Narrow Results

We give the global mathematical formulation of the coupling of four-dimensional scalar sigma models to Abelian gauge fields on a Lorentzian four-manifold, for the generalized situation when the duality structure of the Abelian gauge theory is described by a flat symplectic vector bundle $({𝒮},D,\omega )$ defined over the scalar manifold ${ℳ}$. The construction uses a taming of $({𝒮},\omega )$, which we find to be the correct mathematical object globally encoding the inverse gauge couplings and theta angles of the “twisted” Abelian gauge theory in a manner that makes no use of duality frames. We show that global solutions of the equations of motion of such models give classical locally geometric U-folds. We also describe the groups of duality transformations and scalar-electromagnetic symmetries arising in such models, which involve lifting isometries of ${ℳ}$ to the bundle ${𝒮}$ and hence differ from expectations based on local analysis. The appropriate version of the Dirac quantization condition involves a discrete local system defined over ${ℳ}$ and gives rise to a smooth bundle of polarized Abelian varieties, endowed with a flat symplectic connection. This shows, in particular, that a generalization of part of the mathematical structure familiar from ${𝒩}=2$ supergravity is already present in such purely bosonic models, without any coupling to fermions and hence without any supersymmetry.

We examine duality transformations of supersymmetric and κ-symmetric Dp-brane actions in a general type IIB supergravity background where in particular the dilaton and the axion are not supposed to be zero or a constant but a general superfield. Due to nonconstant dilaton and axion, we can explicitly show that the dilaton and the axion as well as the two two-form gauge potentials transform as doublets under the SL(2,R) transformation from the point of view of the world volume field theory.

We study Myers' world volume effective action of coincident D-branes. We investigate a system of N₀D0-branes in the geometry of Dp-branes with p = 2 or p = 4. The choice of coordinates can make the action simplified and tractable. For p = 4, we show that a certain pointlike D0-brane configuration solving equations of motion of the action can expand to form a fuzzy two-sphere via magnetic moment effect without changing quantum numbers. We compare noncommutative D0-brane configurations with dual spherical D(6 - p)-brane systems. We also discuss the relation between these configurations and giant gravitons in 11 dimensions.

The existence of dark matter was suggested, using simple gravitational arguments, seventy years ago. Although we are now convinced that most of the mass in the Universe is indeed some nonluminous matter, we still do not know its composition. The problem of the dark matter in the Universe is reviewed here. Particle candidates for dark matter are discussed with particular emphasis on Weakly Interacting Massive Particles (WIMP's). Experiments searching for these relic particles, carried out by many groups around the world, are also reviewed, paying special attention to their direct detection by observing the elastic scattering on target nuclei through nuclear recoils. Finally, we concentrate on the theoretical models predicting WIMP's, and in particular on supersymmetric extensions of the standard model, where the leading candidate for WIMP, the neutralino, is present. There, we compute the cross-section for the direct detection of neutralinos, and compare it with the sensitivity of detectors. We mainly discuss supergravity, superstring and M theory scenarios.

We begin with a discussion on two apparently disconnected topics — one related to nonperturbative superpotential generated from wrapping an M2-brane around a supersymmetric three cycle embedded in a G₂-manifold evaluated by the path-integral inside a path-integral approach of Ref. 1, and the other centered around the compact Calabi–Yau CY₃(3, 243) expressed as a blow-up of a degree-24 Fermat hypersurface in WCP⁴[1, 1, 2, 8, 12]. For the former, we compare the results with the ones of Witten on heterotic worldsheet instantons.² The subtopics covered in the latter include an 𝒩=1 triality between Heterotic, M- and F-theories, evaluation of RP²-instanton superpotential, Picard–Fuchs equation for the mirror Landau–Ginzburg model corresponding to CY₃(3, 243), D = 11 supergravity corresponding to M-theory compactified on a "barely" G₂ manifold involving CY₃(3, 243) and a conjecture related to the action of antiholomorphic involution on period integrals. We then shown an indirect connection between the two topics by showing a connection between each one of the two and Witten's MQCD.³ As an aside, we show that in the limit of vanishing "ζ", a complex constant that appears in the Riemann surfaces relevant to defining the boundary conditions for the domain wall in MQCD, the infinite series of Ref. 4 used to represent a suitable embedding of a supersymmetric 3-cycle in a G₂-mannifold, can be summed.

