arXiv subjects
Publications and source records attributed to P. Marios Petropoulos.
We analyze the behaviour of heterotic squashed-Wess-Zumino-Witten backgrounds under renormalization-group flow. The flows we consider are driven by perturbation creating extra gauge fluxes. We show how the conformal point acts as an attractor from both the target-space and world-sheet points of view. We also address the question of instabilities created by the presence of closed time-like curves in string backgrounds
We study renormalization-group flows by deforming a class of conformal sigma-models. We consider overall scale factor perturbation of Einstein spaces as well as more general anisotropic deformations of three-spheres. At leading order in alpha, renormalization-group equations turn out to be Ricci flows. In the three-sphere background, the latter is the Halphen system, which is exactly solvable in terms of modular forms. We also analyze time-dependent deformations of these systems supplemented with an extra time coordinate and time-dependent dilaton. In some regimes time evolution is identified with renormalization-group flow and time coordinate can appear as Liouville field. The resulting space-time interpretation is that of a homogeneous isotropic Friedmann-Robertson-Walker universe in axion-dilaton cosmology. We find as general behaviour the superposition of a big-bang (polynomial) expansion with a finite number of oscillations at early times. Any initial anisotropy disappears during the evolution.
In these introductory lectures we summarize some basic facts and techniques about perturbative string theory (sections 1 to 6). These are further developed (sections 7 and 8) for describing string propagation in the presence of gravitational or gauge fields. We also remind some solutions of the string equations of motion, which correspond to remarkable (NS or D) brane configurations. A part II by Emilian Dudas will be devoted to orientifold constructions and applications to string model building.
We study the class of four-dimensional N=4 supergravities obtained by gauging the axionic shift and axionic rescaling symmetries. We formulate these theories using the machinery of embedding tensors, characterize the full gauge algebras and discuss several specific features of this family of gauged supergravities. We exhibit in particular a generalized duality between massive vectors and massive two-forms in four dimensions, inherited from the gauging of the shift symmetry. We show that these theories can be deduced from higher dimensions by a Scherk-Schwarz reduction, where a twist with respect to a non-compact symmetry is required. The four-dimensional generalized duality plays a crucial role in identifying the higher-dimensional ascendent.
In the framework of orbifold compactifications of heterotic and type II orientifolds, we study effective N = 1 supergravity potentials arising from fluxes and gaugino condensates. These string solutions display a broad phenomenology which we analyze using the method of N = 4 supergravity gaugings. We give examples in type II and heterotic compactifications of combined fluxes and condensates leading to vacua with naturally small supersymmetry breaking scale controlled by the condensate, cases where the supersymmetry breaking scale is specified by the fluxes even in the presence of a condensate and also examples where fluxes and condensates conspire to preserve supersymmetry.
We analyze the class of four-dimensional N = 4 supergravities obtained by gauging the axionic shift and axionic rescaling symmetries. These theories are formulated with the machinery of embedding tensors and shown to be deducible from higher dimensions using a Scherk--Schwarz reduction with a twist by a non-compact symmetry. This allows to evade the usual unimodularity requirement and completes the dictionary between heterotic gaugings and fluxes, at least for the "geometric sector".
We consider NS5-branes distributed along the circumference of an ellipsis and explicitly construct the corresponding gravitational background. This provides a continuous line of deformations between the limiting cases, considered before, in which the ellipsis degenerates into a circle or into a bar. We show that a slight deformation of the background corresponding to a circle distribution into an ellipsoidal one is described by a novel non-factorizable marginal perturbation of bilinears of dressed parafermions. The latter are naturally defined for the circle case since, as it was shown in the past, the background corresponds to an orbifold of the exact conformal field theory coset model SU(2)/U(1) times SL(2,R)/U(1). We explore the possibility to define parafermionic objects at generic points of the ellipsoidal families of backgrounds away from the circle point. We also discuss a new limiting case in which the ellipsis degenerates into two infinitely stretched parallel bars and show that the background is related to the Eguchi-Hanson metric, via T-duality.
