Stability and Duality in {\mathcal{N}\,{=}\,2} Supergravity

The BPS-spectrum is known to change when moduli cross a wall of marginal stability. This paper tests the compatibility of wall-crossing with S-duality and electric-magnetic duality for N=2{\mathcal{N}=2} supergravity. To this end, the BPS-spectrum of D4-D2-D0 branes is analyzed in the large volume limit of Calabi-Yau moduli space. Partition functions are presented, which capture the stability of BPS-states corresponding to two constituents with primitive charges and supported on very ample divisors in a compact Calabi-Yau. These functions are “mock modular invariant” and therefore confirm S-duality. Furthermore, wall-crossing preserves electric-magnetic duality, but is shown to break the “spectral flow” symmetry of the N=(4,0){\mathcal{N}=(4,0)} CFT, which captures the degrees of freedom of a single constituent.     

Brane worlds in collision

We obtain an exact solution of the supergravity equations of motion in which the four-dimensional observed Universe is one of a number of colliding D3 branes in a Calabi-Yau background. The collision results in the ten-dimensional spacetime splitting into disconnected regions, bounded by curvature singularities. However, near the D3 branes the metric remains static during and after the collision. We also obtain a general class of solutions representing p-brane collisions in arbitrary dimensions, including one in which the universe ends with the mutual annihilation of a positive-tension and a negative-tension 3 brane.     

Virial expansion for charged colloids and electrolytes

Using a field-theoretic approach, we derive the first few coefficients of the exact low-density (“virial”) expansion of a binary mixture of positively and negatively charged hard spheres (two-component hard-core plasma, TCPHC). Our calculations are nonperturbative with respect to the diameters d₊ and d_- and charge valences q₊ and q_- of positive and negative ions. Consequently, our closed-form expressions for the coefficients of the free energy and activity can be used to treat dilute salt solutions, where typically d ₊∼d _- and q ₊∼q _-, as well as colloidal suspensions, where the difference in size and valence between macroions and counterions can be very large. We show how to map the TCPHC on a one-component hard-core plasma (OCPHC) in the colloidal limit of large size and valence ratio, in which case the counterions effectively form a neutralizing background. A sizable discrepancy with the standard OCPHC with uniform, rigid background is detected, which can be traced back to the fact that the counterions cannot penetrate the colloids. For the case of electrolyte solutions, we show how to obtain the cationic and anionic radii as independent parameters from experimental data for the activity coefficient. Received 6 September 2001 / Received in final form 20 May 2002 Published online 24 September 2002     

de Sitter branes with a bulk scalar

We propose new brane world models arising from a scalar field in the bulk. In these examples, the induced on-brane line element is de Sitter (or anti de Sitter) and the bulk (five dimensional) Einstein equations can be exactly solved to obtain warped spacetimes. The solutions thus derived are single and two-brane models—one with thin branes while the other one of the thick variety. The field profiles and the potentials are obtained and analysed for each case. We note that for the thick brane scenario the field profile resembles a kink, whereas for one or more thin branes, it is finite and bounded in the domain of the extra dimension. We have also addressed the localisation of gravity and other matter fields on the brane for these braneworld models.     

Crystal Melting and Toric Calabi-Yau Manifolds

We construct a statistical model of crystal melting to count BPS bound states of D0 and D2 branes on a single D6 brane wrapping an arbitrary toric Calabi-Yau threefold. The three-dimensional crystalline structure is determined by the quiver diagram and the brane tiling which characterize the low energy effective theory of D branes. The crystal is composed of atoms of different colors, each of which corresponds to a node of the quiver diagram, and the chemical bond is dictated by the arrows of the quiver diagram. BPS states are constructed by removing atoms from the crystal. This generalizes the earlier results on the BPS state counting to an arbitrary non-compact toric Calabi-Yau manifold. We point out that a proper understanding of the relation between the topological string theory and the crystal melting involves the wall crossing in the Donaldson-Thomas theory.     

Rational Conformal Field Theories and Complex Multiplication

We study the geometric interpretation of two dimensional rational conformal field theories, corresponding to sigma models on Calabi-Yau manifolds. We perform a detailed study of RCFTs corresponding to the T² target and identify the Cardy branes with geometric branes. The T²s leading to RCFTs admit complex multiplication which characterizes Cardy branes as specific D0-branes. We propose a condition for the conformal sigma model to be RCFT for arbitrary Calabi-Yau n-folds, which agrees with the known cases. Together with recent conjectures by mathematicians it appears that rational conformal theories are not dense in the space of all conformal theories, and sometimes appear to be finite in number for Calabi-Yau n-folds for n>2. RCFTs on K3 may be dense. We speculate about the meaning of these special points in the moduli spaces of Calabi-Yau n-folds in connection with freezing geometric moduli.     

