443 research outputs found
On higher-spin supertranslations and superrotations
We study the large gauge transformations of massless higher-spin fields in
four-dimensional Minkowski space. Upon imposing suitable fall-off conditions,
providing higher-spin counterparts of the Bondi gauge, we observe the existence
of an infinite-dimensional asymptotic symmetry algebra. The corresponding Ward
identities can be held responsible for Weinberg's factorization theorem for
amplitudes involving soft particles of spin greater than two.Comment: Motivations and clarifications added. Matches published versio
Deformations of Closed Strings and Topological Open Membranes
We study deformations of topological closed strings. A well-known example is
the perturbation of a topological closed string by itself, where the
associative OPE product is deformed, and which is governed by the WDVV
equations. Our main interest will be closed strings that arise as the boundary
theory for topological open membranes, where the boundary string is deformed by
the bulk membrane operators. The main example is the topological open membrane
theory with a nonzero 3-form field in the bulk. In this case the Lie bracket of
the current algebra is deformed, leading in general to a correction of the
Jacobi identity. We identify these deformations in terms of deformation theory.
To this end we describe the deformation of the algebraic structure of the
closed string, given by the BRST operator, the associative product and the Lie
bracket. Quite remarkably, we find that there are three classes of deformations
for the closed string, two of which are exemplified by the WDVV theory and the
topological open membrane. The third class remains largely mysterious, as we
have no explicit example.Comment: 50 pages, LaTeX; V2: minor changes, 2 references added, V3: typos
corrected, signs added, modified discussion on higher correlator
Linear correlations amongst numbers represented by positive definite binary quadratic forms
Given a positive definite binary quadratic form f, let r(n) = |{(x,y):
f(x,y)=n}| denote its representation function. In this paper we study linear
correlations of these functions. For example, if r_1, ..., r_k are
representation functions, we obtain an asymptotic for sum_{n,d} r_1(n) r_2(n+d)
... r_k(n+ (k-1)d).Comment: 60 pages. Small correction
Special Varieties and classification Theory
A new class of compact K\"ahler manifolds, called special, is defined, which
are the ones having no surjective meromorphic map to an orbifold of general
type. The special manifolds are in many respect higher-dimensional
generalisations of rational and elliptic curves. For example, we show that
being rationally connected or having vanishing Kodaira dimension implies being
special. Moreover, for any compact K\"ahler we define a fibration , which we call its core, such that the general fibres of are
special, and every special subvariety of containing a general point of
is contained in the corresponding fibre of . We then conjecture and prove
in low dimensions and some cases that: 1) Special manifolds have an almost
abelian fundamental group. 2) Special manifolds are exactly the ones having a
vanishing Kobayashi pseudometric. 3) The core is a fibration of general type,
which means that so is its base ,when equipped with its orbifold
structure coming from the multiple fibres of . 4) The Kobayashi
pseudometric of is obtained as the pull-back of the orbifold Kobayashi
pseudo-metric on , which is a metric outside some proper algebraic
subset. 5) If is projective,defined over some finitely generated (over
) subfield of the complex number field, the set of -rational
points of is mapped by the core into a proper algebraic subset of .
These two last conjectures are the natural generalisations to arbitrary of
Lang's conjectures formulated when is of general type.Comment: 72 pages, latex fil
Model spaces and Toeplitz kernels in reflexive Hardy spaces
This paper considers model spaces in an Hp setting. The existence of unbounded
functions and the characterisation of maximal functions in a model space are studied, and decomposition
results for Toeplitz kernels, in terms of model spaces, are establishedFCT/Portuga
Convergence of Fermionic Observables in the Massive Planar FK-Ising Model
We prove convergence of the 2- and 4-point fermionic observables of the
FK-Ising model on simply connected domains discretised by a planar isoradial
lattice in massive (near-critical) scaling limit. The former is alternatively
known as a (fermionic) martingale observable (MO) for the massive interface,
and in particular encapsulates boundary visit probabilties of the interface.
The latter encodes connection probabilities in the 4-point alternating
(generalised Dobrushin) boundary condition, whose exact convergence is then
further analysed to yield crossing estimates for general boundary conditions.
These observables satisfy a massive version of s-holomorphicity [Smi10], and we
develop robust strategies to exploit this condition which do not require any
regularity assumption of the domain or a particular direction of perturbation.Comment: 43 pages, 5 figure
- …