103,168 research outputs found
I-adic towers in topology
A large variety of cohomology theories is derived from complex cobordism
MU^*(-) by localizing with respect to certain elements or by killing regular
sequences in MU_*. We study the relationship between certain pairs of such
theories which differ by a regular sequence, by constructing topological
analogues of algebraic I-adic towers. These give rise to Higher Bockstein
spectral sequences, which turn out to be Adams spectral sequences in an
appropriate sense. Particular attention is paid to the case of completed
Johnson--Wilson theory E(n)-hat and Morava K-theory K(n) for a given prime p.Comment: Published by Algebraic and Geometric Topology at
http://www.maths.warwick.ac.uk/agt/AGTVol5/agt-5-65.abs.htm
Bethe Ansatz Matrix Elements as Non-Relativistic Limits of Form Factors of Quantum Field Theory
We show that the matrix elements of integrable models computed by the
Algebraic Bethe Ansatz can be put in direct correspondence with the Form
Factors of integrable relativistic field theories. This happens when the
S-matrix of a Bethe Ansatz model can be regarded as a suitable non-relativistic
limit of the S-matrix of a field theory, and when there is a well-defined
mapping between the Hilbert spaces and operators of the two theories. This
correspondence provides an efficient method to compute matrix elements of Bethe
Ansatz integrable models, overpassing the technical difficulties of their
direct determination. We analyze this correspondence for the simplest example
in which it occurs, i.e. the Quantum Non-Linear Schrodinger and the Sinh-Gordon
models.Comment: 10 page
The structure of maximally supersymmetric Yang-Mills theory: constraining higher-order corrections
We solve the superspace Bianchi identities for ten-dimensional supersymmetric
Yang-Mills theory without imposing any kind of constraints apart from the
standard conventional one. In this way we obtain a set of algebraic conditions
on certain fields which in the on-shell theory are constructed as composite
ones out of the physical fields. These conditions must hence be satisfied by
any kind of theory in ten dimensions invariant under supersymmetry and some,
abelian or non-abelian, gauge symmetry. Deformations of the ordinary SYM theory
(as well as the fields) are identified as elements of a certain spinorial
cohomology, giving control over field redefinitions and the distinction between
physically relevant higher-order corrections and those removable by field
redefinitions. The conditions derived severely constrain theories involving
F^2-level terms plus higher-order corrections, as for instance those derived
from open strings as effective gauge theories on D-branes.Comment: plain tex, 18 pp., 3 fig
Spectral numbers in Floer theories
The chain complexes underlying Floer homology theories typically carry a
real-valued filtration, allowing one to associate to each Floer homology class
a spectral number defined as the infimum of the filtration levels of chains
representing that class. These spectral numbers have been studied extensively
in the case of Hamiltonian Floer homology by Oh, Schwarz, and others. We prove
that the spectral number associated to any nonzero Floer homology class is
always finite, and that the infimum in the definition of the spectral number is
always attained. In the Hamiltonian case, this implies that what is known as
the ``nondegenerate spectrality'' axiom holds on all closed symplectic
manifolds. Our proofs are entirely algebraic and apply to any Floer-type theory
(including Novikov homology) satisfying certain standard formal properties. The
key ingredient is a theorem about the existence of best approximations of
arbitrary elements of finitely generated free modules over Novikov rings by
elements of prescribed submodules with respect to a certain family of
non-Archimedean metrics.Comment: The main algebraic lemma (the former Theorem 1.6) has been given a
more general statement and a shorter proof. This allows us to generalize the
main results to cover Floer theories with integral or local coefficients.
Submitted version. 13 page
Towards the most general scalar-tensor theories of gravity: a unified approach in the language of differential forms
We use a description based on differential forms to systematically explore
the space of scalar-tensor theories of gravity. Within this formalism, we
propose a basis for the scalar sector at the lowest order in derivatives of the
field and in any number of dimensions. This minimal basis is used to construct
a finite and closed set of Lagrangians describing general scalar-tensor
theories invariant under Local Lorentz Transformations in a pseudo-Riemannian
manifold, which contains ten physically distinct elements in four spacetime
dimensions. Subsequently, we compute their corresponding equations of motion
and find which combinations are at most second order in derivatives in four as
well as arbitrary number of dimensions. By studying the possible exact forms
(total derivatives) and algebraic relations between the basis components, we
discover that there are only four Lagrangian combinations producing second
order equations, which can be associated with Horndeski's theory. In this
process, we identify a new second order Lagrangian, named kinetic Gauss-Bonnet,
that was not previously considered in the literature. However, we show that its
dynamics is already contained in Horndeski's theory. Finally, we provide a full
classification of the relations between different second order theories. This
allows us to clarify, for instance, the connection between different
covariantizations of Galileons theory. In conclusion, our formulation affords
great computational simplicity with a systematic structure. As a first step we
focus on theories with second order equations of motion. However, this new
formalism aims to facilitate advances towards unveiling the most general
scalar-tensor theories.Comment: 28 pages, 1 figure, version published in PRD (minor changes
Anyons in discrete gauge theories with Chern-Simons terms
We study the effect of a Chern-Simons term in a theory with discrete gauge
group H, which in (2+1)-dimensional space time describes (non-abelian) anyons.
As in a previous paper, we emphasize the underlying algebraic structure, namely
the Hopf algebra D(H). We argue on physical grounds that the addition of a
Chern-Simons term in the action leads to a non-trivial 3-cocycle on D(H).
Accordingly, the physically inequivalent models are labelled by the elements of
the cohomology group H^3(H,U(1)). It depends periodically on the coefficient of
the Chern-Simons term which model is realized. This establishes a relation with
the discrete topological field theories of Dijkgraaf and Witten. Some
representative examples are worked out explicitly.Comment: 18 page
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