Space-time Interpretation Research Articles

String dualities from Matrix theory

We suggest that the (2,0) six-dimensional field theory compactified on S 1 × K3 is the Matrix model description of both M-theory on K3 and the heterotic string on T 3. This proposal is different from existing proposals for the heterotic theory. Different limits of the base-space geometry give the different space-time interpretations, making M-theory/heterotic duality manifest. We also present partial results on heterotic/F-theory duality.

The emergence of space-time gravitational physics as an effective theory from the c = 1 matrix model

We discuss further a recent space-time interpretation of the c = 1 matrix model which retains both sides of the inverted harmonic oscillator potential in the underlying free fermion theory and reproduces the physics of the discrete state moduli of two-dimensional string theory. We show that within this framework the linear tachyon background in flat space arises from the Fermi vacuum. We argue that this framework does not suffer from any obvious non-perturbative inconsistency. We also identify and discuss a class of nearly static configurations in the free fermion theory which are interpreted as static metric backgrounds in space-time. These backgrounds are classically absorbing - a beam of tachyons thrown at such a background is only partly reflected back - and are tentatively identified with the eternal black hole of two-dimensional string theory.

Consistency conditions for branes at orbifold singularities

We discuss consistency conditions for branes at orbifold singularities. The conditions have a world-sheet interpretation in terms of tadpole cancellation and a space-time interpretation in terms of anomalies. As examples, we consider type II and type I branes on C 2/ Z M orbifolds. We give orientifold constructions of phases of type I or heterotic string theory, involving branches with extra tensor multiplets, which arise when small SO(32) instantons sit on orbifold singularities.

Path-Integral Quantization of the (2,2) String

A complete treatment of the (2,2) NSR string in flat (2 + 2)-dimensional space–time is given, from the formal path integral over N = 2 super Riemann surfaces to the computational recipe for amplitudes at any loop or gauge instanton number. We perform in detail the superconformal gauge fixing, discuss the spectral flow, and analyze the supermoduli space with emphasis on the gauge moduli. Background gauge field configurations in all instanton sectors are constructed. We develop chiral bosonization on punctured higher-genus surfaces in the presence of gauge moduli and instantons. The BRST cohomology is recapitulated, with a new space–time interpretation for picture-changing. We point out two ways of combining left- and right-movers, which lead to different three-point functions.

What can we learn from three-pion interferometry?

We address the question, what additional information on the source shape and dynamics can be extracted from three-particle Bose-Einstein correlations. For chaotic sources the true three-particle correlation term is shown to be sensitive to the momentum dependence of the saddle point of the source and to its asymmetries around that point. For partially coherent sources the three-pion correlator allows one to measure the degree of coherence without contamination from resonance decays. We derive the most general Gaussian parametrization of the two- and three-particle correlator for this case and discuss the space-time interpretation of the corresponding parameters.

A note on quantum Liouville theory via the quantum group An approach to strong coupling Liouville theory

Quantum Liouville theory is analysed in terms of the infinite dimensional representations of U q sl(2, C) with q a root of unity. Making full use of the characteristic features of the representations, we show that the vertex operators in this Liouville theory are factorized into classical vertex operators and those which are constructed from the finite dimensional representations of U q sl(2, C) We further show explicitly that the fusion rules in this model also enjoy such a factorization. Upon the conjecture that the Liouville action effectively decouples into the classical Liouville action and that of a quantum theory, correlation functions and transition amplitudes are discussed, especially an intimate relation between our model and geometric quantization of the moduli space of Riemann surfaces is suggested. The most important result is that our Liouville theory is in the strong coupling region, i.e. the central charge CL satisfies 1 < C L < 25. An interpretation of the quantum space-time is also given within this formulation.

Resolution of cosmological singularities in string theory

We show that a class of 3+1 dimensional Friedmann-Robertson-Walker cosmologies can be embedded within a variety of solutions of string theory. In some realizations the apparent singularities associated with the big bang or big crunch are resolved at non-singular horizons of higher-dimensional quasi-black hole solutions (with compactified real time); in others plausibly they are resolved at D-brane bound states having no conventional space-time interpretation.

