically de Sitter future. Unfortunately and in spite of much recent attention, various quantum, holographic and cosmological aspects of de Sitter space remain quite enigmatic. With such intrigue in mind, this paper considers the ``construction'' of a toy model that describes an asymptotically de Sitter universe. More specifically, we add fluid-like matter to an otherwise purely de Sitter spacetime, formulate the relevant solutions and then discuss the cosmological and holographic implications. If the objective is to construct an asymptotically de Sitter universe that is free of singularities and has a straightforward holographic interpretation, then the results of this analysis are decidedly negative. Nonetheless, this toy model nicely illustrates the pitfalls that might be encountered in a more realistic type of construction.Comment: 25 pages, Latex; references and footnotes added (other minor changes

Squeezed States in the de Sitter Vacuum

We discuss the treatment of squeezed states as excitations in the Euclidean vacuum of de Sitter space. A comparison with the treatment of these states as candidate no-particle states, or alpha-vacua, shows important differences already in the free theory. At the interacting level alpha-vacua are inconsistent, but squeezed state excitations seem perfectly acceptable. Indeed, matrix elements can be renormalized in the excited states using precisely the standard local counterterms of the Euclidean vacuum. Implications for inflationary scenarios in cosmology are discussed.Comment: 15 pages, no figures. One new citation in version 3; no other change

De Sitter vacua from N=2 gauged supergravity

Typical de Sitter (dS) vacua of gauged supergravity correspond to saddle points of the potential and often the unstable mode runs into a singularity. We explore the possibility to obtain dS points where the unstable mode goes on both sides into a supersymmetric smooth vacuum. Within N=2 gauged supergravity coupled to the universal hypermultiplet, we have found a potential which has two supersymmetric minima (one of them can be flat) and these are connected by a de Sitter saddle point. In order to obtain this potential by an Abelian gauging, it was important to include the recently proposed quantum corrections to the universal hypermultiplet sector. Our results apply to four as well as five dimensional gauged supergravity theories.Comment: 25 pages, 1 figure, add refs and corrected typo