On the Heterotic World-sheet Instanton Superpotential and its individual Contributions

For supersymmetric heterotic string compactifications on a Calabi-Yau threefold $X$ endowed with a vector bundle $V$ the world-sheet superpotential $W$ is a sum of contributions from isolated rational curves \C in $X$; the individual contribution is given by an exponential in the K\"ahler class of the curve times a prefactor given essentially by the Pfaffian which depends on the moduli of $V$ and the complex structure moduli of $X$. Solutions of $DW=0$ (or even of $DW=W=0$) can arise either by nontrivial cancellations between the individual terms in the summation over all contributing curves or because each of these terms is zero already individually. Concerning the latter case conditions on the moduli making a single Pfaffian vanish (for special moduli values) have been investigated. However, even if corresponding moduli - fulfilling these constraints - for the individual contribution of one curve are known it is not at all clear whether {\em one} choice of moduli exists which fulfills the corresponding constraints {\em for all contributing curves simultaneously}. Clearly this will in general happen only if the conditions on the 'individual zeroes' had already a conceptual origin which allows them to fit together consistently. We show that this happens for a class of cases. In the special case of spectral cover bundles we show that a relevant solution set has an interesting location in moduli space and is related to transitions which change the generation number.Comment: 47 page

Perspectives on Pfaffians of Heterotic World-sheet Instantons

To fix the bundle moduli of a heterotic compactification one has to understand the Pfaffian one-loop prefactor of the classical instanton contribution. For compactifications on elliptically fibered Calabi-Yau spaces X this can be made explicit for spectral bundles and world-sheet instantons supported on rational base curves b: one can express the Pfaffian in a closed algebraic form as a polynomial, or it may be understood as a theta-function expression. We elucidate the connection between these two points of view via the respective perception of the relevant spectral curve, related to its extrinsic geometry in the ambient space (the elliptic surface in X over b) or to its intrinsic geometry as abstract Riemann surface. We identify, within a conceptual description, general vanishing loci of the Pfaffian, and derive bounds on the vanishing order, relevant to solutions of W=dW=0.Comment: 40 pages; minor changes, discussion section 1.1 adde

S-Track Stabilization of Heterotic de Sitter Vacua

We present a new mechanism, the S-Track, to stabilize the volume modulus S in heterotic M-theory flux compactifications along with the orbifold-size T besides complex structure and vector bundle moduli stabilization. The key dynamical ingredient which makes the volume modulus stabilization possible, is M5-instantons arising from M5-branes wrapping the whole Calabi-Yau slice. These are natural in heterotic M-theory where the warping shrinks the Calabi-Yau volume along S^1/Z_2. Combined with H-flux, open M2-instantons and hidden sector gaugino condensation it leads to a superpotential W which stabilizes S similar like a racetrack but without the need for multi gaugino condensation. Moreover, W contains two competing non-perturbative effects which stabilize T. We analyze the potential and superpotentials to show that it leads to heterotic de Sitter vacua with broken supersymmetry through non-vanishing F-terms.Comment: 16 pages, 2 figures; final PRD versio

Superpotentials for M-theory on a G_2 holonomy manifold and Triality symmetry

For $M$-theory on the $G_2$ holonomy manifold given by the cone on {\bf S^3}\x {\bf S^3} we consider the superpotential generated by membrane instantons and study its transformations properties, especially under monodromy transformations and triality symmetry. We find that the latter symmetry is, essentially, even a symmetry of the superpotential. As in Seiberg/Witten theory, where a flat bundle given by the periods of an universal elliptic curve over the $u$-plane occurs, here a flat bundle related to the Heisenberg group appears and the relevant universal object over the moduli space is related to hyperbolic geometry.Comment: 58 pages, latex; references adde

String-String triality for d=4, Z_2 orbifolds

We investigate the perturbative and non-perturbative correspondence of a class of four dimensional dual string constructions with N=4 and N=2 supersymmetry, obtained as Z_2 or Z_2 x Z_2 orbifolds of the type II, heterotic and type I string. In particular, we discuss the heterotic and type I dual of all the symmetric Z_2 x Z_2 orbifolds of the type II string, classified in hep-th/9901123. .Comment: latex, 50 pages, figures, final published versio

