On the classification of Kahler-Ricci solitons on Gorenstein del Pezzo surfaces

We give a classification of all pairs (X,v) of Gorenstein del Pezzo surfaces X and vector fields v which are K-stable in the sense of Berman-Nystrom and therefore are expected to admit a Kahler-Ricci solition. Moreover, we provide some new examples of Fano threefolds admitting a Kahler-Ricci soliton.Comment: 21 pages, ancillary files containing calculations in SageMath; minor correction

Kahler-Einstein metrics emerging from free fermions and statistical mechanics

We propose a statistical mechanical derivation of Kahler-Einstein metrics, i.e. solutions to Einstein's vacuum field equations in Euclidean signature (with a cosmological constant) on a compact Kahler manifold X. The microscopic theory is given by a canonical free fermion gas on X whose one-particle states are pluricanonical holomorphic sections on X (coinciding with higher spin states in the case of a Riemann surface). A heuristic, but hopefully physically illuminating, argument for the convergence in the thermodynamical (large N) limit is given, based on a recent mathematically rigorous result about exponentially small fluctuations of Slater determinants. Relations to effective bosonization and the Yau-Tian-Donaldson program in Kahler geometry are pointed out. The precise mathematical details will be investigated elsewhere.Comment: v1: 22 pages v2: 25 pages. The relation to quantum gravity has been further developed by working over the moduli space of all complex structures. Relations to Donaldson's program pointed out. References adde

Instantons and Killing spinors

We investigate instantons on manifolds with Killing spinors and their cones. Examples of manifolds with Killing spinors include nearly Kaehler 6-manifolds, nearly parallel G_2-manifolds in dimension 7, Sasaki-Einstein manifolds, and 3-Sasakian manifolds. We construct a connection on the tangent bundle over these manifolds which solves the instanton equation, and also show that the instanton equation implies the Yang-Mills equation, despite the presence of torsion. We then construct instantons on the cones over these manifolds, and lift them to solutions of heterotic supergravity. Amongst our solutions are new instantons on even-dimensional Euclidean spaces, as well as the well-known BPST, quaternionic and octonionic instantons.Comment: 40 pages, 2 figures v2: author email addresses and affiliations adde

Torus equivariant K-stability

It is conjectured that to test the K-polystability of a polarised variety it is enough to consider test-configurations which are equivariant with respect to a torus in the automorphism group. We prove partial results towards this conjecture. We also show that it would give a new proof of the K-polystability of constant scalar curvature polarised manifolds

Yang-Mills instantons and dyons on homogeneous G_2-manifolds

We consider Lie G-valued Yang-Mills fields on the space R x G/H, where G/H is a compact nearly K"ahler six-dimensional homogeneous space, and the manifold R x G/H carries a G_2-structure. After imposing a general G-invariance condition, Yang-Mills theory with torsion on R x G/H is reduced to Newtonian mechanics of a particle moving in R^6, R^4 or R^2 under the influence of an inverted double-well-type potential for the cases G/H = SU(3)/U(1)xU(1), Sp(2)/Sp(1)xU(1) or G_2/SU(3), respectively. We analyze all critical points and present analytical and numerical kink- and bounce-type solutions, which yield G-invariant instanton configurations on those cosets. Periodic solutions on S^1 x G/H and dyons on iR x G/H are also given.Comment: 1+26 pages, 14 figures, 6 miniplot

Numerical Hermitian Yang-Mills Connections and Kahler Cone Substructure

We further develop the numerical algorithm for computing the gauge connection of slope-stable holomorphic vector bundles on Calabi-Yau manifolds. In particular, recent work on the generalized Donaldson algorithm is extended to bundles with Kahler cone substructure on manifolds with h^{1,1}>1. Since the computation depends only on a one-dimensional ray in the Kahler moduli space, it can probe slope-stability regardless of the size of h^{1,1}. Suitably normalized error measures are introduced to quantitatively compare results for different directions in Kahler moduli space. A significantly improved numerical integration procedure based on adaptive refinements is described and implemented. Finally, an efficient numerical check is proposed for determining whether or not a vector bundle is slope-stable without computing its full connection.Comment: 38 pages, 10 figure

