Narrow Results

We study the cohomological physics of fivebranes in type II and heterotic string theory. We give an interpretation of the one-loop term in type IIA, which involves the first and second Pontrjagin classes of spacetime, in terms of obstructions to having bundles with certain structure groups. Using a generalization of the Green–Schwarz anomaly cancellation in heterotic string theory which demands the target space to have a String structure, we observe that the "magnetic dual" version of the anomaly cancellation condition can be read as a higher analog of String structure, which we call Fivebrane structure. This involves lifts of orthogonal and unitary structures through higher connected covers which are not just 3- but even 7-connected. We discuss the topological obstructions to the existence of Fivebrane structures. The dual version of the anomaly cancellation points to a relation of string and Fivebrane structures under electric-magnetic duality.

The cosmological axion theory leads to the prediction of axionic mini-clusters of mass M ~ 10^-9M_⊙, which form at the time t_e of equipartition of matter and radiation. By applying the two-body relaxation formula of Spitzer and Hart, we show, for the heterotic superstring theory of Gross et al., that these mini-clusters, considered as point masses, themselves cluster into axion mini-stars of mass within the age of the Universe t₀ only if they are located within a distance R ~ 0.1 pc of the Galactic Center. Here, λ ≡ f_B/f_A is the ratio of the second to model-independent axion decay constants, assuming the QCD decay constant to be in the range , and is the strong-interaction coupling parameter. Thus, if axion mini-stars are to explain the microlensing observations by the EROS and MACHO groups towards the Galactic Bulge and the Large and Small Magellanic Clouds, then a collisionless relaxation mechanism is required, as proposed by Seidel and Suen (essentially the violent relaxation of Lynden–Bell), or the four-axion self-interaction effect considered by Tkachev.

The Einstein–Hilbert Lagrangian R is expressed in terms of the chronometrically invariant quantities introduced by Zel'manov for an arbitrary four-dimensional metric g_ij. The chronometrically invariant three-space is the physical space γ_αβ = -g_αβ+e^2ϕ γ_αγ_β, where e^2ϕ = g₀₀ and γ_α = g_0α/g₀₀, and whose determinant is h. The momentum canonically conjugate to γ_αβ is , where and ∂_t≡e^-ϕ∂₀ is the chronometrically invariant derivative with respect to time. The Wheeler–DeWitt equation for the wave function Ψ is derived. For a stationary space-time, such as the Kerr metric, π^αβ vanishes, implying that there is then no dynamics. The most symmetric, chronometrically-invariant space, obtained after setting ϕ = γ_α = 0, is , where δ_αβ is constant and has curvature k. From the Friedmann and Raychaudhuri equations, we find that λ is constant only if k=1 and the source is a perfect fluid of energy-density ρ and pressure p=(γ-1)ρ, with adiabatic index γ=2/3, which is the value for a random ensemble of strings, thus yielding a three-dimensional de Sitter space embedded in four-dimensional space-time. Furthermore, Ψ is only invariant under the time-reversal operator if γ=2/(2n-1), where n is a positive integer, the first two values n=1,2 defining the high-temperature and low-temperature limits ρ ~ T^±2, respectively, of the heterotic superstring theory, which are thus dual to one another in the sense T↔1/2π²α′T.

Previously, we have shown that the Kasner solution

We analyze the propagation of an extremely short optical pulse from the numerical solution of the Maxwell’s equation related to the effective action obtained in the framework of the theory of superstrings in flat time space. The pulse dynamics turned out to be unstable and eventually leads to a collapse. We particularly analyze the Schwinger mechanism which occurs during the collapse of the pulse.

We investigate an alternative quantization of R-NS string theory. In the alternative quantization, we define the distinct vacuum for the left-moving mode and the right-moving mode by exchanging the role of creation operators and annihilation operators in the left-moving sector. The resulting string theory has only a finite number of propagating degrees of freedom. We show that an appropriate choice of the GSO projection makes the theory tachyon free. The spectrum coincides with the massless sector of type IIA or type IIB superstring theory without any massive excitations.

We write down one-to-one mappings between the singular vectors of the Neveu–Schwarz N = 2 superconformal algebra and 16 + 16 types of singular vectors of the topological and of the Ramond N = 2 superconformal algebras. As a result one obtains the construction formulae for the latter using Dörrzapf's construction formulae for the Neveu–Schwarz singular vectors. The indecomposable singular vectors of the topological and of the Ramond N = 2 algebras ("no-label" and "no-helicity" singular vectors) cannot be mapped to singular vectors of the Neveu–Schwarz N = 2 algebra, but to subsingular vectors, for which no construction formulae exist.

In this contribution the tree-level effective actions for gluons and gravitons, as derived from Open and Closed Superstring theories, are reviewed respectively. As known for a long time, at zero order in α′ (the string fundamental constant) the first action is pure Yang-Mills while the second one is pure Einstein-Hilbert. The first Superstring Theory corrections turn up to appear at order in the first case while they appear at in the second one, as known from the three and four-point scattering amplitudes for gluons and gravitons, respectively. Recent work involving the order contributions to the Yang-Mills action is reviewed with some detail, including the authors' present line of research. Also, the uncharted territory of five graviton scattering is commented, looking forward to derive the Superstring Theory corrections to the Einstein-Hilbert action.

We review basic aspects of worldsheet and penta-brane instantons as well as (unoriented) D-brane instantons, which is our main focus here, and threshold corrections to BPS-saturated couplings. We then consider nonperturbative superpotentials generated by "gauge" and "exotic" instantons living on D3-branes at orientifold singularities. Moreover, we discuss the interplay between worldsheet and D-string instantons on T⁴/Z₂. We focus on a 4-Fermi amplitude, give Heterotic and perturbative Type I descriptions, and offer a multi-D-string instanton interpretation. We conclude with possible interesting developments.

