Quantum cohomology of the cotangent bundle of a flag variety as a Yangian Bethe algebra

We interpret the equivariant cohomology algebra H^*_{GL_n\times\C^*}(T^*F_\lambda;\C) of the cotangent bundle of a partial flag variety F_\lambda parametrizing chains of subspaces 0=F_0\subset F_1\subset\dots\subset F_N =\C^n, \dim F_i/F_{i-1}=\lambda_i, as the Yangian Bethe algebra of the gl_N-weight subspace of a gl_N Yangian module. Under this identification the dynamical connection of [TV1] turns into the quantum connection of [BMO] and [MO]. As a result of this identification we describe the algebra of quantum multiplication on H^*_{GL_n\times\C^*}(T^*F_\lambda;\C) as the algebra of functions on fibers of a discrete Wronski map. In particular this gives generators and relations of that algebra. This identification also gives us hypergeometric solutions of the associated quantum differential equation. That fact manifests the Landau-Ginzburg mirror symmetry for the cotangent bundle of the flag variety.Comment: Latex, 45 pages, references added, Conjecture 7.10 is now Theorem 7.10, Theorem 7.13 adde

Chiral differential operators via via quantization of the holomorphic σ -model

ISBN 978-2-85629-919-7 This work would not have been possible without the support of several organizations. First, it was the open and stimulating atmosphere of the Max Planck Institute for Mathematics that made it so easy to begin our collaboration. Moreover, it is through the MPIM’s great generosity that we were able to continue work and finish the paper during several visits by VG and BW. Second, we benefited from the support and convivial setting of the Hausdorff Institute for Mathematics and its Trimester Program “Homotopy theory, manifolds, and field theories” during the summer of 2015. Third, the Oberwolfach Workshop “Factorization Algebras and Functorial Field Theories” in May 2016 allowed us all to gather in person and finish important discussions. In addition, OG enjoyed support from the National Science Foundation as a postdoctoral fellow under Award DMS-1204826, and BW enjoyed support as a graduate student research fellow under Award DGE-1324585. Finally, this research was carried out, in part, within the HSE University Basic Research Program and funded by the Russian Academic Excellence Project 5–100. For OG there is a large cast of mathematicians whose questions, conversation, and interest have kept these issues alive and provided myriad useful insights that are now hard to enumerate in detail. He thanks Kevin Costello for introducing him to the βγ system in graduate school—and for innumerable discussions since—as well as Dan Berwick-Evans, Ryan Grady, and Yuan Shen for grappling collaboratively with [15] throughout that period. Si Li’s many insights and questions have shaped this work substantially. Matt Szczesny’s guidance at the Northwestern CDO Workshop was crucial; his subsequent encouragement is much appreciated. OG would also like to thank Stephan Stolz and Peter Teichner for the still-running conversation about conformal field theory that influences strongly his approach to the subject. Finally, he thanks André Henriques, John Francis, and Scott Carnahan for letting him eavesdrop as they chatted about CDOs over a decade ago. BW feels fortunate to have stepped into this community early in his graduate work and has benefited from the support of many of the individuals mentioned above. First and foremost, he thanks his adviser Kevin Costello for guidance and Si Li for helping him to harness Feynman diagrams in the context of the BV formalism. He also thanks Ryan Grady, Matt Szczesny, and Stephan Stolz for invitations to talk about this project as well as valuable input on various aspects of it. In addition, numerous discussions with Dylan William Butson, Chris Elliott, and Philsang Yoo about perturbative QFT have informed his work. Finally, we would like to thank Matt Szczesny and James Ladouce for pointing out numerous typos and providing feedback on an earlier draft of this paper.Peer reviewedPostprin

