900 research outputs found
Anomalies and divergences in N=4 supergravity
The invariants in D=4, N=4 supergravity are discussed up to the three-loop
order (where one expects a general R^4 structure). Because there is an anomaly
in the rigid SL(2,R) symmetry of this theory, the analysis of possible
restrictions on three-loop divergences due to duality needs careful treatment.
We show that this anomalous symmetry is still strong enough at the three-loop
order to require duality invariance of candidate counterterms. Provided one
makes the additional assumption that there exists a full 16-supercharge
off-shell formulation of the theory, counterterms at L \ge 2 loops would also
have to be writable as full-superspace integrals. At the three-loop order such
a duality-invariant full-superspace integral candidate counterterm exists, but
its duality invariance is marginal in the sense that the full-superspace
counter-Lagrangian is not itself duality invariant. We show that, subject to
the assumption that a full off-shell quantisation formalism exists, such
marginal invariants are not allowable as counterterms.Comment: 15 pages, version published in Phys. Lett.
Invariants and divergences in half-maximal supergravity theories
The invariants in half-maximal supergravity theories in D=4,5 are discussed
in detail up to dimension eight (e.g. R^4). In D=4, owing to the anomaly in the
rigid SL(2,R) duality symmetry, the restrictions on divergences need careful
treatment. In pure N=4 supergravity, this anomalous symmetry still implies
duality invariance of candidate counterterms at three loops. Provided one makes
the additional assumption that there exists a full 16-supercharge off-shell
formulation of the theory, counterterms at L>1 loops would also have to be
writable as full-superspace integrals. At the three-loop order such a
duality-invariant full-superspace integral candidate counterterm exists, but
its duality invariance is marginal in the sense that the full-superspace
counter-Lagrangian is not itself duality-invariant. We show that such marginal
invariants are not allowable as counterterms in a 16-supercharge off-shell
formalism. It is not possible to draw the same conclusion when vector
multiplets are present because of the appearance of F^4 terms in the SL(2,R)
anomaly. In D=5 there is no one-loop anomaly in the shift invariance of the
dilaton, and we argue that this implies finiteness at two loops, again subject
to the assumption that 16 supercharges can be preserved off-shell.Comment: 81 page
Genericity of Fr\'echet smooth spaces
If a separable Banach space contains an isometric copy of every separable
reflexive Fr\'echet smooth Banach space, then it contains an isometric copy of
every separable Banach space. The same conclusion holds if we consider
separable Banach spaces with Fr\'echet smooth dual space. This improves a
result of G. Godefroy and N. J. Kalton.Comment: 34 page
The influence of longwave ultraviolet radiation (u.v.-A) on the photosynthetic activity (14C-assimilation) of phytoplankton
The impact of u.v.-A (315-400 nm) on phytoplanktonic C-assimilation has been studied in situ and in the laboratory under artificial light. Water samples from Lake Lucerne were placed in DURAN-glass bottles and incubated either covered or uncovered with u.v. absorbing transparent tubes. Exposure to u.v.-A clearly inhibited 14C-assimilation in the uncovered samples both in situ and in the laboratory. Variations in visible light intensity and filtering of u.v.-B selectively demonstrated small inhibition of 14C-assimilation. U.v.-A inhibition of productivity is the major factor in the well known depression in productivity for surface water
Classification of BPS instantons in N=4 D=4 supergravity
This talk is based on the recent work in collaboration with M.