Instability of the Randall-Sundrum Model and Exact Bulk Solutions

Five dimensional geodesic equation is used to study the gravitational force acted on a test particle in the bulk of the Randall-Sundrum two-brane model. This force could be interpreted as the gravitational attraction from matters on the two branes and may cause the model to be unstable. By analogy with star models in astrophysics, a fluid RS model is proposed in which the bulk is filled with a fluid and this fluid has an anisotropic pressure to balance the gravity from the two branes. Thus a class of exact bulk solutions is obtained which shows that any 4D Einstein solution with a perfect fluid source can be embedded in y = constant hypersurfaces in the bulk to form an equilibrium state of the brane model. By requiring a 4D effective curvature to have a minimum, the compactification size of the extra dimension is discussed.     

The <Emphasis Type="Italic">A</Emphasis><Emphasis Type="Italic">d</Emphasis><Emphasis Type="Italic">S</Emphasis><Subscript>5</Subscript> Warp of Spatially Hyperbolic Universes,Spinless Modes and Spectra and the Corresponding Wheeler–DeWitt Schrödinger-Like Equation

In this paper, we consider an A d S ₅ bulk with k=?1? FRW branes, together with bosons test particles, evolving in the 5D hyperspace. In the first part, we compute the wave function of the scalar fields in the bulk and the allowed mass spectrum for physically relevant cases. Also, an important quantization law, connecting the mass spectrum of the bosons on the brane and the bulk mass parameter is written down. In the second part, in oder to develop a quantization model, we use the Wheeler-DeWitt equation and solve its Schrödinger-like form, obtaining the wave function of the Universe. The solutions describe a universe emerging out of nothing, without tunneling. Lastly, using a mixture of states, we emphasize a smooth universe, with neither Bangs nor Crunches.     

Linearized Higher-Order Gravity and Stellar Structure

Starting with the general "quadratic gravity" in four dimensions, linearization, assumption of the weak gravitational field to be static and matter to be a perfect fluid, one arrives at the modified Lane-Emden equation. The solutions of the modified Lane-Emden equation are found and the formulas for the stellar radius are obtained in two cases of the polytropic index N = 0 and N = 1. The influence of the additional Yukawa forces in the linearized higher-order gravitation on the Newtonian stellar structure is discussed.     

“Mass inflation” with lightlike branes

We discuss properties of a new class of p-brane models, describing intrinsically lightlike branes for any world-volume dimension, in various gravitational backgrounds of interest in the context of black hole physics. One of the characteristic features of these lightlike p-branes is that the brane tension appears as an additional nontrivial dynamical world-volume degree of freedom. Codimension one lightlike brane dynamics requires that bulk space with a bulk metric of spherically symmetric type must possess an event horizon which is automatically occupied by the lightlike brane while its tension evolves exponentially with time. The latter phenomenon is an analog of the well known “mass inflation” effect in black holes.      

Ricci flat rotating black branes with a conformally invariant Maxwell source

We consider Einstein gravity coupled to an U(1) gauge field for which the density is given by a power of the Maxwell Lagrangian. In d-dimensions the action of Maxwell field is shown to enjoy the conformal invariance if the power is chosen as d/4. We present a class of charge rotating solutions in Einstein-conformally invariant Maxwell gravity in the presence of a cosmological constant. These solutions may be interpreted as black brane solutions with inner and outer event horizons or an extreme black brane depending on the value of the mass parameter. Since we are considering power of the Maxwell density, the black brane solutions exist only for dimensions which are multiples of four. We compute conserved and thermodynamics quantities of the black brane solutions and show that the expression of the electric field does not depend on the dimension. Also, we obtain a Smarr-type formula and show that these conserved and thermodynamic quantities of black branes satisfy the first law of thermodynamics. Finally, we study the phase behavior of the rotating black branes and show that there is no Hawking–Page phase transition in spite of conformally invariant Maxwell field.     

Self-trapping of the <Emphasis Type="Italic">d</Emphasis>-<Emphasis Type="Italic">d</Emphasis> charge transfer exciton in bulk NiO evidenced by X-ray excited luminescence

Soft X-ray (XUV) excitation did make it possible to avoid the predominant role of the surface effects in luminescence of NiO and revealed a bulk luminescence with a puzzling well isolated doublet of very narrow lines with close energies near 3.3 eV which is assigned to recombination transitions in self-trapped d-d charge transfer (CT) excitons formed by coupled Jahn-Teller Ni⁺ and Ni³⁺ centers. The conclusion is supported both by a comparative analysis of the CT luminescence spectra for NiO and solid solutions Ni _x Zn_{1 − x} O, and by a comprehensive cluster model assignment of different p-d and d-d CT transitions, their relaxation channels. To the best of our knowledge, it is the first observation of the luminescence due to self-trapped d-d CT excitons.     

Modified <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">G</Emphasis>) gravity models with curvature–matter coupling

A modified f(G) gravity model with coupling between matter and geometry is proposed, which is described by the product of the Lagrange density of the matter and an arbitrary function of the Gauss–Bonnet term. The field equations and the equations of motion corresponding to this model show the non-conservation of the energy-momentum tensor, the presence of an extra force acting on test particles and non-geodesic motion. Moreover, the energy conditions and the stability criterion at the de Sitter point in modified f(G) gravity models with curvature–matter coupling are derived, which can degenerate to the well-known energy conditions in general relativity. Furthermore, in order to get some insight in the meaning of these energy conditions, we apply them to the specific models of f(G) gravity and the corresponding constraints on the models are given. In addition, the conditions and the candidate for late-time cosmic accelerated expansion in modified f(G) gravity are studied by means of conditions of power-law expansion and the equation of state of matter ω smaller than -\frac13-\frac{1}{3}.     

