Showing papers on "Anomaly (physics) published in 2009"
TL;DR: It is shown that a hitherto discarded term in the conserved current is not only allowed by symmetries, but is in fact required by triangle anomalies and the second law of thermodynamics, which leads to a number of new effects, one of which is chiral separation in a rotating fluid at nonzero chemical potential.
Abstract: We consider the hydrodynamic regime of theories with quantum anomalies for global currents. We show that a hitherto discarded term in the conserved current is not only allowed by symmetries, but is in fact required by triangle anomalies and the second law of thermodynamics. This term leads to a number of new effects, one of which is chiral separation in a rotating fluid at nonzero chemical potential. The new kinetic coefficients can be expressed, in a unique fashion, through the anomaly coefficients and the equation of state. We briefly discuss the relevance of this new hydrodynamic term for physical situations, including heavy-ion collisions.
955 citations
TL;DR: In this paper, the minimal B-L extended standard model was investigated under a hypothesis of classically conformal theories, which naturally provided the seesaw mechanism for explaining tiny neutrino masses.
301 citations
Book•
30 Sep 2009291 citations
TL;DR: In this article, the authors make a comparison between the anomaly method and WKB/tunneling method for obtaining radiation from non-trivial spacetime backgrounds, focusing on Rindler spacetime and the associated Unruh radiation.
140 citations
TL;DR: In this paper, the authors derived a sum rule for the appropriate positive spectral function corresponding to the discontinuity of the triangle amplitude, showing that it becomes proportional to ε(n 2 ) and therefore contains a massless scalar intermediate state.
Abstract: The trace anomaly of quantum fields in electromagnetic or gravitational backgrounds implies the existence of massless scalar poles in physical amplitudes involving the stress-energy tensor. Considering first the axial anomaly and using QED as an example, we compute the full one-loop triangle amplitude of the fermionic stress tensor with two current vertices, $⟨{T}^{\ensuremath{\mu}\ensuremath{
u}}{J}^{\ensuremath{\alpha}}{J}^{\ensuremath{\beta}}⟩$, and exhibit the scalar pole in this amplitude associated with the trace anomaly, in the limit of zero electron mass $m\ensuremath{\rightarrow}0$. To emphasize the infrared aspect of the anomaly, we use a dispersive approach and show that this amplitude and the existence of the massless scalar pole is determined completely by its ultraviolet finite terms, together with the requirements of Poincar\'e invariance of the vacuum, Bose symmetry under interchange of ${J}^{\ensuremath{\alpha}}$ and ${J}^{\ensuremath{\beta}}$, and vector current and stress-tensor conservation. We derive a sum rule for the appropriate positive spectral function corresponding to the discontinuity of the triangle amplitude, showing that it becomes proportional to $\ensuremath{\delta}({k}^{2})$ and therefore contains a massless scalar intermediate state in the conformal limit of zero electron mass. The effective action corresponding to the trace of the triangle amplitude can be expressed in local form by the introduction of two scalar auxiliary fields which satisfy massless wave equations. These massless scalar degrees of freedom couple to classical sources, contribute to gravitational scattering processes, and can have long range gravitational effects.
136 citations
04 Nov 2009
TL;DR: This paper uses meta-data provided by several histogram-based detectors to identify suspicious flows, and then applies association rule mining to find and summarize anomalous flows, which significantly reduces the work-hours needed for analyzing alarms, making anomaly detection systems more practical.
Abstract: Anomaly extraction is an important problem essential to several applications ranging from root cause analysis, to attack mitigation, and testing anomaly detectors. Anomaly extraction is preceded by an anomaly detection step, which detects anomalous events and may identify a large set of possible associated event flows. The goal of anomaly extraction is to find and summarize the set of flows that are effectively caused by the anomalous event.In this work, we use meta-data provided by several histogram-based detectors to identify suspicious flows and then apply association rule mining to find and summarize the event flows. Using rich traffic data from a backbone network (SWITCH/AS559), we show that we can reduce the classification cost, in terms of items (flows or rules) that need to be classified, by several orders of magnitude. Further, we show that our techniques effectively isolate event flows in all analyzed cases and that on average trigger between 2 and 8.5 false positives, which can be trivially sorted out by an administrator.