Invariant chiral differential operators and the W_3 algebra

Attached to a vector space V is a vertex algebra S(V) known as the beta-gamma system or algebra of chiral differential operators on V. It is analogous to the Weyl algebra D(V), and is related to D(V) via the Zhu functor. If G is a connected Lie group with Lie algebra g, and V is a linear G-representation, there is an action of the corresponding affine algebra on S(V). The invariant space S(V)^{g[t]} is a commutant subalgebra of S(V), and plays the role of the classical invariant ring D(V)^G. When G is an abelian Lie group acting diagonally on V, we find a finite set of generators for S(V)^{g[t]}, and show that S(V)^{g[t]} is a simple vertex algebra and a member of a Howe pair. The Zamolodchikov W_3 algebra with c=-2 plays a fundamental role in the structure of S(V)^{g[t]}.Comment: a few typos corrected, final versio

A heterotic sigma model with novel target geometry

We construct a (1,2) heterotic sigma model whose target space geometry consists of a transitive Lie algebroid with complex structure on a Kaehler manifold. We show that, under certain geometrical and topological conditions, there are two distinguished topological half--twists of the heterotic sigma model leading to A and B type half--topological models. Each of these models is characterized by the usual topological BRST operator, stemming from the heterotic (0,2) supersymmetry, and a second BRST operator anticommuting with the former, originating from the (1,0) supersymmetry. These BRST operators combined in a certain way provide each half--topological model with two inequivalent BRST structures and, correspondingly, two distinct perturbative chiral algebras and chiral rings. The latter are studied in detail and characterized geometrically in terms of Lie algebroid cohomology in the quasiclassical limit.Comment: 83 pages, no figures, 2 references adde

Two-Dimensional Twisted Sigma Models, the Mirror Chiral de Rham Complex, and Twisted Generalised Mirror Symmetry

In this paper, we study the perturbative aspects of a "B-twisted" two-dimensional $(0,2)$ heterotic sigma model on a holomorphic gauge bundle $\mathcal E$ over a complex, hermitian manifold $X$. We show that the model can be naturally described in terms of the mathematical theory of ``Chiral Differential Operators". In particular, the physical anomalies of the sigma model can be reinterpreted as an obstruction to a global definition of the associated sheaf of vertex superalgebras derived from the free conformal field theory describing the model locally on $X$. In addition, one can also obtain a novel understanding of the sigma model one-loop beta function solely in terms of holomorphic data. At the $(2,2)$ locus, one can describe the resulting half-twisted variant of the topological B-model in terms of a $\it{mirror}$ "Chiral de Rham complex" (or CDR) defined by Malikov et al. in \cite{GMS1}. Via mirror symmetry, one can also derive various conjectural expressions relating the sheaf cohomology of the mirror CDR to that of the original CDR on pairs of Calabi-Yau mirror manifolds. An analysis of the half-twisted model on a non-K\"ahler group manifold with torsion also allows one to draw conclusions about the corresponding sheaves of CDR (and its mirror) that are consistent with mathematically established results by Ben-Bassat in \cite{ben} on the mirror symmetry of generalised complex manifolds. These conclusions therefore suggest an interesting relevance of the sheaf of CDR in the recent study of generalised mirror symmetry.Comment: 97 pages. Companion paper to hep-th/0604179. Published versio

Quantum cohomology of the cotangent bundle of a flag variety as a Yangian Bethe algebra

We interpret the equivariant cohomology algebra H∗GLn×C*(T*Fλ;C) of the cotangent bundle of a partial flag variety Fλ parametrizing chains of subspaces 0 = F0 ⊂ F1 ⊂ · · · ⊂ FN = Cn, dim Fi/Fi−1 = λi, as the Yangian Bethe algebra B∞( 1DV−λ) of the glN-weight subspace 1/DV−λ of a Y (glN)-module 1/DV−. Under this identification the dynamical connection of [TV1] turns into the quantum connection of [BMO] and [MO]. As a result of this identification we describe the algebra of quantum multiplication on H∗GLn×C*(T ∗Fλ;C) as the algebra of functions on fibers of a discrete Wronski map. In particular this gives generators and relations of that algebra. This identification also gives us hypergeometric solutions of the associated quantum differential equation. That fact manifests the Landau-Ginzburg mirror symmetry for the cotangent bundle of the flag variety

Impact of Production Pathway on Nanoporosity of Carbonaceous Sorbents for CO2 Adsorption

