528 research outputs found
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
E{7(7)} Symmetry and Finiteness of N=8 Supergravity
We study N=8 supergravity deformed by the presence of the candidate
counterterms. We show that even though they are invariant under undeformed
E{7(7)}, all of the candidate counterterms violate the deformed E{7(7)} current
conservation. The same conclusion follows from the uniqueness of the Lorentz
and SU(8) covariant, E{7(7)} invariant unitarity constraint expressing the
56-dimensional E{7(7)} doublet via 28 independent vectors. Therefore E{7(7)}
duality predicts the all-loop UV finiteness of perturbative N=8 supergravity.Comment: 18 page
N=8 Counterterms and E7(7) Current Conservation
We examine conservation of the E7(7) Noether-Gaillard-Zumino current in the
presence of N=8 supergravity counterterms using the momentum space helicity
formalism, which significantly simplifies the calculations. The main result is
that the 4-point counterterms at any loop order L are forbidden by the E7(7)
current conservation identity. We also clarify the relation between linearized
and full non-linear superinvariants as candidate counterterms. This enables us
to show that all n-point counterterms at L=7, 8 are forbidden since they
provide a non-linear completions of the 4-point ones. This supports and
exemplifies our general proof in arXiv:1103.4115 of perturbative UV finiteness
of N=8 supergravity.Comment: 18 page
Testing of an Annular Linear Induction Pump for the Fission Surface Power Technology Demonstration Unit
Results of performance testing of an annular linear induction pump that has been designed for integration into a fission surface power technology demonstration unit are presented. The pump electromagnetically pushes liquid metal (NaK) through a specially-designed apparatus that permits quantification of pump performance over a range of operating conditions. Testing was conducted for frequencies of 40, 55, and 70 Hz, liquid metal temperatures of 125, 325, and 525 C, and input voltages from 30 to 120 V. Pump performance spanned a range of flow rates from roughly 0.3 to 3.1 L/s (4.8 to 49 gpm), and pressure heads of <1 to 104 kPa (<0.15 to 15 psi). The maximum efficiency measured during testing was 5.4%. At the technology demonstration unit operating temperature of 525 C the pump operated over a narrower envelope, with flow rates from 0.3 to 2.75 L/s (4.8 to 43.6 gpm), developed pressure heads from <1 to 55 kPa (<0.15 to 8 psi), and a maximum efficiency of 3.5%. The pump was supplied with three-phase power at 40 and 55 Hz using a variable-frequency motor drive, while power at 55 and 70 Hz was supplied using a variable-frequency power supply. Measured performance of the pump at 55 Hz using either supply exhibited good quantitative agreement. For a given temperature, the peak in efficiency occurred at different flow rates as the frequency was changed, but the maximum value of efficiency was relative insensitive within 0.3% over the frequency range tested, including a scan from 45 to 78 Hz. The objectives of the FSP technology project are as follows:5
Develop FSP concepts that meet expected surface power requirements at reasonable cost with added benefits over other options.
Establish a nonnuclear hardware-based technical foundation for FSP design concepts to reduce overall development risk.
Reduce the cost uncertainties for FSP and establish greater credibility for flight system cost
estimates.
Generate the key nonnuclear products to allow Agency decision makers to consider FSP as a viable option for potential future flight development.