Constraining the Kahler Moduli in the Heterotic Standard Model

Phenomenological implications of the volume of the Calabi-Yau threefolds on the hidden and observable M-theory boundaries, together with slope stability of their corresponding vector bundles, constrain the set of Kaehler moduli which give rise to realistic compactifications of the strongly coupled heterotic string. When vector bundles are constructed using extensions, we provide simple rules to determine lower and upper bounds to the region of the Kaehler moduli space where such compactifications can exist. We show how small these regions can be, working out in full detail the case of the recently proposed Heterotic Standard Model. More explicitely, we exhibit Kaehler classes in these regions for which the visible vector bundle is stable. On the other hand, there is no polarization for which the hidden bundle is stable.Comment: 28 pages, harvmac. Exposition improved, references and one figure added, minor correction

World-sheet Instanton Superpotentials in Heterotic String theory and their Moduli Dependence

To understand in detail the contribution of a world-sheet instanton to the superpotential in a heterotic string compactification, one has to understand the moduli dependence (bundle and complex structure moduli) of the one-loop determinants from the fluctuations, which accompany the classical exponential contribution (involving K\"ahler moduli) when evaluating the world-volume partition function. Here we use techniques to describe geometrically these Pfaffians for spectral bundles over rational base curves in elliptically fibered Calabi-Yau threefolds, and provide a (partially exhaustive) list of cases involving {\em factorising} (or vanishing) superpotential. This gives a conceptual explanation and generalisation of the few previously known cases which were obtained just experimentally by a numerical computation.Comment: 57 pages; minor changes, discussion section 1.3 adde

Vector Bundle Moduli and Small Instanton Transitions

We give the general presciption for calculating the moduli of irreducible, stable SU(n) holomorphic vector bundles with positive spectral covers over elliptically fibered Calabi-Yau threefolds. Explicit results are presented for Hirzebruch base surfaces B=F_r. The transition moduli that are produced by chirality changing small instanton phase transitions are defined and specifically enumerated. The origin of these moduli, as the deformations of the spectral cover restricted to the ``lift'' of the horizontal curve of the M5-brane, is discussed. We present an alternative description of the transition moduli as the sections of rank n holomorphic vector bundles over the M5-brane curve and give explicit examples. Vector bundle moduli appear as gauge singlet scalar fields in the effective low-energy actions of heterotic superstrings and heterotic M-theory.Comment: 52 pages, LATEX, corrected typo

MQCD, ('Barely') G_2 Manifolds and (Orientifold of) a Compact Calabi-Yau

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 G_2-manifold evaluated by the path-integral inside a path-integral approach of [1], and the other centered around the compact Calabi-Yau CY_3(3,243) expressed as a blow-up of a degree-24 Fermat hypersurface in WCP^4[1,1,2,8,12]. For the former, we compare the results with the ones of Witten on heterotic world-sheet instantons [2]. The subtopics covered in the latter include an N=1 triality between Heterotic, M- and F-theories, evaluation of RP^2-instanton superpotential, Picard-Fuchs equation for the mirror Landau-Ginsburg model corresponding to CY_3(3,243), D=11 supergravity corresponding to M-theory compactified on a `barely' G_2 manifold involving CY_3(3,243) and a conjecture related to the action of antiholomorphic involution on period integrals. We then show 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 "\zeta", a complex constant that appears in the Riemann surfaces relevant to definining the boundary conditions for the domain wall in MQCD, the infinite series of [4] used to represent a suitable embedding of a supersymmetric 3-cycle in a G_2-mannifold, can be summed.Comment: 37 pages, LaTex; PARTLY based on talks given at ``Seventh Workshop on QCD" [session on "Strings, Branes and (De-)Construction"], Jan 6-10, 2003, La Cittadelle, Villefranche-sur-Mer, France; Fourth Workshop on ``Gauge Fields and Strings", Feb 25-Mar 1, 2003, Jena, Germany; ``XII Oporto Meeting on Geometry, Topology and Strings", July 17-20, 2003, Oporto, Portugal; "SQS03" - International Workshop on "Supersymmetries and Quantum Symmetries', July 24-29, 2003, JINR, Dubna, Russia; poster presented at ``XIV International Congress on Mathematical Physics", July 28-Aug 2, 2003, Lisbon, Portuga

Assessing Drivers’ Vigilance State During Monotonous Driving

The differential effects of three hours of monotonous daytime driving on subjective (sleepiness, inattention, monotony), performance (choice reaction time), and physiological (EEG alpha power, P300-amplitude, heart rate) vigilance measures were examined. A linear degradation of drivers’ subjective state, mean long reaction times (as opposed to short ones), P300-amplitude and parietal alpha power with time spent on the highway was identified. An improvement of the subjective measures towards the end of the driving task was not accompanied by any improvement in performance or physiological measures. This dissociation of self-assessment and objective vigilance measures has important implications for the design of modern driver assistant systems that aim to adapt to the driver’s state