20 research outputs found
Matrix Norms, BPS Bounds and Marginal Stability in N=8 Supergravity
We study the conditions of marginal stability for two-center extremal black
holes in N-extended supergravity in four dimensions, with particular emphasis
on the N=8 case. This is achieved by exploiting triangle inequalities satisfied
by matrix norms. Using different norms and relative bounds among them, we
establish the existence of marginal stability and split attractor flows both
for BPS and some non-BPS solutions. Our results are in agreement with previous
analysis based on explicit construction of multi-center solutions.Comment: 1+15 pages; v2: some new formulas added and misprints corrected; v3:
typos fixed, various refinements, Sec. 2.4 rewritten; to appear on JHE
Fake Superpotential for Large and Small Extremal Black Holes
We consider the fist order, gradient-flow, description of the scalar fields
coupled to spherically symmetric, asymptotically flat black holes in extended
supergravities. Using the identification of the fake superpotential with
Hamilton's characteristic function we clarify some of its general properties,
showing in particular (besides reviewing the issue of its duality invariance)
that W has the properties of a Liapunov's function, which implies that its
extrema (associated with the horizon of extremal black holes) are
asymptotically stable equilibrium points of the corresponding first order
dynamical system (in the sense of Liapunov). Moreover, we show that the fake
superpotential W has, along the entire radial flow, the same flat directions
which exist at the attractor point. This allows to study properties of the ADM
mass also for small black holes where in fact W has no critical points at
finite distance in moduli space. In particular the W function for small non-BPS
black holes can always be computed analytically, unlike for the large
black-hole case.Comment: 30 pages, LaTeX source. Discussion on the radial evolution of the
scalar fields, in relation to the symmetries of the W-function, extended.
Table 1 added. Typos correcte
Observations on Integral and Continuous U-duality Orbits in N=8 Supergravity
One would often like to know when two a priori distinct extremal black
p-brane solutions are in fact U-duality related. In the classical supergravity
limit the answer for a large class of theories has been known for some time.
However, in the full quantum theory the U-duality group is broken to a discrete
subgroup and the question of U-duality orbits in this case is a nuanced matter.
In the present work we address this issue in the context of N=8 supergravity in
four, five and six dimensions. The purpose of this note is to present and
clarify what is currently known about these discrete orbits while at the same
time filling in some of the details not yet appearing in the literature. To
this end we exploit the mathematical framework of integral Jordan algebras and
Freudenthal triple systems. The charge vector of the dyonic black string in D=6
is SO(5,5;Z) related to a two-charge reduced canonical form uniquely specified
by a set of two arithmetic U-duality invariants. Similarly, the black hole
(string) charge vectors in D=5 are E_{6(6)}(Z) equivalent to a three-charge
canonical form, again uniquely fixed by a set of three arithmetic U-duality
invariants. The situation in four dimensions is less clear: while black holes
preserving more than 1/8 of the supersymmetries may be fully classified by
known arithmetic E_{7(7)}(Z) invariants, 1/8-BPS and non-BPS black holes yield
increasingly subtle orbit structures, which remain to be properly understood.
However, for the very special subclass of projective black holes a complete
classification is known. All projective black holes are E_{7(7)}(Z) related to
a four or five charge canonical form determined uniquely by the set of known
arithmetic U-duality invariants. Moreover, E_{7(7)}(Z) acts transitively on the
charge vectors of black holes with a given leading-order entropy.Comment: 43 pages, 8 tables; minor corrections, references added; version to
appear in Class. Quantum Gra
R^4 counterterm and E7(7) symmetry in maximal supergravity
The coefficient of a potential R^4 counterterm in N=8 supergravity has been
shown previously to vanish in an explicit three-loop calculation. The R^4 term
respects N=8 supersymmetry; hence this result poses the question of whether
another symmetry could be responsible for the cancellation of the three-loop
divergence. In this article we investigate possible restrictions from the coset
symmetry E7(7)/SU(8), exploring the limits as a single scalar becomes soft, as
well as a double-soft scalar limit relation derived recently by Arkani-Hamed et
al. We implement these relations for the matrix elements of the R^4 term that
occurs in the low-energy expansion of closed-string tree-level amplitudes. We
find that the matrix elements of R^4 that we investigated all obey the
double-soft scalar limit relation, including certain
non-maximally-helicity-violating six-point amplitudes. However, the single-soft
limit does not vanish for this latter set of amplitudes, which suggests that
the E7(7) symmetry is broken by the R^4 term.Comment: 33 pages, typos corrected, published versio
Hypermultiplets, domain walls and supersymmetric attractors
We establish general properties of supersymmetric flow equations and of the
superpotential of five-dimensional N = 2 gauged supergravity coupled to vector
and hypermultiplets. We provide necessary and sufficient conditions for BPS
domain walls and find a set of algebraic attractor equations for N = 2 critical
points.