130 citations
TL;DR: In this article, the authors presented holographic computations of the time-dependent chiral magnetic conductivity in the framework of gauge/gravity correspondence, motivated by a recent weak-coupling perturbative QCD calculation.
Abstract: We present holographic computations of the time-dependent chiral magnetic conductivity in the framework of gauge/gravity correspondence. Chiral magnetic effect is a phenomenon where an electromagnetic current parallel to an applied magnetic field is induced in the presence of a finite axial chemical potential. Motivated by a recent weak-coupling perturbative QCD calculation, our aim is to provide a couple of complementary computations for strongly coupled regime which might be relevant for strongly coupled RHIC plasma. We take two prototypical holographic set-ups for computing chiral magnetic conductivity; the first model is Einstein gravity with U(1)L × U(1)R Maxwell theory, and our second set-up is based on the Sakai-Sugimoto model in a deconfined and chiral symmetry restored phase. While the former takes into account full back-reaction while the latter not, the common feature is an important role played by the appropriate 5-dimensional Chern-Simons term corresponding to the 4-dimensional axial anomaly.
127 citations
TL;DR: In this paper, a linear sigma model with N{sub f} = 3 light quark flavors was investigated for chiral symmetry restoration at nonzero temperature and quark densities.
Abstract: Chiral symmetry restoration at nonzero temperature and quark densities are investigated in the framework of a linear sigma model with N{sub f}=3 light quark flavors. After the derivation of the grand potential in mean-field approximation, the nonstrange and strange condensates, the in-medium masses of the scalar and pseudoscalar nonets are analyzed in hot and dense medium. The influence of the axial anomaly on the nonet masses and the isoscalar mixings on the pseudoscalar {eta}-{eta}{sup '} and scalar {sigma}(600)-f{sub 0}(1370) complex are examined. The sensitivity of the chiral phase transition as well as the existence and location of a critical end point in the phase diagram on the value of the sigma mass are explored. The chiral critical surface with and without the influence of the axial U(1){sub A} anomaly is elaborated as a function of the pion and kaon masses for several values of the sigma mass.
122 citations
TL;DR: In this paper, the Sakai-Sugimoto model was used to model the chiral magnetic effect in a dual N_c QCD axial anomaly model, and it was shown that this model correctly contains the consistent anomaly, but requires the introduction of a (holographic) finite counterterm to yield the correct covariant anomaly.
Abstract: In the chiral magnetic effect an imbalance in the number of left- and right-handed quarks gives rise to an electromagnetic current parallel to the magnetic field produced in noncentral heavy-ion collisions. The chiral imbalance may be induced by topologically nontrivial gluon configurations via the QCD axial anomaly, while the resulting electromagnetic current itself is a consequence of the QED anomaly. In the Sakai-Sugimoto model, which in a certain limit is dual to large-N_c QCD, we discuss the proper implementation of the QED axial anomaly, the (ambiguous) definition of chiral currents, and the calculation of the chiral magnetic effect. We show that this model correctly contains the so-called consistent anomaly, but requires the introduction of a (holographic) finite counterterm to yield the correct covariant anomaly. Introducing net chirality through an axial chemical potential, we find a nonvanishing vector current only before including this counterterm. This seems to imply the absence of the chiral magnetic effect in this model. On the other hand, for a conventional quark chemical potential and large magnetic field, which is of interest in the physics of compact stars, we obtain a nontrivial result for the axial current that is in agreement with previous calculations and known exact results for QCD.
121 citations
TL;DR: In this paper, it was shown that if the only left-handed neutral fermions are the active neutrinos, B − L is a gauge symmetry, and the L assignment is restricted to the integer numbers, the anomaly cancellation imply that at least three right-handed neutrino must be added to the minimal representation content of the electroweak standard model.
115 citations
TL;DR: A computer-simulation study of the equilibrium phase diagram of a three-dimensional system of particles with a repulsive-shoulder potential shows that at certain values of the potential parameters the system exhibits the waterlike thermodynamic anomalies: a density anomaly and a diffusion anomaly.
Abstract: We report a computer-simulation study of the equilibrium phase diagram of a three-dimensional system of particles with a repulsive-shoulder potential. The phase diagram was obtained using free-energy calculations. At low temperatures, we observe a number of distinct crystal phases. We show that at certain values of the potential parameters the system exhibits the waterlike thermodynamic anomalies: a density anomaly and a diffusion anomaly. The anomalies disappear with increasing the repulsive step width: more precisely, their locations move to the region where the crystalline phase is stable.
