Eluding SUSY at every genus on stable closed string vacua

In closed string vacua, ergodicity of unipotent flows provide a key for relating vacuum stability to the UV behavior of spectra and interactions. Infrared finiteness at all genera in perturbation theory can be rephrased in terms of cancelations involving only tree-level closed strings scattering amplitudes. This provides quantitative results on the allowed deviations from supersymmetry on perturbative stable vacua. From a mathematical perspective, diagrammatic relations involving closed string amplitudes suggest a relevance of unipotent flows dynamics for the Schottky problem and for the construction of the superstring measure.Comment: v2, 17 pages, 8 figures, typos corrected, new figure added with 3 modular images of long horocycles,(obtained with Mathematica

The Asymptotic Dynamics of two-dimensional (anti-)de Sitter Gravity

We show that the asymptotic dynamics of two-dimensional de Sitter or anti-de Sitter Jackiw-Teitelboim (JT) gravity is described by a generalized two-particle Calogero-Sutherland model. This correspondence is established by formulating the JT model of (A)dS gravity in two dimensions as a topological gauge theory, which reduces to a nonlinear 0+1-dimensional sigma model on the boundary of (A)dS space. The appearance of cyclic coordinates allows then a further reduction to the Calogero-Sutherland quantum mechanical model.Comment: 16 pages, LaTeX, no figures, uses JHEP.cls. v2: Some references and comments added. v3: Minor errors correcte

Gravity on a fuzzy sphere

We propose an action for gravity on a fuzzy sphere, based on a matrix model. We find striking similarities with an analogous model of two dimensional gravity on a noncommutative plane, i.e. the solution space of both models is spanned by pure U(2) gauge transformations acting on the background solution of the matrix model, and there exist deformations of the classical diffeomorphisms which preserve the two-dimensional noncommutative gravity actions.Comment: 14 pages, no figures, LaTe

Integral group actions on symmetric spaces and discrete duality symmetries of supergravity theories

For $G(\mathbb{R})$ a split, simply connected, semisimple Lie group of rank $n$ and $K$ the maximal compact subgroup of $G$, we give a method for computing Iwasawa coordinates of $G/K$ using the Chevalley generators and the Steinberg presentation. When $G/K$ is a scalar coset for a supergravity theory in dimensions $\geq 3$, we determine the action of the integral form $G(\mathbb{Z})$ on $G/K$. We give explicit results for the action of the discrete $U$--duality groups $SL_2(\mathbb{Z})$ and $E_7(\mathbb{Z})$ on the scalar cosets $SL_2(\mathbb{R})/SO_2(\mathbb{R})$ and $E_{7(+7)}(\mathbb{R})/[SU(8,\mathbb{R})/\{\pm Id\}]$ for type IIB supergravity in ten dimensions and 11--dimensional supergravity in $D=4$ dimensions, respectively. For the former, we use this to determine the discrete U--duality transformations on the scalar sector in the Borel gauge and we describe the discrete symmetries of the dyonic charge lattice. We determine the spectrum--generating symmetry group for fundamental BPS solitons of type IIB supergravity in $D=10$ dimensions at the classical level and we propose an analog of this symmetry at the quantum level. We indicate how our methods can be used to study the orbits of discrete U--duality groups in general

Supersymmetric solutions of gauged five-dimensional supergravity with general matter couplings

We perform the characterization program for the supersymmetric configurations and solutions of the $\mathcal{N}=1$, $d=5$ Supergravity Theory coupled to an arbitrary number of vectors, tensors and hypermultiplets and with general non-Abelian gaugins. By using the conditions yielded by the characterization program, new exact supersymmetric solutions are found in the $SO(4,1)/SO(4)$ model for the hyperscalars and with $SU(2)\times U(1)$ as the gauge group. The solutions also content non-trivial vector and massive tensor fields, the latter being charged under the U(1) sector of the gauge group and with selfdual spatial components. These solutions are black holes with $AdS_2 \times S^3$ near horizon geometry in the gauged version of the theory and for the ungauged case we found naked singularities. We also analyze supersymmetric solutions with only the scalars $\phi^x$ of the vector/tensor multiplets and the metric as the non-trivial fields. We find that only in the null class the scalars $\phi^x$ can be non-constant and for the case of constant $\phi^x$ we refine the classification in terms of the contributions to the scalar potential.Comment: Minor changes in wording and some typos corrected. Version to appear in Class. Quantum Grav. 38 page

