414 research outputs found
The big de Rham-Witt complex
This paper gives a new and direct construction of the multi-prime big de
Rham-Witt complex which is defined for every commutative and unital ring; the
original construction by the author and Madsen relied on the adjoint functor
theorem and accordingly was very indirect. (The construction given here also
corrects the 2-torsion which was not quite correct in the original version.)
The new construction is based on the theory of modules and derivations over a
lambda-ring which is developed first. The main result in this first part of the
paper is that the universal derivation of a lambda-ring is given by the
universal derivation of the underlying ring together with an additional
structure depending on the lambda-ring structure in question. In the case of
the ring of big Witt vectors, this additional structure gives rise to divided
Frobenius operators on the module of K\"ahler differentials. It is the
existence of these divided Frobenius operators that makes the new construction
of the big de Rham-Witt complex possible. It is further shown that the big de
Rham-Witt complex behaves well with respect to \'etale maps, and finally, the
big de Rham-Witt complex of the ring of integers is explicitly evaluated. The
latter complex may be interpreted as the complex of differentials along the
leaves of a foliation of Spec Z.Comment: 63 page
Form and index of Ginsparg-Wilson fermions
We clarify the questions rised by a recent example of a lattice Dirac
operator found by Chiu. We show that this operator belongs to a class based on
the Cayley transformation and that this class on the finite lattice generally
does not admit a nonvanishing index, while in the continuum limit, due to
operator properties in Hilbert space, this defect is no longer there. Analogous
observations are made for the chiral anomaly. We also elaborate on various
aspects of the underlying sum rule for the index.Comment: 10 pages; v2: equation corrected, conclusions unchange
3D N = 1 SYM Chern-Simons theory on the Lattice
We present a method to implement 3-dimensional N = 1 SUSY Yang-Mills theory
(a theory with two real supercharges containing gauge fields and an adjoint
Majorana fermion) on the lattice, including a way to implement the Chern-Simons
term present in this theory. At nonzero Chern-Simons number our implementation
suffers from a sign problem which will make the numerical effort grow
exponentially with volume. We also show that the theory with vanishing
Chern-Simons number is anomalous; its partition function identically vanishes.Comment: v2, minor changes: expanded discussion in section III c, typos
corrected, 17 pages, 9 figure
Moduli spaces of vector bundles over a Klein surface
A compact topological surface S, possibly non-orientable and with non-empty
boundary, always admits a Klein surface structure (an atlas whose transition
maps are dianalytic). Its complex cover is, by definition, a compact Riemann
surface M endowed with an anti-holomorphic involution which determines
topologically the original surface S. In this paper, we compare dianalytic
vector bundles over S and holomorphic vector bundles over M, devoting special
attention to the implications that this has for moduli varieties of semistable
vector bundles over M. We construct, starting from S, totally real, totally
geodesic, Lagrangian submanifolds of moduli varieties of semistable vector
bundles of fixed rank and degree over M. This relates the present work to the
constructions of Ho and Liu over non-orientable compact surfaces with empty
boundary (arXiv:math/0605587) .Comment: 19 pages, 1 figur
Instanton vibrations of the 3-Skyrmion
The Atiyah-Drinfeld-Hitchin-Manin matrix corresponding to a tetrahedrally
symmetric 3-instanton is calculated. Some small variations of the matrix
correspond to vibrations of the instanton-generated 3-Skyrmion. These
vibrations are decomposed under tetrahedral symmetry and this decomposition is
compared to previous knowledge of the 3-Skyrmion vibration spectrum.Comment: 10 pages, LaTeX, no figures, PRD version with longer introduction and
minor change
A note on the index bundle over the moduli space of monopoles
Donaldson has shown that the moduli space of monopoles is diffeomorphic
to the space \Rat_k of based rational maps from the two-sphere to itself. We
use this diffeomorphism to give an explicit description of the bundle on
\Rat_k obtained by pushing out the index bundle from . This gives an
alternative and more explicit proof of some earlier results of Cohen and Jones.Comment: 9 page
Moduli of symplectic instanton vector bundles of higher rank on projective space P3
Symplectic instanton vector bundles on the projective space P3 constitute a natural generalization of mathematical instantons of rank 2. We study the moduli space In,r of rank-2r symplectic instanton vector bundles on P3 with r 65 2 and second Chern class n 65 r, n 61 r(mod2). We give an explicit construction of an irreducible component In 17,r of this space for each such value of n and show that In 17,r has the expected dimension 4n(r + 1) 12 r(2r + 1). \ua9 2012 Versita Warsaw and Springer-Verlag Wien
On the Structure of the Fusion Ideal
We prove that there is a finite level-independent bound on the number of
relations defining the fusion ring of positive energy representations of the
loop group of a simple, simply connected Lie group. As an illustration, we
compute the fusion ring of at all levels
Derivation of Index Theorems by Localization of Path Integrals
We review the derivation of the Atiyah-Singer and Callias index theorems
using the recently developed localization method to calculate exactly the
relevant supersymmetric path integrals. (Talk given at the III International
Conference on Mathematical Physics, String Theory and Quantum Gravity, Alushta,
Ukraine, June 13-24, 1993)Comment: 11 pages in LaTeX, HU-TFT-93-3
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