Semiorthogonal decompositions of derived categories of equivariant coherent sheaves

Let X be an algebraic variety with an action of an algebraic group G. Suppose X has a full exceptional collection of sheaves, and these sheaves are invariant under the action of the group. We construct a semiorthogonal decomposition of bounded derived category of G-equivariant coherent sheaves on X into components, equivalent to derived categories of twisted representations of the group. If the group is finite or reductive over the algebraically closed field of zero characteristic, this gives a full exceptional collection in the derived equivariant category. We apply our results to particular varieties such as projective spaces, quadrics, Grassmanians and Del Pezzo surfaces.Comment: 28 pages, uses XY-pi

Interaction between spin and Abrikosov vortices in doped topological insulators

In the topological superconductor with the nematic superconductivity in $E_u$ representation, it is possible to have different types of vortices. One is associated with the vorticity in the particle-hole space and corresponds to the Abrikosov vortex. Another type corresponds to the vorticity in the spin space and is called spin vortex. We study the interaction of the Abrikosov vortex with the spin vortices. We derive the free energy of the sample with the Abrikosov and the strain-induced spin vortices using the Ginzburg-Landau approach for the two-component superconducting order parameter. We calculate the critical strain at which the spin vortex is formed. We show that the spin vortex and the Abrikosov vortex attract to each other and, as a result, they have a common core. We show that there are no zero-energy states (Majorana fermions) localized near the common vortex core of the Abrikosov vortex and the spin vortex of any type. Possible experimental realization is discussed

Magnetization control of the nematicity direction and nodal points in a superconducting doped topological insulator

We study the effects of magnetization on the properties of the doped topological insulator with nematic superconductivity. We found that the direction of the in-plane magnetization fixes the direction of the nematicity in the system. The chiral state is more favorable than the nematic state for large values of out-of-plane magnetization. Overall, the critical temperature of the nematic state is resilient against magnetization. We explore the spectrum of the system with the pinned direction of the nematic order parameter $\Delta_{y}$ in details. Without magnetization, there is a full gap in the spectrum. At strong enough out-of-plane $m_z$ or orthogonal in-plane $m_x$ magnetization, the spectrum is closed at the nodal points that are split by the magnetization. Flat Majorana surface states connect such split bulk nodal points. Parallel magnetization $m_y$ lifts nodal points and opens a full gap in the spectrum. We discuss relevant experiments and propose experimental verifications of our theory

Lectures on BCOV holomorphic anomaly equations

The present article surveys some mathematical aspects of the BCOV holomorphic anomaly equations introduced by Bershadsky, Cecotti, Ooguri and Vafa. It grew from a series of lectures the authors gave at the Fields Institute in the Thematic Program of Calabi-Yau Varieties in the fall of 2013.Comment: reference added, typos correcte

Towards Integrability of Topological Strings I: Three-forms on Calabi-Yau manifolds

The precise relation between Kodaira-Spencer path integral and a particular wave function in seven dimensional quadratic field theory is established. The special properties of three-forms in 6d, as well as Hitchin's action functional, play an important role. The latter defines a quantum field theory similar to Polyakov's formulation of 2d gravity; the curious analogy with world-sheet action of bosonic string is also pointed out.Comment: 31 page

Sums over Graphs and Integration over Discrete Groupoids

We show that sums over graphs such as appear in the theory of Feynman diagrams can be seen as integrals over discrete groupoids. From this point of view, basic combinatorial formulas of the theory of Feynman diagrams can be interpreted as pull-back or push-forward formulas for integrals over suitable groupoids.Comment: 27 pages, 4 eps figures; LaTeX2e; uses Xy-Pic. Some ambiguities fixed, and several proofs simplifie

Improvement of nutrient absorption may enhance systemic oxidative stress in cystic fibrosis patients.

BACKGROUND: The life expectancy of patients with cystic fibrosis (CF) is largely dependent on the pulmonary disease severity and progress. Malnutrition may be an important complicating factor in active and chronic lung disease. AIMS: The focus of this study was to investigate several inflammatory markers in pancreatic-insufficient CF patients with different enzyme treatment regimens. METHODS: CF patients with pancreatic insufficiency were examined at a time of symptomatic exacerbation of their lung disease. Group A (n = 11) regularly received microspheric enzymes. Group B (n = 8) were treated with enzymes during the hospitalization period only and demonstrated the presence of malnutrition. Inflammatory markers in the sputa (neutrophil elastase activity, interleukin-8 and tumour necrosis factor-alpha levels) and in the peripheral blood (plasma malondialdehyde (MDA), lymphocyte response to PHA, and the cell sensitivity to steroid suppression) have been investigated. RESULTS: During acute lung exacerbation, group B demonstrated reduced levels of lymphocyte proliferation. This parameter was normalized after combined antibiotic and pancreatic enzyme therapy. Simultaneously, plasma MDA in group B markedly increased following treatment. For this group, a significant positive linear association between values of plasma MDA and lymphocyte proliferation has been observed. For group A, neither the same correlation nor changes in MDA levels and lymphocyte proliferation have been found. CONCLUSIONS: Our data indicate that acute lung exacerbation in malnourished CF patients may be associated with alteration in T-lymphocyte activity. Adequate therapy normalizes lymphocyte function but results in systemic oxidative stress