Heterotic Sigma Models with N=2 Space-Time Supersymmetry

We study the non-linear sigma model realization of a heterotic vacuum with N=2 space-time supersymmetry. We examine the requirements of (0,2) + (0,4) world-sheet supersymmetry and show that a geometric vacuum must be described by a principal two-torus bundle over a K3 manifold.Comment: 20 pages, uses xy-pic; v3: typos corrected, reference added, discussion of constraints on Hermitian form modifie

Weierstrass meets Enriques

We study in detail the degeneration of K3 to T^4/Z_2. We obtain an explicit embedding of the lattice of collapsed cycles of T^4/Z_2 into the lattice of integral cycles of K3 in two different ways. Our first method exploits the duality to the heterotic string on T^3. This allows us to describe the degeneration in terms of Wilson lines. Our second method is based on the blow-up of T^4/Z_2. From this blow-up, we directly construct the full lattice of integral cycles of K3. Finally, we use our results to describe the action of the Enriques involution on elliptic K3 surfaces, finding that a Weierstrass model description is consistent with the Enriques involution only in the F-theory limit.Comment: 35 pages, 9 figure

Heterotic type IIA duality with fluxes - towards the complete story

In this paper we study the heterotic type IIA duality when fluxes are turned on. We show that many of the known fluxes are dual to each other and claim that certain fluxes on the heterotic side require that the type IIA picture is lifted to M or even F-theory compactifications with geometric fluxes.Comment: 31 pages, references adde

D-brane Charges in Gravitational Duals of 2+1 Dimensional Gauge Theories and Duality Cascades

We perform a systematic analysis of the D-brane charges associated with string theory realizations of d=3 gauge theories, focusing on the examples of the N=4 supersymmetric U(N)xU(N+M) Yang-Mills theory and the N=3 supersymmetric U(N)xU(N+M) Yang-Mills-Chern-Simons theory. We use both the brane construction of these theories and their dual string theory backgrounds in the supergravity approximation. In the N=4 case we generalize the previously known gravitational duals to arbitrary values of the gauge couplings, and present a precise mapping between the gravity and field theory parameters. In the N=3 case, which (for some values of N and M) flows to an N=6 supersymmetric Chern-Simons-matter theory in the IR, we argue that the careful analysis of the charges leads to a shift in the value of the B-field in the IR solution by 1/2, in units where its periodicity is one, compared to previous claims. We also suggest that the N=3 theories may exhibit, for some values of N and M, duality cascades similar to those of the Klebanov-Strassler theory.Comment: 47 pages, 9 figures; minor changes, references adde

Spinning strings and integrable spin chains in the AdS/CFT correspondence

In this introductory review we discuss dynamical tests of the AdS_5 x S^5 string/N=4 super Yang-Mills duality. After a brief introduction to AdS/CFT we argue that semiclassical string energies yield information on the quantum spectrum of the string in the limit of large angular momenta on the S^5. The energies of the folded and circular spinning string solutions rotating on a S^3 within the S^5 are derived, which yield all loop predictions for the dual gauge theory scaling dimensions. These follow from the eigenvalues of the dilatation operator of N=4 super Yang-Mills in a minimal SU(2) subsector and we display its reformulation in terms of a Heisenberg s=1/2 spin chain along with the coordinate Bethe ansatz for its explicit diagonalization. In order to make contact to the spinning string energies we then study the thermodynamic limit of the one-loop gauge theory Bethe equations and demonstrate the matching with the folded and closed string result at this loop order. Finally the known gauge theory results at higher-loop orders are reviewed and the associated long-range spin chain Bethe ansatz is introduced, leading to an asymptotic all-loop conjecture for the gauge theory Bethe equations. This uncovers discrepancies at the three-loop order between gauge theory scaling dimensions and string theory energies and the implications of this are discussed. Along the way we comment on further developments and generalizations of the subject and point to the relevant literature.Comment: 40 pages, invited contribution to Living Reviews in Relativity. v2: improvements in the text and references adde

Super Weyl invariance: BPS equations from heterotic worldsheets

It is well-known that the beta functions on a string worldsheet correspond to the target space equations of motion, e.g. the Einstein equations. We show that the BPS equations, i.e. the conditions of vanishing supersymmetry variations of the space-time fermions, can be directly derived from the worldsheet. To this end we consider the RNS-formulation of the heterotic string with (2,0) supersymmetry, which describes a complex torsion target space that supports a holomorphic vector bundle. After a detailed account of its quantization and renormalization, we establish that the cancellation of the Weyl anomaly combined with (2,0) finiteness implies the heterotic BPS conditions: At the one loop level the geometry is required to be conformally balanced and the gauge background has to satisfy the Hermitean Yang-Mills equations.Comment: 1+31 pages LaTeX, 5 figures; final version, discussion relation Weyl invariance and (2,0) finiteness extended, typos correcte