We construct a two-stage inflationary model which can accommodate early inflation at a scale Λ₁ as well as a second stage of inflation at Λ₂ with a single scalar field ϕ. We use a symmetric potential, valid in a frictionless world, in which the two inflationary periods have exactly the same scale, i.e. Λ₁ = Λ₂. However, we see today Λ₁ ≫ Λ₂ due to the friction terms (expansion of the universe and interaction with matter). These type of models can be motivated from supergravity. Inflation occurs close to the maxima of the potential. As a consequence both inflations are necessarily finite. This opens the interesting possibility that the second inflation has already or is about to end. A first inflation is produced when fluctuations displace the inflaton field from its higher maximum rolling down the potential as in new inflation. Instead of rolling towards a global minimum the inflaton approaches a lower maximum where a second inflation takes place.

We investigate the time-dependent behaviour of brane-antibrane orbital systems, mainly concentrating on the stability of the "Branonium" configuration.

A derivation of N = 1 supergravity action from string theory is presented. Starting from a Nambu–Goto bosonic string, matter field is introduced to obtain a superstring in four dimensions. The excitation quanta of this string contain graviton and the gravitino. Using the principle of equivalence, the action in curved space–time are found and the sum of them is the Deser–Zumino N = 1 supergravity action. The energy tensor is Lorentz invariant due to supersymmetry.

Recently it was found that the complete integration of the Einstein-dilaton-antisymmetric form equations depending on one variable and describing static singly charged p-branes leads to two and only two classes of solutions: the standard asymptotically flat black p-brane and the asymptotically nonflat p-brane approaching the linear dilaton background at spatial infinity. Here we analyze this issue in more details and generalize the corresponding uniqueness argument to the case of partially delocalized branes. We also consider the special case of codimension one and find, in addition to the standard domain wall, the black wall solution. Explicit relations between our solutions and some recently found p-brane solutions "with extra parameters" are presented.

Recently Lin, Lunin and Maldacena (LLM)¹ explicitly mapped 1/2 BPS excitations of type IIB supergravity on AdS₅ × S⁵ into free fermion configurations. We discuss thermal coarse-gaining of LLM geometries by explicitly mapping the corresponding equilibrium finite temperature fermion configuration into supergravity. Following Mathur conjecture, a prescription of this sort should generate a horizon in the geometry. We did not find a horizon in finite temperature equilibrium LLM geometry. This most likely is due to the fact that coarse-graining is performed only in a half-BPS sector of the full Hilbert space of type IIB supergravity. For temperatures much less than the AdS curvature scale the equilibrium background corresponding to nearly degenerate dual Fermi-gas is found analytically.

We study a U(N) gauged supergravity model with one hypermultiplet parametrizing SO(4, 1)/SO(4) quaternionic manifold. Local supersymmetry is known to be spontaneously broken to in the Higgs phase of U(1)_graviphoton × U(1). Several properties are obtained of this model in the vacuum of unbroken SU(N) gauge group. In particular, we derive mass spectrum analogous to the rigid counterpart and put the entire resulting potential on this vacuum in the standard superpotential form of supergravity.

We study the critical points of the black hole scalar potential V_BH in N = 2, d = 4 supergravity coupled to n_V vector multiplets, in an asymptotically flat extremal black hole background described by a 2(n_V+1)-dimensional dyonic charge vector and (complex) scalar fields which are coordinates of a special Kähler manifold.

For the case of homogeneous symmetric spaces, we find three general classes of regular attractor solutions with nonvanishing Bekenstein–Hawking entropy. They correspond to three (inequivalent) classes of orbits of the charge vector, which is in a 2(n_V+1)-dimensional representation R_V of the U-duality group. Such orbits are nondegenerate, namely they have nonvanishing quartic invariant (for rank-3 spaces). Other than the ½-BPS one, there are two other distinct non-BPS classes of charge orbits, one of which has vanishing central charge.