TL;DR: In this article, the authors presented holographic computations of the time-dependent chiral magnetic conductivity in the framework of gauge/gravity correspondence, motivated by a recent weak-coupling perturbative QCD calculation.
Abstract: We present holographic computations of the time-dependent chiral magnetic conductivity in the framework of gauge/gravity correspondence. Chiral magnetic effect is a phenomenon where an electromagnetic current parallel to an applied magnetic field is induced in the presence of a finite axial chemical potential. Motivated by a recent weak-coupling perturbative QCD calculation, our aim is to provide a couple of complementary computations for strongly coupled regime which might be relevant for strongly coupled RHIC plasma. We take two prototypical holographic set-ups for computing chiral magnetic conductivity; the first model is Einstein gravity with U(1)_L X U(1)_R Maxwell theory, and our second set-up is based on the Sakai-Sugimoto model in a deconfined and chiral symmetry restored phase. While the former takes into account full back-reaction while the latter not, the common feature is an important role played by the appropriate 5-dimensional Chern-Simons term corresponding to the 4-dimensional axial anomaly.
Posted Content•
TL;DR: In this article, a non-parametric adaptive anomaly detection algorithm for high dimensional data based on score functions derived from nearest neighbor graphs on $n$-point nominal data is proposed.
Abstract: We propose a novel non-parametric adaptive anomaly detection algorithm for high dimensional data based on score functions derived from nearest neighbor graphs on $n$-point nominal data. Anomalies are declared whenever the score of a test sample falls below $\alpha$, which is supposed to be the desired false alarm level. The resulting anomaly detector is shown to be asymptotically optimal in that it is uniformly most powerful for the specified false alarm level, $\alpha$, for the case when the anomaly density is a mixture of the nominal and a known density. Our algorithm is computationally efficient, being linear in dimension and quadratic in data size. It does not require choosing complicated tuning parameters or function approximation classes and it can adapt to local structure such as local change in dimensionality. We demonstrate the algorithm on both artificial and real data sets in high dimensional feature spaces.
TL;DR: In this paper, the authors describe two inequivalent ways of defining the renormalization group of matter-coupled four-dimensional gravity, in the approximation where only the conformal factor is dynamical and taking the trace anomaly explicitly into account.
Abstract: Applying functional renormalization group methods, we describe two inequivalent ways of defining the renormalization group of matter-coupled four-dimensional gravity, in the approximation where only the conformal factor is dynamical and taking the trace anomaly explicitly into account. We make contact with earlier work and briefly discuss the presence or absence of fixed points, depending on the truncation of the action and other approximations.
TL;DR: In this paper, a class of smooth supersymmetric heterotic solutions with a non-compact Eguchi-Hanson space is presented, embedded as the base of a six-dimensional non-Kahler manifold.
Abstract: We present a class of smooth supersymmetric heterotic solutions with a non-compact Eguchi-Hanson space. The non-compact geometry is embedded as the base of a six-dimensional non-Kahler manifold with a non-trivial torus fiber. We solve the non-linear anomaly equation in this background exactly. We also define a new charge that detects the non-Kahlerity of our solutions.
TL;DR: In this article, it was shown that the PAMELA anomaly in the positron fraction as well as the ATIC/PPBBETS excesses in the e − +e + flux are simultaneously explained in the scenario that a hidden U (1)H gauge boson constitutes dark matter of the universe and decays into the standard model particles through a kinetic mixing with an U(1)B−L gauge bosons.
Abstract: We show that the PAMELA anomaly in the positron fraction as well as the ATIC/PPBBETS excesses in the e − +e + flux are simultaneously explained in our scenario that a hidden U (1)H gauge boson constitutes dark matter of the Universe and decays into the standardmodel particles through a kinetic mixing with an U (1)B−L gauge boson. Interestingly, the
Proceedings Article•
07 Dec 2009TL;DR: The resulting anomaly detector is shown to be asymptotically optimal in that it is uniformly most powerful for the specified false alarm level, α, for the case when the anomaly density is a mixture of the nominal and a known density.