Branes, Calabi-Yau spaces, and toroidal compactification of the N = 1 six-dimensional E8 theory

We consider compactifications of the N = 1, d = 6, E 8 theory on tori to five, four, and three dimensions and learn about some properties of this theory. As a by-product we derive the SL(2, Z) duality of the N = 2, d = 4, SU(2) theory with N f = 4. Using this theory on a D-brane probe we shed new light on the singularities of F-theory compactifications to eight dimensions. As another application we consider compactifications of F-theory, M-theory and the IIA string on (singular) Calabi-Yau spaces where our theory appears in space-time. Our viewpoint leads to a new perspective on the nature of the singularities in the moduli space and their space-time interpretations. In particular, we have a universal understanding of how the singularities in the classical moduli space of Calabi-Yau spaces are modified by world-sheet instantons to singularities in the moduli space of the corresponding conformal field theories.

Discrete-state moduli of string theory from the c = 1 matrix model

We propose a new formulation of the space-time interpretation of the c = 1 matrix model. Our formulation uses the well-known leg-pole factor that relates the matrix model amplitudes to that of the 2-dimensional string theory, but includes fluctuations around the Fermi vacuum on both sides of the inverted harmonic oscillator potential of the double-scaled model, even when the fluctuations are small and confined entirely within the asymptotes in the phase plane. We argue that including fluctuations on both sides of the potential is essential for a consistent interpretation of the leg-pole transformed theory as a theory of space-time gravity. We reproduce the known results for the string theory tree-level scattering amplitudes for flat space and linear dilaton background as a special case. We show that the generic case corresponds to more general space-time backgrounds. In particular, we identify the parameter corresponding to background metric perturbation in string theory (black-hole mass) in terms of the matrix model variables. Possible implications of our work for a consistent non-perturbative definition of string theory as well as for quantized gravity and black-hole physics are discussed.

Exactly solvable string models of curved space-time backgrounds

We consider a new 3-parameter class of exact 4-dimensional solutions in closed string theory and solve the corresponding string model, determining the physical spectrum and the partition function. The background fields (4-metric, antisymmetric tensor, two Kaluza-Klein vector fields, dilaton and modulus) generically describe axially symmetric stationary rotating (electro) magnetic flux-tube type universes. Backgrounds of this class include both the “dilatonic” ( a = 1) and “Kaluza-Klein” ( a = √3) Melvin solutions and the uniform magnetic field solution, as well as some singular space-times. Solvability of the string σ-model is related to its connection via duality to a simpler model which is a “twisted” product of a flat 2-space and a space dual to 2-plane. We discuss some physical properties of this model (tachyonic instabilities in the spectrum, gyromagnetic ratio, issue of singularities, etc.). It provides one of the first examples of a consistent solvable conformal string model with explicit D = 4 curved space-time interpretation.

GENERALIZED W3-STRINGS FROM FREE FIELDS

The conventional quantization of w3-strings gives theories which are equivalent to special cases of bosonic strings. We explore whether a more general quantization can lead to new generalized W3-string theories by seeking to construct quantum BRST charges directly without requiring the existence of a quantum W3-algebra. We study W3-like strings with a direct space-time interpretation — that is, with matter given by explicit free field realizations. Special emphasis is placed on the attempt to construct a quantum W-string associated with the magic realizations of the classical w3-algebra. We give the general conditions for the existence of W3-like strings, and comment on how the known results fit into our general construction. Our results are negative: we find no new consistent string theories, and in particular rule out the possibility of critical strings based on the magic realizations.

Space time interpretation of S-duality and supersymmetry violations of T-duality

The S-duality transformations of the lowest order string effective theory admit a space time interpretation for 4-dim backgrounds with one Killing symmetry. Starting from pure gravity and performing a sequence of interwined T-S-T duality transformations we obtain new solutions which are always purely gravitational. In this fashion, S-duality induces an SL(2, R) transformation in the space of target space metrics, which coincides with the action of the Ehlers-Geroch group and interchanges the electric with the magnetic aspects of gravity. Specializing to gravitational instanton backgrounds, we show that ALE instantons are mapped to (multi) Taub-NUT backgrounds and vice versa. We find, however, that the self-duality of the metric is not generically preserved, unless the corresponding Killing vector field has self-dual covariant derivatives. Thus, the T-S-T transformations are not always compatible with the world-sheet supersymmetry of N = 4 superconformal string vacua. We also provide an algebraic characterization of the corresponding obstruction and associate it with a breakdown of space time supersymmetry under rotational T-duality transformations.

Covariant two-particle world lines in relativistic Hamiltonian mechanics

On the basis of the space-time interpretation of relativistic classical Hamiltonian mechanics for various classes of two-particle models we study the restrictions on the general solution imposed by the condition of invariance of world lines and on the particle interaction for the purpose of guaranteeing that the world lines are timelike, the instantaneous configurations are spacelike, and that the system is predictive.