The pump must be compatible with the liquid NaK coolant and have adequate performance to enable a viable flight system. Idaho National Laboratory (INL) was tasked with the design and fabrication of an ALIP suitable for the FSP reference mission. Under the program, a quarter-scale FSP technology demonstration is under construction to test the end-to-end conversion of simulated nuclear thermal power to usable electrical power intended to raise the entire FSP system to Technology Readiness Level 6. An ALIP for this TDU was fabricated under the direction of the INL and shipped to NASA Marshall Space Flight Center (MSFC) for testing at representative operating conditions. This pump was designed to meet the requirements of the TDU experiment. The ALIP test circuit (ATC) at MSFC, previously used to conduct performance evaluation on another ALIP6 was used to test the present TDU pump for the FSP Technology Development program
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
An R^4 non-renormalisation theorem in N=4 supergravity
We consider the four-graviton amplitudes in CHL constructions providing
four-dimensional N=4 models with various numbers of vector multiplets. We show
that in these models the two-loop amplitude has a prefactor of d^2R^4. This
implies a non-renormalisation theorem for the R^4 term, which forbids the
appearance of a three-loop ultraviolet divergence in four dimensions in the
four-graviton amplitude. We connect the special nature of the R^4 term to the
U(1) anomaly of pure N=4 supergravity.Comment: v2: added comments about one-loop UV divergences. Assorted stylistic
corrections. Added references. v3: Eq. III.21 corrected and assorted minor
corrections and clarifications. Version to be published. v4: minor
corrections. 18 pages. one figur
Black holes in supergravity and integrability
Stationary black holes of massless supergravity theories are described by
certain geodesic curves on the target space that is obtained after dimensional
reduction over time. When the target space is a symmetric coset space we make
use of the group-theoretical structure to prove that the second order geodesic
equations are integrable in the sense of Liouville, by explicitly constructing
the correct amount of Hamiltonians in involution. This implies that the
Hamilton-Jacobi formalism can be applied, which proves that all such black hole
solutions, including non-extremal solutions, possess a description in terms of
a (fake) superpotential. Furthermore, we improve the existing integration
method by the construction of a Lax integration algorithm that integrates the
second order equations in one step instead of the usual two step procedure. We
illustrate this technology with a specific example.Comment: 44 pages, small typos correcte
All the timelike supersymmetric solutions of all ungauged d=4 supergravities
We determine the form of all timelike supersymmetric solutions of all N
greater or equal than 2, d=4 ungauged supergravities, for N less or equal than
4 coupled to vector supermultiplets, using the $Usp(n+1,n+1)-symmetric
formulation of Andrianopoli, D'Auria and Ferrara and the spinor-bilinears
method, while preserving the global symmetries of the theories all the way. As
previously conjectured in the literature, the supersymmetric solutions are
always associated to a truncation to an N=2 theory that may include
hypermultiplets, although fields which are eliminated in the truncations can
have non-trivial values, as is required by the preservation of the global
symmetry of the theories. The solutions are determined by a number of
independent functions, harmonic in transverse space, which is twice the number
of vector fields of the theory (n+1). The transverse space is flat if an only
if the would-be hyperscalars of the associated N=2 truncation are trivial.Comment: v3: Some changes in the introduction. Version to be published in JHE
Stringy KLT relations, global symmetries, and E_7(7) violation
We study consequences of the Kawai-Lewellen-Tye (KLT) relations applied to
tree amplitudes in toroidal compactifications of string theory to four
dimensions. The closed string tree amplitudes with massless external states
respect a global SU(4)xSU(4) symmetry, which is enhanced to the SU(8)
R-symmetry of N=8 supergravity in the field theory limit. Our analysis focuses
on two aspects: (i) We provide a detailed account of the simplest
SU(8)-violating amplitudes. We classify these processes and derive explicit
superamplitudes for all local 5- and 6-point operators with SU(4)xSU(4)
symmetry at order alpha'^3. Their origin is the dilatonic operator exp(-6 phi)
R^4 in the closed-string effective action. (ii) We expand the 6-point closed
string tree amplitudes to order alpha'^3 and use two different methods to
isolate the SU(8)-singlet contribution from exp(-6 phi) R^4. This allows us to
extract the matrix elements of the unique SU(8)-invariant supersymmetrization
of R^4. Their single-soft scalar limits are non-vanishing. This demonstrates
that the N=8 supergravity candidate counterterm R^4 is incompatible with
continuous E_7(7) symmetry. From the soft scalar limits, we reconstruct to
quadratic order the SU(8)-invariant function of scalars that multiplies R^4,
and show that it satisfies the Laplace eigenvalue equation derived recently
from supersymmetry and duality constraints.Comment: 23 pages, published versio
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