Abstract: We propose a novel non-parametric adaptive anomaly detection algorithm for high dimensional data based on score functions derived from nearest neighbor graphs on n-point nominal data. Anomalies are declared whenever the score of a test sample falls below α, which is supposed to be the desired false alarm level. The resulting anomaly detector is shown to be asymptotically optimal in that it is uniformly most powerful for the specified false alarm level, α, for the case when the anomaly density is a mixture of the nominal and a known density. Our algorithm is computationally efficient, being linear in dimension and quadratic in data size. It does not require choosing complicated tuning parameters or function approximation classes and it can adapt to local structure such as local change in dimensionality. We demonstrate the algorithm on both artificial and real data sets in high dimensional feature spaces.
TL;DR: In this paper, an alternative procedure to derive anomaly-free Lemaitre-Tolman-Bondi (LTB) models with corrections from loop quantum gravity has been presented.
Abstract: Marginal Lemaitre-Tolman-Bondi (LTB) models with corrections from loop quantum gravity have recently been studied with an emphasis on potential singularity resolution This paper corroborates and extends the analysis in two regards: (i) the whole class of LTB models, including nonmarginal ones, is considered, and (ii) an alternative procedure to derive anomaly-free models is presented which first implements anomaly freedom in spherical symmetry and then the LTB conditions rather than the other way around While the two methods give slightly different equations of motion, not altogether surprisingly given the ubiquitous sprawl of quantization ambiguities, final conclusions remain unchanged: compared to quantizations of homogeneous models, bounces seem to appear less easily in inhomogeneous situations, and even the existence of homogeneous solutions as special cases in inhomogeneous models may be precluded by quantum effects However, compared to marginal models, bouncing solutions seem more likely with nonmarginal models
Patent•
14 Apr 2009
TL;DR: In this article, a real-time monitoring of a powered-on electrical network in a facility in order to detect an electrical anomaly while the electrical network is in use is presented.
Abstract: There are provided a method and a system for real time monitoring of a powered-on electrical network in a facility in order to detect an electrical anomaly while the electrical network is in use. The system comprises a sensor data receiver for receiving real time sensor data including at least one measured value measured in real time by at least one sensor installed on a conductor of the electrical network in the facility while the electrical network is in use; an anomaly detector for retrieving an anomaly detection rule from an anomaly detection rule database, the rule having an identification of a required input, a formula, and a threshold reference value, for a detection of an anomaly; receiving the real time sensor data from the sensor data receiver and extracting at least one relevant measured value from the at least one measured value using the identification of the required input; comparing the at least one relevant measured value to the threshold reference value according to the formula to determine one of a presence and an absence of the anomaly in the real time sensor data; an event generator controlled by the processor for retrieving and providing anomaly monitoring data if the anomaly is determined to be present by the processor, the anomaly monitoring data including an indication of a monitoring course of action to be carried out to address the anomaly determined to be present.
TL;DR: In this article, the authors report on progress towards constructing string models incorporating both realistic D-brane matter content and moduli stabilisation with dynamical low-scale super- symmetry breaking.
Abstract: We report on progress towards constructing string models incorporating both realistic D-brane matter content and moduli stabilisation with dynamical low-scale super- symmetry breaking. The general framework is that of local D-brane models embedded into the LARGE volume approach to moduli stabilisation. We review quiver theories on del Pezzo n (dPn) singularities including both D3 and D7 branes. We provide supersymmet- ric examples with three quark/lepton families and the gauge symmetries of the Standard, Left-Right Symmetric, Pati-Salam and Trinification models, without unwanted chiral ex- otics. We describe how the singularity structure leads to family symmetries governing the Yukawa couplings which may give mass hierarchies among the different generations. We outline how these models can be embedded into compact Calabi-Yau compactifications with LARGE volume moduli stabilisation, and state the minimal conditions for this to be possible. We study the general structure of soft supersymmetry breaking. At the singular- ity all leading order contributions to the soft terms (both gravity- and anomaly-mediation) vanish. We enumerate subleading contributions and estimate their magnitude. We also de- scribe model-independent physical implications of this scenario. These include the masses of anomalous and non-anomalous U(1)'s and the generic existence of a new hyperweak force under which leptons and/or quarks could be charged. We propose that such a gauge boson could be responsible for the ghost muon anomaly recently found at the Tevatron's CDF detector.
TL;DR: In this article, a previously unrecognized MOND effect that may act in the inner Solar system, and is due to the galactic acceleration gg = ηa 0 : a byproduct of the MOND external-field effect.