Extending the Belavin-Knizhnik "wonderful formula" by the characterization of the Jacobian

A long-standing question in string theory is to find the explicit expression of the bosonic measure, a crucial issue also in determining the superstring measure. Such a measure was known up to genus three. Belavin and Knizhnik conjectured an expression for genus four which has been proved in the framework of the recently introduced vector-valued Teichmueller modular forms. It turns out that for g>3 the bosonic measure is expressed in terms of such forms. In particular, the genus four Belavin-Knizhnik "wonderful formula" has a remarkable extension to arbitrary genus whose structure is deeply related to the characterization of the Jacobian locus. Furthermore, it turns out that the bosonic string measure has an elegant geometrical interpretation as generating the quadrics in P^{g-1} characterizing the Riemann surface. All this leads to identify forms on the Siegel upper half-space that, if certain conditions related to the characterization of the Jacobian are satisfied, express the bosonic measure as a multiresidue in the Siegel upper half-space. We also suggest that it may exist a super analog on the super Siegel half-space.Comment: 15 pages. Typos corrected, refs. and comments adde

Gravity in the 3+1-Split Formalism II: Self-Duality and the Emergence of the Gravitational Chern-Simons in the Boundary

We study self-duality in the context of the 3+1-split formalism of gravity with non-zero cosmological constant. Lorentzian self-dual configurations are conformally flat spacetimes and have boundary data determined by classical solutions of the three-dimensional gravitational Chern-Simons. For Euclidean self-dual configurations, the relationship between their boundary initial positions and initial velocity is also determined by the three-dimensional gravitational Chern-Simons. Our results imply that bulk self-dual configurations are holographically described by the gravitational Chern-Simons theory which can either viewed as a boundary generating functional or as a boundary effective action.Comment: 25 pages; v2: minor improvements, references adde

Noncommutative Gravity in two Dimensions

We deform two-dimensional topological gravity by making use of its gauge theory formulation. The obtained noncommutative gravity model is shown to be invariant under a class of transformations that reduce to standard diffeomorphisms once the noncommutativity parameter is set to zero. Some solutions of the deformed model, like fuzzy AdS_2, are obtained. Furthermore, the transformation properties of the model under the Seiberg-Witten map are studied.Comment: 20 pages, LaTeX, references and some comments adde

Emission of correlated photon pairs from superluminal perturbations in dispersive media

We develop a perturbative theory that describes a superluminal refractive perturbation propagating in a dispersive medium and the subsequent excitation of the quantum vacuum zero-point fluctuations. We find a process similar to the anomalous Doppler effect: photons are emitted in correlated pairs and mainly within a Cerenkov-like cone, one on the forward and the other in backward directions. The number of photon pairs emitted from the perturbation increases strongly with the degree of superluminality and under realizable experimental conditions, it can reach up to ~0.01 photons per pulse. Moreover, it is in principle possible to engineer the host medium so as to modify the effective group refractive index. In the presence of "fast light" media, e.g. a with group index smaller than unity, a further ~10x enhancement may be achieved and the photon emission spectrum is characterized by two sharp peaks that, in future experiments would clearly identify the correlated emission of photon pairs.Comment: 9 pages, 7 figure

Null Deformed Domain Wall

We study null 1/4 BPS deformations of flat domain wall solutions (NDDW) in N=2, d=5 gauged supergravity with hypermultiplets and vector multiplets coupled. These are uncharged time-dependent configurations and contain as special case, 1/2 supersymmetric flat domain walls (DW), as well as 1/2 BPS null solutions of the ungauged supergravity. Combining our analysis with the classification method initiated by Gauntlett et al., we prove that all the possible deformations of the DW have origin in the hypermultiplet sector or/and are null. Here, we classify all the null deformations: we show that they naturally organize themselves into "gauging" (v-deformation) and "non gauging" (u-deformation). They have different properties: only in presence of v-deformation is the solution supported by a time-dependent scalar potential. Furthermore we show that the number of possible deformations equals the number of matter multiplets coupled. We discuss the general procedure for constructing explicit solutions, stressing the crucial role taken by the integrability conditions of the scalars as spacetime functions. Two analytical solutions are presented. Finally, we comment on the holographic applications of the NDDW, in relation to the recently proposed time-dependent AdS/CFT.Comment: 38 pages; minor changes, references added; text revised, minor changes, final version published in JHE