Type IIB Green-Schwarz superstrings in AdS 5 × S 5 from the supercoset approach

We consider superstrings moving in the AdS ₅ × S ⁵ space-time and find their Green-Schwarz action using the supercoset approach based on the supergroup PSU(2, 2|4). We describe several parametrizations of the relevant supercoset and present the action in different κ-symmetry gauges. In particular, we discuss a gauge where all the fermionic coordinates corresponding to the conformal (S) supercharges are gauged away and also a light-cone type gauge where half of the Q and S supercoordinates are gauged away. The resulting action contains terms that are quadratic and quartic in fermions. In the flat-space limit, it reduces to the standard light-cone Green-Schwarz action. We comment on the possibility of fixing the bosonic light-cone gauge and of reformulating the action in terms of two-dimensional Dirac spinors.     

On holomorphic maps and Generalized Complex Geometry

We introduce a natural notion of holomorphic map between generalized complex manifolds and we prove some related results on Dirac structures and generalized Kähler manifolds.     

Torsion-Free Generalized Connections and Heterotic Supergravity

This work revisits the notions of connection and curvature in generalized geometry, with emphasis on torsion-free generalized connections on a transitive Courant algebroid. As an application, we provide a mathematical derivation of the equations of motion of heterotic supergravity in terms of the Ricci tensor of a generalized metric, inspired by the work of Coimbra, Strickland-Constable and Waldram.     

Supersymmetric WZ-Poisson Sigma Model and Twisted Generalized Complex Geometry

It has been shown recently that extended supersymmetry in twisted first-order sigma models is related to twisted generalized complex geometry in the target. In the general case there are additional algebraic and differential conditions relating the twisted generalized complex structure and the geometrical data defining the model. We study in the Hamiltonian formalism the case of vanishing metric, which is the supersymmetric version of the WZ-Poisson sigma model. We prove that the compatibility conditions reduce to an algebraic equation, which represents a considerable simplification with respect to the general case. We also show that this algebraic condition has a very natural geometrical interpretation. In the derivation of these results the notion of contravariant connections on twisted Poisson manifolds turns out to be very useful.     

Quasi-normal Modes of AdS5 Black Hole at $\mathcal{N}=2$ Supergravity

In this paper we consider the AdS ₅ black hole at the \(\mathcal{N}=2\) supergravity background. By using the AdS/CFT correspondence we discuss about the quasi-normal modes of the scalar field in the black hole, which is dual of the scalar glueballs spectrum on the boundary. We obtain phase transition conditions from stable to unstable theory, which interpreted as confinement and deconfinement states in the QCD. We obtain the specific heat in terms of the temperature and charge of black hole, we find the temperature where the black hole is stable. Also we rewrite the equation of motion in the Schrödinger form and discuss the effective potential.     

On the Geometry and Mass of Static,Asymptotically AdS Spacetimes,and the Uniqueness of the AdS Soliton

We prove two theorems, announced in [6], for static spacetimes that solve Einstein's equation with negative cosmological constant. The first is a general structure theorem for spacetimes obeying a certain convexity condition near infinity, analogous to the structure theorems of Cheeger and Gromoll for manifolds of non-negative Ricci curvature. For spacetimes with Ricci-flat conformal boundary, the convexity condition is associated with negative mass. The second theorem is a uniqueness theorem for the negative mass AdS soliton spacetime. This result lends support to the new positive mass conjecture due to Horowitz and Myers which states that the unique lowest mass solution which asymptotes to the AdS soliton is the soliton itself. This conjecture was motivated by a nonsupersymmetric version of the AdS/CFT correspondence. Our results add to the growing body of rigorous mathematical results inspired by the AdS/CFT correspondence conjecture. Our techniques exploit a special geometric feature which the universal cover of the soliton spacetime shares with familiar ``ground state' spacetimes such as Minkowski spacetime, namely, the presence of a null line, or complete achronal null geodesic, and the totally geodesic null hypersurface that it determines. En route, we provide an analysis of the boundary data at conformal infinity for the Lorentzian signature static Einstein equations, in the spirit of the Fefferman-Graham analysis for the Riemannian signature case. This leads us to generalize to arbitrary dimension a mass definition for static asymptotically AdS spacetimes given by Chruciel and Simon. We prove equivalence of this mass definition with those of Ashtekar-Magnon and Hawking-Horowitz.     

Solutions of free higher spins in AdS

We consider free massive and massless higher integer spins in AdS backgrounds in general D dimensions. We obtain the solutions corresponding to the highest-weight state of the spin-? representations of the SO(2,D−1) isometry groups. The solution for the spin-? field is expressed recursively in terms of that for the spin-(?−1). Thus starting from the explicit spin-0, all the higher-spin solutions can be obtained. These solutions allow us to derive the generalized Breitenlohner-Freedman bound, and analyze the asymptotic falloffs. In particular, solutions with negative mass square in general have falloffs slower than those of the Schwarzschild AdS black holes in the AdS boundaries.     

Two-Soliton Solutions and Interactions for the Generalized Complex Coupled Kortweg-de Vries Equations

Kortweg-de Vries (KdV)-typed equations have been used to describe certain nonlinear phenomena in fluids and plasmas. Generalized complex coupled KdV(GCCKdV) equations are investigated in this paper. Through the dependent variable transformations and symbolic computation, GCCKdV equations are transformed into their bilinear forms, based on which the one- and two-soliton solutions are obtained. Through the interactions of two solitons, the regular elastic collision are shown. When the wave numbers are complex, three kinds of solitonic collisions are presented: (i) two solitons merge and separate fromeach other periodically; (ii) two solitons exhibit the attraction and repulsion nearly twice, and finally separate from each other after such type of interaction; (iii) two solitons are fluctuant in the central region of the collision. Propagation features ofsolitons are investigated with the effects of the coefficients in the GCCKdV equations considered. Velocity of soliton increase with the α increasing. Amplitude of v increase with the α increasing and decrease with the β increasing.     