The three species of solutions to the N = 2 extremal black hole attractor equations give rise to different mass spectra of the scalar fluctuations, whose pattern can be inferred by using invariance properties of the critical points of V_BH and some group theoretical considerations on homogeneous symmetric special Kähler geometry.

The solvable Lie algebra parametrization of the symmetric spaces is discussed. Based on the solvable Lie algebra gauge two equivalent formulations of the symmetric space sigma model are studied. Their correspondence is established by inspecting the normalization conditions and deriving the field transformation laws.

We review the theory and phenomenology of effective supergravity theories based on orbifold compactifications of the weakly-coupled heterotic string. In particular, we consider theories in which the four-dimensional theory displays target space modular invariance and where the dilatonic mode undergoes Kähler stabilization. A self-contained exposition of effective Lagrangian approaches to gaugino condensation and heterotic string theory is presented, leading to the development of the models of Binétruy, Gaillard and Wu. Various aspects of the phenomenology of this class of models are considered. These include issues of supersymmetry breaking and superpartner spectra, the role of anomalous U(1) factors, issues of flavor and R-parity conservation, collider signatures, axion physics, and early universe cosmology. For the vast majority of phenomenological considerations the theories reviewed here compare quite favorably to other string-derived models in the literature. Theoretical objections to the framework and directions for further research are identified and discussed.

We study the hierarchy of hidden space–time symmetries of noncritical strings in RNS formalism, realized nonlinearly. Under these symmetry transformations the variation of the matter part of the RNS action is canceled by that of the ghost part. These symmetries, referred to as the α-symmetries, are induced by special space–time generators, violating the equivalence of ghost pictures. We classify the α-symmetry generators in terms of superconformal ghost cohomologies H_n ~ H_-n-2(n≥0) and associate these generators with a chain of hidden space–time dimensions, with each ghost cohomology H_n ~ H_-n-2 "contributing" an extra dimension. Namely, we show that each ghost cohomology H_n ~ H_-n-2 of noncritical superstring theory in d-dimensions contains d+n+1 α-symmetry generators and the generators from H_k ~ H_-k-2, 1≤k ≤n, combined together, extend the space–time isometry group from the naive SO(d, 2) to SO(d+n, 2). In the simplest case of n = 1 the α-generators are identified with the extra symmetries of the 2T-physics formalism, also known to originate from a hidden space–time dimension.

The first-order bosonic field equations of the D-dimensional effective low energy theory which describes the massless background coupling of the D-dimensional fully Higgsed heterotic string are derived.

We analyze the coupled supergravity and Yang-Mills system using holomorphy, near the rigid limit where the former decouples from the latter. We find that there appears generically a new mass scale around gM_pl where g is the gauge coupling constant and M_pl is the Planck scale. This is in accord with the weak-gravity conjecture proposed recently.

We analyze the attractor mechanism for the D0-D4 black hole solution in the four-dimensional supergravity. Our analyses are based on new exact solutions, which show explicitly the attractor mechanism for the extremal non-BPS black holes. Our solutions take into account the moduli as general complex fields, while in almost all the non-BPS solutions obtained by previous authors, the moduli fields are restricted to be purely imaginary.

We address the question of determining the prepotential of the gauged supergravity resulting from a compactification of M-theory on AdS₄ × Y₇. We make a concrete proposal for the prepotential in the case of toric Sasaki-Einstein Y₇. Comparison with direct Kaluza-Klein computations show that the proposal is correct in certain cases, but requires modification in general.

By studying the BPS equations for electrostatic and spherically symmetric configurations in N = 2, d = 5 gauged supergravity with vector multiplets and hypermultiplets coupled, we demonstrate that no regular supersymmetric black hole solutions of this kind exist. Furthermore, we demonstrate that it is not possible to construct supersymmetric regular solitons that have the above symmetries. As a consequence the scalar flow associated to the BPS solutions is always unbounded.