Model-building for fractional superstrings

We investigate heterotic string-type model-building for the recently proposed fractional superstring theories. We concentrate on the cases with critical space-time dimensions four and six, and find that a correspondence can be drawn between the new fractional superstring models and a special subset of the traditional heterotic string models. This allows us to generate the partition functions of the new models, and demonstrate that their number is indeed relatively limited. It also appears that these strings have uniquely natural compactifications to lower dimensions. In particular, the D c = 6 fractional superstring has a natural interpretation in four-dimensional space-time.

World-sheet and space-time physics in two-dimensional (super)string theory

We show that tree-level “resonant” N-tachyon scattering amplitudes, which define a sensible “bulk” S-matrix in critical (super)string theory in any dimension, have a simple structure in two-dimensional space-time, due to partial decoupling of a certain infinite set of discrete states. We also argue that the general (non-resonant) amplitudes are determined by the resonant ones, and calculate them explicitly, finding an interesting analytic structure. Finally, we discuss the space-time interpretation of our results.

Single-particle trajectories and interferences in quantum mechanics

In this paper some topics concerning the possibility of describing phenomena of quantum interference in terms of individual particle spacetime trajectories are reviewed. We focus our attention, on the one hand, on the recent experimental advances in neutron and photon interferometry and, on the other hand, on a theoretical analysis of the description of these experiments allowed by stochastic mechanics. It is argued that, even if no conclusive argument is yet at hand in both the theoretical and the experimental fields, the researches of the last 10 years now seem to favor Einstein's and de Broglie's realistic spacetime description and interpretation of quantum mechanics.

On W 3 strings

We construct a non-chiral anomaly-free theory of W 3 gravity and investigate its spacetime interpretation as a theory of critical W 3 strings

Spin, statistics, and geometry of random walks

We develop and unify two complementary descriptions of propagation of spinning particles: the directed random walk representation and the “spin factor” approach. Working in an arbitrary number of dimensions D, we first represent the Dirac propagator in terms of a directed random walk. We then derive the general and explicit form of the gauge connection describing parallel transport of spin and investigate the resulting quantum-mechanical problem of a particle moving on a sphere in the field of a nonabelian SO( D − 1) monopole. This construction, generalizing Polyakov's results, enables us to prove the equivalence of the random walk and path-integral (spin factor) representation. As an alternative, we construct and discuss various Wess-Zumino-Witten forms of the spin factor. We clarify the role played by the coupling between the particle's spin and translational degrees of freedom in establishing the geometrical properties of particle's paths in spacetime. To this end, we carefully define and evaluate Hausdorff dimensions of bosonic and fermionic sample paths, in the covariant as well as nonrelativistic formulations. Finally, as an application of the developed formalism, we give an intuitive spacetime interpretation of chiral anomalies in terms of the geometry of fermion trajectories.

Substances and space-time: What Aristotle would have said to Einstein

This essay consists of two parts. The first is an exegetical analysis of the “stripping” argument of Metaphysics Z.3. I contend that the passage is not in propria persona and that the resolution of the aporia depends upon a careful consideration of the metaphysical relationship between essential properties and the subjects of which they are predicated. The second part applies this conclusion to a problem recently raised by John Earman and John Norton about whether the general theory of relativity is compatible with both determinism and a substantivalist interpretation of space-time. I argue that their difficulty can be avoided by an Aristotelian account of the essential properties of space-time.

Quantum measurement and geometry.

A model for the interpretation of spacetime as a Weyl geometry is proposed, based on the hypothesis that a system moves on any given path with a probability which is inversely proportional to the resulting change in length of the system. The results of physical measurements are calculated as the product of Weyl-conjugate gauge-dependent probabilities for the detection of conjugate objects. Each probability, expressed as a Wiener integral, is the Green's function for a diffusion equation. If the line integral of the Weyl field equals the action functional divided by $\ensuremath{\hbar}$ this equation provides the stochastic equivalent of the Schr\"odinger equation, with expanding and contracting states replacing the oscillating states of standard quantum theory. These dilatations are not directly measurable within the theory, but the rates of expansion and contraction are. We establish the classical limit of the theory by proving that the most general form of the Weyl field which gives an extremum of the action is restricted to be of a special form. Particles obeying the equations of motion for these extremal Weyl fields experience no measurable dilatation. However, the Weyl field itself is classically detectable, and gives a correct description of the electromagnetic interaction of a point particle.