Climate change requires immediate action from humanity with Carbon Capture and Storage (CCS) standing out as one of the prominent mitigation techniques. Adsorption CCS using carbonaceous nanoporous sorbents has been shown to be a promising route for industrial decarbonization. Such sorbents are often derived from organic waste, with the production pathway consisting of different steps, namely, carbonization, pelletization (with various binders) and activation. The latter two steps, however, could vary in their order, i.e. activation of the pellet versus the pelletization of the activated powder. Herein, both of these approaches have been conducted and the impact of the production pathway (as well as the presence of the binder itself) on the nano-structure of the material has been examined and compared to the “baseline-case” of the non-activated carbon (both powder and pellet). The samples were analyzed via Proximate Analysis, Fourier-Transform Infrared Spectroscopy and Scanning Electron Microscopy. CO2 adsorption was evaluated via Thermogravimetric Analysis (TGA). Further, the mechanical properties of the nanoporous pellets were studied.10.13039/501100000266-Engineering and Physical Sciences Research Council (EPSRC) UK Carbon Capture and Storage Research Centre (EP/W002841/1) through the flexible funded research programme “Investigation of Environmental and Operational Challenges of Adsorbents Synthesised from Industrial Grade Biomass Combustion Residues”; EPSRC Impact Accelerator Award (2022

Fully Integrated Glass Microfluidic Device for Performing High-Efficiency Capillary Electrophoresis and Electrospray Ionization Mass Spectrometry

A microfabricated device has been developed in which electrospray ionization is performed directly from the corner of a rectangular glass microchip. The device allows highly efficient electrokinetically driven separations to be coupled directly to a mass spectrometer (MS) without the use of external pressure sources or the insertion of capillary spray tips. An electrokinetic-based hydraulic pump is integrated on the chip that directs eluting materials to the monolithically integrated spray tip. A positively charged surface coating, PolyE-323, is used to prevent surface interactions with peptides and proteins and to reverse the electroosmotic flow in the separation channel. The device has been used to perform microchip CE-MS analysis of peptides and proteins with efficiencies over 200 000 theoretical plates (1 000 000 plates/m). The sensitivity and stability of the microfabricated ESI source were found to be comparable to that of commercial pulled fused-silica capillary nanospray sources

Open and Hidden Charm Production in 920 GeV Proton-Nucleus Collisions

The HERA-B collaboration has studied the production of charmonium and open charm states in collisions of 920 GeV protons with wire targets of different materials. The acceptance of the HERA-B spectrometer covers negative values of xF up to xF=-0.3 and a broad range in transverse momentum from 0.0 to 4.8 GeV/c. The studies presented in this paper include J/psi differential distributions and the suppression of J/psi production in nuclear media. Furthermore, production cross sections and cross section ratios for open charm mesons are discussed.Comment: 5 pages, 9 figures, to be published in the proceedings of the 6th International Conference on Hyperons, Charm & Beauty Hadrons (BEACH04), Chicago, IL, June 27 - July 3, 200

Inclusive V0V^0 Production Cross Sections from 920 GeV Fixed Target Proton-Nucleus Collisions

Inclusive differential cross sections $d\sigma_{pA}/dx_F$ and $d\sigma_{pA}/dp_t^2$ for the production of \kzeros, \lambdazero, and \antilambda particles are measured at HERA in proton-induced reactions on C, Al, Ti, and W targets. The incident beam energy is 920 GeV, corresponding to $\sqrt {s} = 41.6$ GeV in the proton-nucleon system. The ratios of differential cross sections \rklpa and \rllpa are measured to be $6.2\pm 0.5$ and $0.66\pm 0.07$, respectively, for \xf $\approx-0.06$. No significant dependence upon the target material is observed. Within errors, the slopes of the transverse momentum distributions $d\sigma_{pA}/dp_t^2$ also show no significant dependence upon the target material. The dependence of the extrapolated total cross sections $\sigma_{pA}$ on the atomic mass $A$ of the target material is discussed, and the deduced cross sections per nucleon $\sigma_{pN}$ are compared with results obtained at other energies.Comment: 17 pages, 7 figures, 5 table