Azreg-A\"{\i}nou and G. Cl\'ement devoted to extremal instantons in the
one-vector truncation of the Euclidean theory. Extremal
solutions satisfying the no-force condition can be associated with null
geodesic curves in the homogeneous target space of the three-dimensional sigma
model arising in toroidal reduction of the four-dimensional theory. Here we
(preliminarily) discuss the case of two vector fields sufficient to find all
relevant metrics in the full theory. Classification of
instanton solutions is given along the following lines. The first is their
possible asymptotic structure: asymptotically locally flat (ALF),
asymptotically locally Euclidean (ALE) and ALF or ALE with the dilaton growing
at infinity. The second is the algebraic characterization of matrix generators
according to their rank and the nature of the charge vectors in an associated
Lorentzian space. Finally, solutions are distinguished by the number of
independent harmonic functions with unequal charges (up to four).Comment: Submitted to Proceedings of "Quantum Theory and Symmetries" (QTS-7),
Prague, August 7-13, 201
On duality symmetries of supergravity invariants
The role of duality symmetries in the construction of counterterms for maximal supergravity theories is discussed in a field-theoretic context from different points of view. These are: dimensional reduction, the question of whether appropriate superspace measures exist and information about non-linear invariants that can be gleaned from linearised ones. In D=4, N=8 supergravity we find that all three of these arguments suggest that F-term counterterms cannot be E7(7)-invariant and that the theory should be finite up to seven loops as a consequence. We also argue that N=6 supergravity is finite at three and four loops and that N=5 supergravity should be three-loop finite
Counterterms vs. Dualities
We investigate and clarify the mutual compatibility of the higher order
corrections arising in supergravity and string theory effective actions and the
non-linear duality symmetries of these theories. Starting from a conventional
tree level action leading to duality invariant equations of motion, we show how
to accommodate duality invariant counterterms given as functionals of both
electric and magnetic fields in a perturbative expansion, and to deduce from
them a non-polynomial bona fide action satisfying the Gaillard-Zumino
constraint. There exists a corresponding consistency constraint in the
non-covariant Henneaux-Teitelboim formalism which ensures that one can always
restore diffeomorphism invariance by perturbatively solving this functional
identity. We illustrate how this procedure works for the R^2 \nabla F \nabla F
and F^4 counterterms in Maxwell theory.Comment: 15 page
Finiteness Properties of the N=4 Super-Yang--Mills Theory in Supersymmetric Gauge
With the introduction of shadow fields, we demonstrate the renormalizability of the N=4 super-Yang--Mills theory in component formalism, independently of the choice of UV regularization. Remarkably, by using twisted representations, one finds that the structure of the theory and its renormalization is determined by a subalgebra of supersymmetry that closes off-shell. Starting from this subalgebra of symmetry, we prove some features of the superconformal invariance of the theory. We give a new algebraic proof of the cancellation of the function and we show the ultraviolet finiteness of the 1/2 BPS operators at all orders in perturbation theory. In fact, using the shadow field as a Maurer--Cartan form, the invariant polynomials in the scalar fields in traceless symmetric representations of the internal R-symmetry group are simply related to characteristic classes. Their UV finiteness is a consequence of the Chern--Simons formula
Multi-Centered Black Hole Flows
We describe the systematical construction of the first order formalism for
multi-centered black holes with flat three dimensional base-space, within the
so-called model of N=2, D=4 ungauged Maxwell-Einstein supergravity. The
three possible flow classes (BPS, composite non-BPS and almost-BPS) are
analyzed in detail, and various solutions, such as single-centered (static or
under-rotating) and all known multi-centered black holes, are recovered in this
unified framework. We also consider the possibility of obtaining new solutions.
The almost-BPS class is proved to split into two general sub-classes,
corresponding to a positive or negative value of the duality-invariant
polynomial for the total charge; the well known almost BPS system is shown to
be a particular solution of the second sub-class.Comment: 17 pages,no figure
Duality covariant non-BPS first order systems
We study extremal black hole solutions to four dimensional N=2 supergravity
based on a cubic symmetric scalar manifold. Using the coset construction
available for these models, we define the first order flow equations implied by
the corresponding nilpotency conditions on the three-dimensional scalar momenta
for the composite non-BPS class of multi-centre black holes. As an application,
we directly solve these equations for the single-centre subclass, and write the
general solution in a manifestly duality covariant form. This includes all
single-centre under-rotating non-BPS solutions, as well as their
non-interacting multi-centre generalisations.Comment: 31 pages, v2: Discussion of the quadratic constraint clarified,
references added, typos corrected, published versio
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