Fluxes and Warping for Gauge Couplings in F-theory

We compute flux-dependent corrections in the four-dimensional F-theory effective action using the M-theory dual description. In M-theory the 7-brane fluxes are encoded by four-form flux and modify the background geometry and Kaluza-Klein reduction ansatz. In particular, the flux sources a warp factor which also depends on the torus directions of the compactification fourfold. This dependence is crucial in the derivation of the four-dimensional action, although the torus fiber is auxiliary in F-theory. In M-theory the 7-branes are described by an infinite array of Taub-NUT spaces. We use the explicit metric on this geometry to derive the locally corrected warp factor and M-theory three-from as closed expressions. We focus on contributions to the 7-brane gauge coupling function from this M-theory back-reaction and show that terms quadratic in the internal seven-brane flux are induced. The real part of the gauge coupling function is modified by the M-theory warp factor while the imaginary part is corrected due to a modified M-theory three-form potential. The obtained contributions match the known weak string coupling result, but also yield additional terms suppressed at weak coupling. This shows that the completion of the M-theory reduction opens the way to compute various corrections in a genuine F-theory setting away from the weak string coupling limit.Comment: 46 page

Recycled gabbro signature in hotspot magmas unveiled by plume–ridge interactions

Lavas erupted within plate interiors above upwelling mantle plumes have chemical signatures that are distinct from midocean ridge lavas. When a plume interacts with a mid-ocean ridge, the compositions of both their lavas changes, but there is no consensus as to how this interaction occurs1–3. For the past 15 Myr, the Pacific–Antarctic mid-ocean ridge has been approaching the Foundation hotspot4 and erupted lavas have formed seamounts. Here we analyse the noble gas isotope and trace element signature of lava samples collected from the seamounts. We find that both intraplate and on-axis lavas have noble gas isotope signatures consistent with the contribution from a primitive plume source. In contrast, nearaxis lavas show no primitive noble gas isotope signatures, but are enriched in strontium and lead, indicative of subducted former oceanic lower crust melting within the plume source5–7. We propose that, in a near-ridge setting, primitive, plumesourced magmas formed deep in the plume are preferentially channelled to and erupted at the ridge-axis. The remaining residue continues to rise and melt, forming the near-axis seamounts. With the deep melts removed, the geochemical signature of subduction contained within the residue becomes apparent. Lavas with strontium and lead enrichments are found worldwide where plumes meet mid-ocean ridges6–8, suggesting that subducted lower crust is an important but previously unrecognised plume component

Domestic Violence and its Determinants: A cross-sectional study among women in a slum of Kolkata

Background: Violence against women is one of the major public health and human rights issue in the world today which is prevalent in all human societies irrespective of religion, socioeconomic status, and culture. Therefore, recognized as a significant barrier to women empowerment and their health. Aims & Objectives: The aim of this study was to find out the extent of different type of domestic violence and to identify various risk factors for domestic violence against married women. Material & Methods: The present study is a community based cross-sectional study carried out in a slum of Kolkata. Simple random sampling technique was used for the selection of the samples. The study participants were interviewed using a pretested semi-structured questionnaire. Result: 97 married women participated in the study. 32.9% of the study population reported some form of domestic violence. In a logistic regression analysis, significant association was found between domestic violence and alcohol abuse by the spouse, level of education of the spouse, per capita income and occupation of the women. Conclusion: This study confirms, high prevalence of all forms of violence against women, which underscores the need for policy makers to increase their recognition of domestic violence as a critical target in public health concern

Nf2/Merlin controls spinal cord neural progenitor function in a Rac1/ErbB2-dependent manner

Objective: Individuals with the neurofibromatosis type 2 (NF2) cancer predisposition syndrome develop spinal cord glial tumors (ependymomas) that likely originate from neural progenitor cells. Whereas many spinal ependymomas exhibit indolent behavior, the only treatment option for clinically symptomatic tumors is surgery. In this regard, medical therapies are unfortunately lacking due to an incomplete understanding of the critical growth control pathways that govern the function of spinal cord (SC) neural progenitor cells (NPCs). Methods: To identify potential therapeutic targets for these tumors, we leveraged primary mouse Nf2-deficient spinal cord neural progenitor cells. Results: We demonstrate that the Nf2 protein, merlin, negatively regulates spinal neural progenitor cell survival and glial differentiation in an ErbB2-dependent manner, and that NF2-associated spinal ependymomas exhibit increased ErbB2 activation. Moreover, we show that Nf2-deficient SC NPC ErbB2 activation results from Rac1-mediated ErbB2 retention at the plasma membrane. Significance: Collectively, these findings establish ErbB2 as a potential rational therapeutic target for NF2-associated spinal ependymoma