Four-dimensional high-branes as intersecting D-branes

We show that a class of external four-dimensional supersymmetric “high-branes”, i.e. string and domain wall solutions, can be interpreted as intersections of four ten-dimensional Dirichlet branes. These d = 4 solutions are related, via T-duality in ten dimensions, to the four-dimensional extermal Maxwell/scalar black holes that are characterized by a scalar coupling parameter a with a = 0,1

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Composite S-Brane Solutions on the Product of Ricci-Flat Spaces

A family of generalized S-brane solutions with orthogonal intersection rules and n Ricci-flat factor spaces in the theory with several scalar fields and antisymmetric forms is considered. Two subclasses of solutions with power-law and exponential behaviour of scale factors are singled out. These subclasses contain sub-families of solutions with accelerated expansion of certain factor spaces. The solutions depend on charge densities of branes, their dimensions and intersections, dilatonic couplings and the number of dilatonic fields.     

Arithmetic properties of mirror map and quantum coupling

We study some arithmetic properties of the mirror maps and the quantum Yukawa couplings for some 1-parameter deformations of Calabi-Yau manifolds. First we use the Schwarzian differential equation, which we derived previously, to characterize the mirror map in each case. For algebraic K3 surfaces, we solve the equation in terms of theJ-function. By deriving explicit modular relations we prove that some K3 mirror maps are algebraic over the genus zero function fieldQ(J). This leads to a uniform proof that those mirror maps have integral Fourier coefficients. Regarding the maps as Riemann mappings, we prove that they are genus zero functions. By virtue of the Conway-Norton conjecture (proved by Borcherds using Frenkel-Lepowsky-Meurman's Moonshine module), we find that these maps are actually the reciprocals of the Thompson series for certain conjugacy classes in the Griess-Fischer group. This also gives, as an immediate consequence, a second proof that those mirror maps are integral. We thus conjecture a surprising connection between K3 mirror maps and the Thompson series. For threefolds, we construct a formal nonlinear ODE for the quantum coupling reduced modp. Under the mirror hypothesis and an integrality assumption, we derive modp congurences for the Fourier coefficients. For the quintics, we deduce, (at least for 5×d) that the degreed instanton numbersn _d are divisible by 5³ — a fact first conjectured by Clemens.Research supported by grant DE-FG02-88-ER-25065     

Singleton Field Theory and Flato–Frønsdal Dipole Equation

We study solutions of the equations ( - ) = 0 and ( - )² = 0 in global coordinates on the covering space CAdS _d of the d-dimensional Anti de-Sitter space subject to various boundary conditions and their connection to the unitary irreducible representations of (d-1,2). The vanishing flux boundary conditions at spatial infinity lead to the standard quantization scheme for CAdS _d in which solutions of the second- and the fourth-order equations are equivalent. To include fields realizing the singleton unitary representation in the bulk of CAdS _d one has to relax the boundary conditions thus allowing for the nontrivial space of solutions of the dipole equation known as the Gupta–Bleuler triplet. We obtain explicit expressions for the modes of the Gupta–Bleuler triplet and the corresponding two-point function. To avoid negative-energy states one must also introduce an additional constraint in the space of solutions of the dipole equation.     

A Cosmological Model of Holographic Brane Gravity

A cosmological scenario with two branes (A and B) moving in a 5-dimensional bulk is considered. As in the case of ecpyrotic and born-again braneworld models it is possible that the branes collide. The energy-momentum tensor is taken to describe a perfect barotropic fluid on the A-brane and a phenomenological time-dependent cosmological constant on the B-brane. The A-brane is identified with our Universe and its cosmological evolution in the approximation of a homogeneous and isotropic brane is analysed. The dynamics of the radion (a scalar field on the brane) contains information about the proper distance between the branes. It is demonstrated that the deSitter type solutions are obtained for late time evolution of the braneworld and accelerative behaviour is anticipated at the present time.     

A Vertex Formalism for Local Ruled Surfaces

We develop a vertex formalism for topological string amplitudes on ruled surfaces with an arbitrary number of reducible fibers embedded in a Calabi-Yau threefold. Our construction is based on large N duality and localization with respect to a degenerate torus action. We also discuss potential generalizations of our formalism to a broader class of Calabi-Yau threefolds using the same underlying principles.     

Finite size effects in layered superconductors

We investigate the transition temperature of layered superconductors by considering a stack ofL _z superconducting layers, separated by insulating material. We adopt a pairing Hamiltonian, invoke the variational principle and solve the resulting gap equations numerically. Our results confirm previous weak coupling and Ginzburg-Landau treatments and reveal a rise ofT _c withL _z and saturation at the bulk transition temperature. Thus, the rise ofT _c is traced back to a finite size effect, corresponding to a crossover from 2-d to 3-d superconductivity. The results also reveal a sizeable variation of the gap along the stack with pronounced variation at the ends.