We present new exact three-dimensional black-string backgrounds, which contain both NS--NS and electromagnetic fields, and generalize the BTZ black holes and the black string studied by Horne and Horowitz. They are obtained as deformations of the Sl(2,R) WZW model. Black holes resulting from purely continuous deformations possess true curvature singularities. When discrete identifications are introduced, extra chronological singularities appear, which under certain circumstances turn out to be naked. The backgrounds at hand appear in the moduli space of the Sl(2,R) WZW model. Hence, they provide exact string backgrounds and allow for a more algebraical CFT description. This makes possible the determination of the spectrum of primaries.
We derive the effective N=1, D=4 supergravity for the seven main moduli of type IIA orientifolds with D6 branes, compactified on T^6/(Z_2xZ_2) in the presence of general fluxes. We illustrate and apply a general method that relates the N=1 effective Kahler potential and superpotential to a consistent truncation of gauged N=4 supergravity. We identify the correspondence between various admissible fluxes, N=4 gaugings and N=1 superpotential terms. We construct explicit examples with different features: in particular, new IIA no-scale models and a model which admits a supersymmetric AdS_4 vacuum with all seven main moduli stabilized.
We analyze asymmetric marginal deformations of SU(2)_k and SL(2,R)_k WZW models. These appear in heterotic string backgrounds with non-vanishing Neveu--Schwarz three-forms plus electric or magnetic fields, depending on whether the deformation is elliptic, hyperbolic or parabolic. Asymmetric deformations create new families of exact string vacua. The geometries which are generated in this way, deformed S^3 or AdS_3, include in particular geometric cosets such as S^2, AdS_2 or H_2. Hence, the latter are consistent, exact conformal sigma models, with electric or magnetic backgrounds. We discuss various geometric and symmetry properties of the deformations at hand as well as their spectra and partition functions, with special attention to the supersymmetric AdS_2 x S^2 background. We also comment on potential holographic applications.
We construct heterotic string backgrounds corresponding to families of homogeneous spaces as exact conformal field theories. They contain left cosets of compact groups by their maximal tori supported by NS-NS 2-forms and gauge field fluxes. We give the general formalism and modular-invariant partition functions, then we consider some examples such as SU(2)/U(1) ~ S^2 (already described in a previous paper) and the SU(3)/U(1)^2 flag space. As an application we construct new supersymmetric string vacua with magnetic fluxes and a linear dilaton.
String theory on curved backgrounds has received much attention on account of both its own interest, and of its relation with gauge theories. Despite the progress made in various directions, several quite elementary questions remain unanswered, in particular in the very simple case of three-dimensional anti-de Sitter space. I will very briefly review these problems, discuss in some detail the important issue of constructing a consistent spectrum for a string propagating on ADS3 plus torsion background, and comment on potential solutions.
String theory on curved backgrounds has received much attention on account of both its own interest, and of its relation with gauge theories. Despite the progress made in various directions, several quite elementary questions remain unanswered, in particular in the very simple case of three-dimensional anti-de Sitter space. I briefly review these problems.
We investigate the non-perturbative equivalence of some heterotic/type II dual pairs with N=2 supersymmetry. The perturbative heterotic scalar manifolds are respectively SU(1, 1)/U(1) x SO(2, 2+NV)/ SO(2) x SO(2+NV) and SO(4, 4+NH)/ SO(4) x SO(4+NH) for moduli in the vector multiplets and hypermultiplets. The models under consideration correspond, on the type II side, to self-mirror Calabi-Yau threefolds with Hodge numbers h(1,1)= NV +3= h(2,1)= NH +3, which are K3 fibrations. We consider three classes of dual pairs, with NV=NH=8, 4 and 2. The models with h(1,1)=7 and 5 provide new constructions, while the h(1,1)=11, already studied in the literature, is reconsidered here. Perturbative R2-like corrections are computed on the heterotic side by using a universal operator whose amplitude has no singularities in the (T,U) space, and can therefore be compared with the type II side result. We point out several properties connecting K3 fibrations and spontaneous breaking of the N=4 supersymmetry to N=2. As a consequence of the reduced S- and T- duality symmetries, the instanton numbers in these three classes are restricted to integers, which are multiples of 2, 2 and 4, for NV=8, 4 and 2, respectively.