Abstract: I pinpoint a previously unrecognized MOND effect that may act in the inner Solar system, and is due to the galactic acceleration gg = ηa 0 : a byproduct of the MOND external-field effect. Predictions of the effect are not generic to the MOND paradigm, but depend on the particular MOND formulation at hand. However, the modified Poisson formulation, on which I concentrate, uniquely predicts a subtle anomaly that may be detected in planetary and spacecraft motions (and perhaps in other precision systems, such as binary pulsars), despite their very high accelerations, and even if the MOND interpolating function is arbitrarily close to unity at high accelerations. Near the Sun, this anomaly appears as a quadrupole field, with the acceleration at position u from the Sun being g a i (u) = -q a ij u j , with q a ij diagonal, axisymmetric and traceless: -2q a xx = -2q a yy = q a zz = q(η)(a 0 /R M ,), where R M = (M ⊙ G/a 0 ) 1/2 ≈ 8 × 10 3 au is the MOND transition radius of the Sun. The anomaly is described and analysed as the Newtonian field of the fictitious cloud of 'phantom matter' that hovers around the Sun. I find, for the relevant range of η values and for a range of interpolating functions, μ(x), values of 10 -2 ≤ -q ≤ 0.3, which turn out to be sensitive to the form of μ(x) around the MOND-to-Newtonian transition. This range verges on the present bounds from Solar system measurements. There might thus exist favourable prospects for either measuring the effect or constraining the theory and relevant parameters. Probing this anomaly may also help distinguish between modified-inertia and modified-gravity formulations of MOND. I also discuss briefly an anomaly that is generic to MOND in all its formulations, and competes with the quadrupole anomaly in the special case that 1 - μ(x) vanishes as x -3/2 as x → ∞.
TL;DR: A neutron or proton excess in nuclei leads to an isovector-vector mean field which, through its coupling to the quarks in a bound nucleon, implies a shift in the quark distributions with respect to the Bjorken scaling variable.
Abstract: A neutron or proton excess in nuclei leads to an isovector-vector mean-field which, through its coupling to the quarks in a bound nucleon, implies a shift in the quark distributions with respect to the Bjorken scaling variable. We show that this result leads to an additional correction to the NuTeV measurement of sin^2Theta_W. The sign of this correction is largely model independent and acts to reduce the NuTeV result. Explicit calculation within a covariant and confining Nambu Jona-Lasinio model predicts that this vector field correction accounts for approximately two-thirds of the NuTeV anomaly. We are therefore led to offer a new interpretation of the NuTeV measurement, namely, that it is further evidence for the medium modification of the bound nucleon wavefunction.
TL;DR: In this article, the classical structure of Dirac spinors on an arbitrary globally hyperbolic, Lorentzian spacetime, their formulation as a locally covariant quantum field theory, and the associated notion of a Hadamard state are discussed.
Abstract: We discuss from scratch the classical structure of Dirac spinors on an arbitrary globally hyperbolic, Lorentzian spacetime, their formulation as a locally covariant quantum field theory, and the associated notion of a Hadamard state. Eventually, we develop the notion of Wick polynomials for spinor fields, and we employ the latter to construct a covariantly conserved stress-energy tensor suited for back-reaction computations. We shall explicitly calculate its trace anomaly in particular.
TL;DR: A new anomaly is found, a bump and a peak, in the temperature dependence of the transverse acoustic impedance of superfluid 3He-B with a wall coated by several layers of 4He that agrees with a theoretical calculation using a partially specular wall boundary condition.
Abstract: We measured the transverse acoustic impedance of superfluid $^{3}\mathrm{He}\mathrm{\text{\ensuremath{-}}}\mathrm{B}$ with a wall coated by several layers of $^{4}\mathrm{He}$. The coating is known to enhance the specularity in quasiparticle scattering by the wall. We found a new anomaly, a bump and a peak, in the temperature dependence of the transverse acoustic impedance. This agrees with a theoretical calculation using a partially specular wall boundary condition. The new anomaly is shown to arise from a change in the surface density of states by coating and the scattering of thermally occupied surface bound states to other states. The change is towards the density of states of Majorana cone in the specular limit.
TL;DR: In this article, the classical structure of Dirac spinors on an arbitrary globally hyperbolic, Lorentzian spacetime, their formulation as a locally covariant quantum field theory, and the associated notion of a Hadamard state are discussed.