Two-Brane Randall-Sundrum Model in AdS 5 and dS 5

Two flat Randall-Sundrum three-branes are analyzed, at fixed mutual distance, in the case where each brane contains an ideal isotropic fluid. Both fluids are to begin with assumed to obey the equation of state p = ( – 1), where is a constant. Thereafter, we impose the condition that there is zero energy flux from the branes into the bulk, and assume that the tension on either brane is zero. It then follows that constant values of the fluid energies at the branes are obtained only if the value of is equal to zero (i.e., a vacuum fluid). The fluids on the branes are related: if one brane is a dS ₄ brane (the effective four-dimensional constant being positive), then the other brane is dS ₄ also, and if the fluid energy density on one brane is positive, the energy density on the other brane is larger in magnitude but negative. This is a non-acceptable result, which sheds some light on how far it is possible to give a physical interpretation of the two-brane scenario. Also, we discuss the graviton localization problem in the two-brane setting, generalizing prior works.     

Hermitian Geometry and Complex Space-Time

We consider a complex Hermitian manifold of complex dimensions four with a Hermitian metric and a Chern connection. It is shown that the action that determines the dynamics of the metric is unique, provided that the linearized Einstein action coupled to an antisymmetric tensor is obtained, in the limit when the imaginary coordinates vanish. The unique action is of the Chern-Simons type when expressed in terms of the Kähler form. The antisymmetric tensor field has gauge transformations coming from diffeomorphism invariance in the complex directions. The equations of motion must be supplemented by boundary conditions imposed on the Hermitian metric to give, in the limit of vanishing imaginary coordinates, the low-energy effective action for a curved metric coupled to an antisymmetric tensor.     

Complex Geometry and Dirac Equation

Complex geometry represents a fundamentalingredient in the formulation of the Dirac equation bythe Clifford algebra. The choice of appropriate complexgeometries is strictly related to the geometricinterpretation of the complex imaginary unit . We discuss two possibilities which appearin the multivector algebra approach: the₁₂₃ and ₂₁ complexgeometries. Our formalism provides a set of rules which allows an immediate translation between thecomplex standard Dirac theory and its version withingeometric algebra. The problem concerning a doublegeometric interpretation for the complex imaginary unit is also discussed.     

Existence of Global-In-Time Solutions to a Generalized Dirac-Fock Type Evolution Equation

We consider a generalized DiracFock type evolution equation deduced from nophoton Quantum Electrodynamics, which describes the selfconsistent timeevolution of relativistic electrons, the observable ones as well as those filling up the Dirac sea. This equation has been originally introduced by Dirac in 1934 in a simplified form. Since we work in a Hartree-Fock type approximation, the elements describing the physical state of the electrons are infinite rank projectors. Using the Bogoliubov-Dirac-Fock formalism, introduced by ChaixIracane (J. Phys. B., 22, 37913814, 1989), and recently established by Hainzl-Lewin-Séré, we prove the existence of globalintime solutions of the considered evolution equation.     

Geometry and thermodynamics of smeared Reissner–Nordstrm black holes in d-dimensional AdS spacetime

We construct a family of d-dimensional Reissner–Nordstr o¨m-Ad S black holes inspired by noncommutative geometry. The density distribution of the gravitational source is determined by the dimension of space, the minimum length of spacetime l, and other parameters(e.g., n relating to the central matter density). The curvature of the center and some thermodynamic properties of these black holes are investigated. We find that the center of the source is nonsingular for n 0(under certain conditions it is also nonsingular for-2 n 0), and the properties at the event horizon, including the Hawking temperature, entropy, and heat capacity, are regular for n -2. Due to the presence of l, there is an exponentially small correction to the usual entropy.     

Non-Semisimple and Complex Gaugings of <Emphasis Type="Italic">N</Emphasis>=16 Supergravity

Maximal and non-maximal supergravities in three dimensions allow for a large variety of semisimple (Chern-Simons) gauge groups. In this paper, we analyze non-semisimple and complex gauge groups that satisfy the pertinent consistency relations for a maximal (N=16) gauged supergravity to exist. We give a general procedure how to generate non-semisimple gauge groups from known admissible semisimple gauge groups by a singular boost within E₈₍₈₎. Examples include the theories with gauge group SO(8)×T₂₈ that describe the reduction of IIA/IIB supergravity on the seven-sphere. In addition, we exhibit two strange embeddings of the complex gauge group into (real) E₈₍₈₎ and prove that both can be consistently gauged. We discuss the structure of the associated scalar potentials as well as their relation to those of D4 gauged supergravities.This work is partly supported by EU contract HPRN-CT-2000-00122 and HPRN-CT-2000-00131.     

AdS5 (×)S1,AdS5(×)S5和AdS2(×)S2超弦模型的一种KRR参数化新方法

给出了3种典型超弦模型AdS5 (×)S1,AdS5(×)S5和AdS2(×)S2的一种简单的KRR参数化新方法,并结合这些超弦模型所具有的κ对称性给出了它们的卡当1-form,Maurer-Cartan方程,作用量和运动方程.     

On the Number of Type Change Loci of a Generalized Complex Structure

In this note, we describe a procedure to construct generalized complex structures whose type change locus has arbitrarily many path components on products of the circle with a connected sum of closed 3-manifolds. As an application, we use the procedure to exhibit such geometric structures on a myriad of simply connected 4-manifolds among many others.