Interactions in vivo between the Vif protein of HIV-1 and the precursor (Pr55GAG) of the virion nucleocapsid proteins

The abnormality of viral core structure seen in vif-defective HIV-1 grown in PBMCs has suggested a role for Vif in viral morphogenesis. Using an in vivo mammalian two-hybrid assay, the interaction between Vif and the precursor (Pr55GAG) of the virion nucleocapsid proteins has been analysed. This revealed the amino-terminal (aa 1–22) and central (aa 70–100) regions of Vif to be essential for its interaction with Pr55GAG, but deletion of the carboxy-terminal (aa 158–192) region of the protein had only a minor effect on its interaction. Initial deletion studies carried out on Pr55GAG showed that a 35-amino-acid region of the protein bridging the MA(p17)–CA(p24) junction was essential for its ability to interact with Vif. Site-directed mutagenesis of a conserved tryptophan (Trp21) near the amino terminus of Vif showed it to be important for the interaction with Pr55GAG. By contrast, mutagenesis of the highly conserved YLAL residues forming part of the BC-box motif, shown to be important in Vif promoting degradation of APOBEC3G/3F, had little or no effect on the Vif–Pr55GAG interaction

Contact Manifolds, Contact Instantons, and Twistor Geometry

Recently, Kallen and Zabzine computed the partition function of a twisted supersymmetric Yang-Mills theory on the five-dimensional sphere using localisation techniques. Key to their construction is a five-dimensional generalisation of the instanton equation to which they refer as the contact instanton equation. Subject of this article is the twistor construction of this equation when formulated on K-contact manifolds and the discussion of its integrability properties. We also present certain extensions to higher dimensions and supersymmetric generalisations.Comment: v3: 28 pages, clarifications and references added, version to appear in JHE

Metabolic control of BRISC–SHMT2 assembly regulates immune signalling

Serine hydroxymethyltransferase 2 (SHMT2) regulates one-carbon transfer reactions that are essential for amino acid and nucleotide metabolism, and uses pyridoxal-5′-phosphate (PLP) as a cofactor. Apo SHMT2 exists as a dimer with unknown functions, whereas PLP binding stabilizes the active tetrameric state. SHMT2 also promotes inflammatory cytokine signalling by interacting with the deubiquitylating BRCC36 isopeptidase complex (BRISC), although it is unclear whether this function relates to metabolism. Here we present the cryo-electron microscopy structure of the human BRISC–SHMT2 complex at a resolution of 3.8 Å. BRISC is a U-shaped dimer of four subunits, and SHMT2 sterically blocks the BRCC36 active site and inhibits deubiquitylase activity. Only the inactive SHMT2 dimer—and not the active PLP-bound tetramer—binds and inhibits BRISC. Mutations in BRISC that disrupt SHMT2 binding impair type I interferon signalling in response to inflammatory stimuli. Intracellular levels of PLP regulate the interaction between BRISC and SHMT2, as well as inflammatory cytokine responses. These data reveal a mechanism in which metabolites regulate deubiquitylase activity and inflammatory signalling

Numerical Hermitian Yang-Mills Connections and Vector Bundle Stability in Heterotic Theories

A numerical algorithm is presented for explicitly computing the gauge connection on slope-stable holomorphic vector bundles on Calabi-Yau manifolds. To illustrate this algorithm, we calculate the connections on stable monad bundles defined on the K3 twofold and Quintic threefold. An error measure is introduced to determine how closely our algorithmic connection approximates a solution to the Hermitian Yang-Mills equations. We then extend our results by investigating the behavior of non slope-stable bundles. In a variety of examples, it is shown that the failure of these bundles to satisfy the Hermitian Yang-Mills equations, including field-strength singularities, can be accurately reproduced numerically. These results make it possible to numerically determine whether or not a vector bundle is slope-stable, thus providing an important new tool in the exploration of heterotic vacua.Comment: 52 pages, 15 figures. LaTex formatting of figures corrected in version 2