Abstract: We discuss from scratch the classical structure of Dirac spinors on an arbitrary globally hyperbolic, Lorentzian spacetime, their formulation as a locally covariant quantum field theory, and the associated notion of a Hadamard state. Eventually, we develop the notion of Wick polynomials for spinor fields, and we employ the latter to construct a covariantly conserved stress-energy tensor suited for back-reaction computations. We shall explicitly calculate its trace anomaly in particular.
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TL;DR: In this article, the trace of the heat kernel and the one-loop effective action for the generic differential operator are calculated to third order in the background curvatures: the Riemann curvature, the commutator curvature and the potential.
Abstract: The trace of the heat kernel and the one-loop effective action for the generic differential operator are calculated to third order in the background curvatures: the Riemann curvature, the commutator curvature and the potential. In the case of effective action, this is equivalent to a calculation (in the covariant form) of the one-loop vertices in all models of gravitating fields. The basis of nonlocal invariants of third order in the curvature is built, and constraints arising between these invariants in low-dimensional manifolds are obtained. All third-order form factors in the heat kernel and effective action are calculated, and several integral representations for them are obtained. In the case of effective action, this includes a specially generalized spectral representation used in applications to the expectation-value equations. The results for the heat kernel are checked by deriving all the known coefficients of the Schwinger-DeWitt expansion including $a_3$ and the cubic terms of $a_4$. The results for the effective action are checked by deriving the trace anomaly in two and four dimensions. In four dimensions, this derivation is carried out by several different techniques elucidating the mechanism by which the local anomaly emerges from the nonlocal action. In two dimensions, it is shown by a direct calculation that the series for the effective action terminates at second order in the curvature. The asymptotic behaviours of the form factors are calculated including the late-time behaviour in the heat kernel and the small-$\Box$ behaviour in the effective action. In quantum gravity, the latter behaviour contains the effects of vacuum radiation including the Hawking effect.
TL;DR: In this paper, an asymptotic expansion formula for matrix integrals, including oscillatory terms (derivatives of theta-functions) to all orders is proposed.
Abstract: We propose an asymptotic expansion formula for matrix integrals, including oscillatory terms (derivatives of theta-functions) to all orders. This formula is heuristically derived from the analogy between matrix integrals, and formal matrix models (combinatorics of discrete surfaces), after summing over filling fractions. The whole oscillatory series can also be resummed into a single theta function. We also remark that the coefficients of the theta derivatives, are the same as those which appear in holomorphic anomaly equations in string theory, i.e. they are related to degeneracies of Riemann surfaces. Moreover, the expansion presented here, happens to be independent of the choice of a background filling fraction.
TL;DR: In this paper, it was shown that there are only finitely many distinct semi-simple gauge groups and matter representations possible in consistent 6D chiral (1,0) supergravity theories with one tensor multiplet.
Abstract: We prove that there are only finitely many distinct semi-simple gauge groups and matter representations possible in consistent 6D chiral (1,0) supergravity theories with one tensor multiplet. The proof relies only on features of the low-energy theory; the consistency conditions we impose are that anomalies should be cancelled by the Green- Schwarz mechanism, and that the kinetic terms for all fields should be positive in some region of moduli space. This result does not apply to the case of the non-chiral (1,1) supergravities, which are not constrained by anomaly cancellation.
TL;DR: In this paper, the authors studied the large volume scenario on explicit, new, compact, four-modulus Calabi-Yau manifolds and showed that the Freed-Witten anomaly on non-spin cycles and the K?hler cone conditions imposes severe constraints on the models Nevertheless, they were able to create setups where the constraints are solved, and up to three moduli are stabilized.
Abstract: We study the `Large Volume Scenario' on explicit, new, compact, four-modulus Calabi-Yau manifolds We pay special attention to the chirality problem pointed out by Blumenhagen, Moster and Plauschinn Namely, we thoroughly analyze the possibility of generating neutral, non-perturbative superpotentials from Euclidean D3-branes in the presence of chirally intersecting D7-branes We find that taking proper account of the Freed-Witten anomaly on non-spin cycles and of the K?hler cone conditions imposes severe constraints on the models Nevertheless, we are able to create setups where the constraints are solved, and up to three moduli are stabilized