465 research outputs found
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
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