694 research outputs found
Supersolutions
We develop classical globally supersymmetric theories. As much as possible,
we treat various dimensions and various amounts of supersymmetry in a uniform
manner. We discuss theories both in components and in superspace. Throughout we
emphasize geometric aspects. The beginning chapters give a general discussion
about supersymmetric field theories; then we move on to detailed computations
of lagrangians, etc. in specific theories. An appendix details our sign
conventions. This text will appear in a two-volume work "Quantum Fields and
Strings: A Course for Mathematicians" to be published soon by the American
Mathematical Society. Some of the cross-references may be found at
http://www.math.ias.edu/~drm/QFT/Comment: 130 pages, AMSTe
On Nori's Fundamental Group Scheme
We determine the quotient category which is the representation category of
the kernel of the homomorphism from Nori's fundamental group scheme to its
\'etale and local parts. Pierre Deligne pointed out an error in the first
version of this article. We profoundly thank him, in particular for sending us
his enlightning example reproduced in Remark 2.4 2).Comment: 29 page
Non-Abelian statistics versus the Witten anomaly
This paper is motivated by prospects for non-Abelian statistics of deconfined
particle-like objects in 3+1 dimensions, realized as solitons with localized
Majorana zeromodes. To this end, we study the fermionic collective coordinates
of magnetic monopoles in 3+1 dimensional spontaneously-broken SU(2) gauge
theories with various spectra of fermions. We argue that a single Majorana
zeromode of the monopole is not compatible with cancellation of the Witten
SU(2) anomaly. We also compare this approach with other attempts to realize
deconfined non-Abelian objects in 3+1 dimensions.Comment: 11 pages, 3 figures; v2: added refs, minor corrections, published
versio
A representation formula for maps on supermanifolds
In this paper we analyze the notion of morphisms of rings of superfunctions
which is the basic concept underlying the definition of supermanifolds as
ringed spaces (i.e. following Berezin, Leites, Manin, etc.). We establish a
representation formula for all morphisms from the algebra of functions on an
ordinary manifolds to the superalgebra of functions on an open subset of
R^{p|q}. We then derive two consequences of this result. The first one is that
we can integrate the data associated with a morphism in order to get a (non
unique) map defined on an ordinary space (and uniqueness can achieved by
restriction to a scheme). The second one is a simple and intuitive recipe to
compute pull-back images of a function on a manifold by a map defined on a
superspace.Comment: 23 page
The Uncertainty of Fluxes
In the ordinary quantum Maxwell theory of a free electromagnetic field,
formulated on a curved 3-manifold, we observe that magnetic and electric fluxes
cannot be simultaneously measured. This uncertainty principle reflects torsion:
fluxes modulo torsion can be simultaneously measured. We also develop the
Hamilton theory of self-dual fields, noting that they are quantized by
Pontrjagin self-dual cohomology theories and that the quantum Hilbert space is
Z/2-graded, so typically contains both bosonic and fermionic states.
Significantly, these ideas apply to the Ramond-Ramond field in string theory,
showing that its K-theory class cannot be measured.Comment: 33 pages; minor modifications for publication in Commun. Math. Phy
Exponential sums with coefficients of certain Dirichlet series
Under the generalized Lindel\"of Hypothesis in the t- and q-aspects, we bound
exponential sums with coefficients of Dirichlet series belonging to a certain
class. We use these estimates to establish a conditional result on squares of
Hecke eigenvalues at Piatetski-Shapiro primes.Comment: 13 page
On the transcendence degree of the differential field generated by Siegel modular forms
It is a classical fact that the elliptic modular functions satisfies an
algebraic differential equation of order 3, and none of lower order. We show
how this generalizes to Siegel modular functions of arbitrary degree. The key
idea is that the partial differential equations they satisfy are governed by
Gauss--Manin connections, whose monodromy groups are well-known. Modular theta
functions provide a concrete interpretation of our result, and we study their
differential properties in detail in the case of degree 2.Comment: 21 pages, AmSTeX, uses picture.sty for 1 LaTeX picture; submitted for
publicatio
The Minkowski and conformal superspaces
We define complex Minkowski superspace in 4 dimensions as the big cell inside
a complex flag supermanifold. The complex conformal supergroup acts naturally
on this super flag, allowing us to interpret it as the conformal
compactification of complex Minkowski superspace. We then consider real
Minkowski superspace as a suitable real form of the complex version. Our
methods are group theoretic, based on the real conformal supergroup and its
Lie superalgebra.Comment: AMS LaTeX, 44 page
The Geography of Non-formal Manifolds
We show that there exist non-formal compact oriented manifolds of dimension
and with first Betti number if and only if and
, or and . Moreover, we present explicit
examples for each one of these cases.Comment: 8 pages, one reference update
The Neron-Severi group of a proper seminormal complex variety
We prove a Lefschetz (1,1)-Theorem for proper seminormal varieties over the
complex numbers. The proof is a non-trivial geometric argument applied to the
isogeny class of the Lefschetz 1-motive associated to the mixed Hodge structure
on H^2.Comment: 16 pages; Mathematische Zeitschrift (2008
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