The study of AdS/CFT (or gauge/gravity) duality has been one of the most active and illuminating areas of research in string theory over the past decade. The scope of its relevance and the insights it is providing seem to be ever expanding. In this talk I briefly describe some of the attempts to explore how the duality works for maximally supersymmetric systems.

We study the Lorentzian version of the type IIB matrix model as a nonperturbative formulation of superstring theory in (9+1)-dimensions. Monte Carlo results show that not only space but also time emerges dynamically in this model. Furthermore, the real-time dynamics extracted from the matrices turns out to be remarkable: 3 out of 9 spatial directions start to expand at some critical time. This can be interpreted as the birth of our Universe.

Quantum M-theory is formulated using the current algebra technique. The current algebra is based on a Kac–Moody algebra rather than usual finite dimensional Lie algebra. Specifically, I study the $E_{11}$ Kac–Moody algebra that was shown recently${}^{1-5}$ to contain all the ingredients of M-theory. Both the internal symmetry and the external Lorentz symmetry can be realized inside $E_{11}$, so that, by constructing the current algebra of $E_{11}$, I obtain both internal gauge theory and gravity theory. The energy–momentum tensor is constructed as the bilinear form of the currents, yielding a system of quantum equations of motion of the currents/fields. Supersymmetry is incorporated in a natural way. The so-called “field-current identity” is built in and, for example, the gravitino field is itself a conserved supercurrent. One unanticipated outcome is that the quantum gravity equation is not identical to the one obtained from the Einstein–Hilbert action.

In this paper, the open string is quantized in a time-dependent black hole background. By time-dependent black hole, one means a Vaydia geometry in the adiabatic approximation, which in $2+1$ dimensions is a BTZ black hole with a time-dependent mass. The worldsheet two-point function is derived and it is shown to have the same type of singularity as the flat space one. However, the equal times two-point function depends on the particular Cauchy surface where the worldsheet fields are defined. Finite temperature effects are incorporated through the Liouville–von Neumann approach to nonequilibrium thermodynamics.

In this paper we present a model where the modified Landau-like levels of charged particles in a magnetic field are determined due to the modified smoothness of ℝ⁴ as underlying structure of the Minkowski spacetime. The standard smoothness of ℝ⁴ is shifted to the exotic , k = 2p, p = 1, 2, …. This is achieved by superstring theory using gravitational backreaction induced from a strong, almost constant magnetic field on standard ℝ⁴. The exact string background containing flat ℝ⁴ is replaced consistently by the curved geometry of SU(2)_k × ℝ as part of the modified exact backgrounds. This corresponds to the change of smoothness on ℝ⁴ from the standard ℝ⁴ to some exotic . The calculations of the spectra are using the CFT marginal deformations and Wess–Zumino–Witten (WZW) models. The marginal deformations capture the effects of the magnetic field as well as its gravitational backreactions. The spectra depend on even level k of WZW on SU(2). At the same time the WZ term as element of H³(SU(2), ℝ) determines also the exotic smooth . As the consequence we obtain that a nonzero mass-gap induced by the exotic emerges in the spectrum.

Using dyonic solutions in the type IIA superstring theory on Calabi–Yau (CY) manifolds, we reconsider the study of black objects and quantum information theory using string/string duality in six dimensions. Concretely, we relate four-qubits with a stringy quaternionic moduli space of type IIA compactification associated with a dyonic black solution formed by black holes (BHs) and black 2-branes (B2B) carrying eight electric charges and eight magnetic charges. This connection is made by associating the cohomology classes of the heterotic superstring on $T^4$ to four-qubit states. These states are interpreted in terms of such dyonic charges resulting from the quaternionic symmetric space $\frac{\mathrm{\text{SO}}(4,4)}{\mathrm{\text{SO}}(4)\times \mathrm{\text{SO}}(4)}$ corresponding to a $N=4$ sigma model superpotential in two dimensions. The superpotential is considered as a functional depending on four quaternionic fields mapped to a class of Clifford algebras denoted as ${\mathrm{\text{Cl}}}_{0,4}$. A link between such an algebra and the cohomology classes of $T^4$ in heterotic superstring theory is also given.

Using the toroidal compactification of string theory on $n$-dimensional tori, ${𝕋}^n$, we investigate dyonic objects in arbitrary dimensions. First, we present a class of dyonic black solutions formed by two different D-branes using a correspondence between toroidal cycles and objects possessing both magnetic and electric charges, belonging to $\text{U}{(1)}_e^{2^{n-1}}\times \text{U}{(1)}_m^{2^{n-1}}$ dyonic gauge symmetry. This symmetry could be associated with electrically charged magnetic monopole solutions in stringy model buildings of the standard model (SM) extensions. Then, we consider in some detail such black hole classes obtained from even-dimensional toroidal compactifications, and we find that they are linked to $Cl(n)$ Clifford algebras using the vee product. It is believed that this analysis could be extended to dyonic objects which can be obtained from local Calabi–Yau manifold compactifications.

The study of AdS/CFT (or gauge/gravity) duality has been one of the most active and illuminating areas of research in string theory over the past decade. The scope of its relevance and the insights it is providing seem to be ever expanding. In this talk I briefly describe some of the attempts to explore how the duality works for maximally supersymmetric systems.

Much of modern string theory research concerns AdS/CFT duality, or more generally, gauge/gravity duality. The main subjects are

• Testing and understanding such dualities by exploring how they work for systems with a lot of supersymmetry;

• Constructing and exploring approximate string theory duals of QCD;

• Applying gauge/gravity duality to other areas of physics such as condensed matter and nuclear physics.

I will briefly discuss the first topic.