Operations on integral lifts of K(n)

This very rough sketch is a sequel to arXiv:1808.08587; it presents evidence that operations on lifts of the functors K(n) to cohomology theories with values in modules over valuation rings of local number fields, indexed by Lubin-Tate groups of such fields, are extensions of the groups of automorphisms of the indexing group laws, by the exterior algebras on the normal bundle to the orbits of the group laws in the space of lifts.Comment: \S 2.0 hopefully less cryptic. To appear in the proceedings of the 2015 Nagoya conference honoring T Ohkawa. Comments very welcome

Poincare isomorphism in K-theory on manifolds with edges

The aim of this paper is to construct the Poincare isomorphism in K-theory on manifolds with edges. We show that the Poincare isomorphism can naturally be constructed in the framework of noncommutative geometry. More precisely, to a manifold with edges we assign a noncommutative algebra and construct an isomorphism between the K-group of this algebra and the K-homology group of the manifold with edges viewed as a compact topological space.Comment: 15 pages, no figure

Muon capture on light nuclei

This work investigates the muon capture reactions 2H(\mu^-,\nu_\mu)nn and 3He(\mu^-,\nu_\mu)3H and the contribution to their total capture rates arising from the axial two-body currents obtained imposing the partially-conserved-axial-current (PCAC) hypothesis. The initial and final A=2 and 3 nuclear wave functions are obtained from the Argonne v_{18} two-nucleon potential, in combination with the Urbana IX three-nucleon potential in the case of A=3. The weak current consists of vector and axial components derived in chiral effective field theory. The low-energy constant entering the vector (axial) component is determined by reproducting the isovector combination of the trinucleon magnetic moment (Gamow-Teller matrix element of tritium beta-decay). The total capture rates are 393.1(8) s^{-1} for A=2 and 1488(9) s^{-1} for A=3, where the uncertainties arise from the adopted fitting procedure.Comment: 6 pages, submitted to Few-Body Sys

On Free Quotients of Complete Intersection Calabi-Yau Manifolds

In order to find novel examples of non-simply connected Calabi-Yau threefolds, free quotients of complete intersections in products of projective spaces are classified by means of a computer search. More precisely, all automorphisms of the product of projective spaces that descend to a free action on the Calabi-Yau manifold are identified.Comment: 39 pages, 3 tables, LaTe

Weyl Equation and (Non)-Commutative SU(n+1) BPS Monopoles

We apply the ADHMN construction to obtain the SU(n+1)(for generic values of n) spherically symmetric BPS monopoles with minimal symmetry breaking. In particular, the problem simplifies by solving the Weyl equation, leading to a set of coupled equations, whose solutions are expressed in terms of the Whittaker functions. Next, this construction is generalized for non-commutative SU(n+1) BPS monopoles, where the corresponding solutions are given in terms of the Heun B functions.Comment: 16 pages, Latex. Few typos corrected, version to appear in JHE

Surface Operators in N=2 4d Gauge Theories

N=2 four dimensional gauge theories admit interesting half BPS surface operators preserving a (2,2) two dimensional SUSY algebra. Typical examples are (2,2) 2d sigma models with a flavor symmetry which is coupled to the 4d gauge fields. Interesting features of such 2d sigma models, such as (twisted) chiral rings, and the tt* geometry, can be carried over to the surface operators, and are affected in surprising ways by the coupling to 4d degrees of freedom. We will describe in detail a relation between the parameter space of twisted couplings of the surface operator and the Seiberg-Witten geometry of the bulk theory. We will discuss a similar result about the tt* geometry of the surface operator. We will predict the existence and general features of a wall-crossing formula for BPS particles bound to the surface operator.Comment: 25 pages, 4 figure

On SUSY curves

In this note we give a summary of some elementary results in the theory of super Riemann surfaces (SUSY curves)

Sub-Riemannian geodesics on nested principal bundles

We study the interplay between geodesics on two non-holono\-mic systems that are related by the action of a Lie group on them. After some geometric preliminaries, we use the Hamiltonian formalism to write the parametric form of geodesics. We present several geometric examples, including a non-holonomic structure on the Gromoll-Meyer exotic sphere and twistor space.Comment: 10 page

A fixed point formula for the index of multi-centered N=2 black holes

We propose a formula for computing the (moduli-dependent) contribution of multi-centered solutions to the total BPS index in terms of the (moduli-independent) indices associated to single-centered solutions. The main tool in our analysis is the computation of the refined index Tr(-y)^{2J_3} of configurational degrees of freedom of multi-centered BPS black hole solutions in N=2 supergravity by localization methods. When the charges carried by the centers do not allow for scaling solutions (i.e. solutions where a subset of the centers can come arbitrarily close to each other), the phase space of classical BPS solutions is compact and the refined index localizes to a finite set of isolated fixed points under rotations, corresponding to collinear solutions. When the charges allow for scaling solutions, the phase space is non-compact but appears to admit a compactification with finite volume and additional non-isolated fixed points. We give a prescription for determining the contributions of these fixed submanifolds by means of a `minimal modification hypothesis', which we prove in the special case of dipole halo configurations.Comment: 61 pages, 3 figure

From hermitean clifford analysis to subelliptic dirac operators on odd dimensional spheres and other CR manifolds

We show that the two Dirac operators arising in Hermitian Clifford analysis are identical to standard differential operators arising in several complex variables. We also show that the maximal subgroup that preserves these operators are generated by translations, dilations and actions of the unitary n-group. So the operators are not invariant under Kelvin inversion. We also show that the Dirac operators constructed via two by two matrices in Hermitian Clifford analysis correspond to standard Dirac operators in euclidean space. In order to develop Hermitian Clifford analysis in a different direction we introduce a sub elliptic Dirac operator acting on sections of a bundle over odd dimensional spheres. The particular case of the three sphere is examined in detail. We conclude by indicating how this construction could extend to other CR manifolds.publishe