As an example we describe in detail the gauging of the universal
hypermultiplet and a vector multiplet. We study a two-parameter family of
superpotentials with supersymmetric AdS critical points and we find, in
particular, an N = 2 embedding for the UV-IR solution of Freedman, Gubser,
Pilch and Warner of the N = 8 theory. We comment on the relevance of these
results for brane world constructions.Comment: 49 pages, 5 figures, v2: small corrections including references.
Version to be published in Phys.Rev.D; v3: correction in eqn.(4.40
Moduli flow and non-supersymmetric AdS attractors
We investigate the attractor mechanism in gauged supergravity in the presence
of higher derivatives terms. In particular, we discuss the attractor behaviour
of static black hole horizons in anti-de Sitter spacetime by using the
effective potential approach as well as Sen's entropy function formalism. We
use the holographic techniques to interpret the moduli flow as an RG flow
towards the IR attractor horizon. We find that the holographic c-function obeys
the expected properties and point out some subtleties in understanding
attractors in AdS.Comment: 41 pages, 3 figures, JHEP style; V2: misprints corrected, expanded
references; V3: few typo's fixed in section
N >= 4 Supergravity Amplitudes from Gauge Theory at Two Loops
We present the full two-loop four-graviton amplitudes in N=4,5,6
supergravity. These results were obtained using the double-copy structure of
gravity, which follows from the recently conjectured color-kinematics duality
in gauge theory. The two-loop four-gluon scattering amplitudes in N=0,1,2
supersymmetric gauge theory are a second essential ingredient. The gravity
amplitudes have the expected infrared behavior: the two-loop divergences are
given in terms of the squares of the corresponding one-loop amplitudes. The
finite remainders are presented in a compact form. The finite remainder for N=8
supergravity is also presented, in a form that utilizes a pure function with a
very simple symbol.Comment: 31 pages, 2 figures, 1 table. v2: minor corrections, and references
adde
Planck 2015 results. XIII. Cosmological parameters
We present results based on full-mission Planck observations of temperature and polarization anisotropies of the CMB. These data are consistent with the six-parameter inflationary LCDM cosmology. From the Planck temperature and lensing data, for this cosmology we find a Hubble constant, H0= (67.8 +/- 0.9) km/s/Mpc, a matter density parameter Omega_m = 0.308 +/- 0.012 and a scalar spectral index with n_s = 0.968 +/- 0.006. (We quote 68% errors on measured parameters and 95% limits on other parameters.) Combined with Planck temperature and lensing data, Planck LFI polarization measurements lead to a reionization optical depth of tau = 0.066 +/- 0.016. Combining Planck with other astrophysical data we find N_ eff = 3.15 +/- 0.23 for the effective number of relativistic degrees of freedom and the sum of neutrino masses is constrained to < 0.23 eV. Spatial curvature is found to be |Omega_K| < 0.005. For LCDM we find a limit on the tensor-to-scalar ratio of r <0.11 consistent with the B-mode constraints from an analysis of BICEP2, Keck Array, and Planck (BKP) data. Adding the BKP data leads to a tighter constraint of r < 0.09. We find no evidence for isocurvature perturbations or cosmic defects. The equation of state of dark energy is constrained to w = -1.006 +/- 0.045. Standard big bang nucleosynthesis predictions for the Planck LCDM cosmology are in excellent agreement with observations. We investigate annihilating dark matter and deviations from standard recombination, finding no evidence for new physics. The Planck results for base LCDM are in agreement with BAO data and with the JLA SNe sample. However the amplitude of the fluctuations is found to be higher than inferred from rich cluster counts and weak gravitational lensing. Apart from these tensions, the base LCDM cosmology provides an excellent description of the Planck CMB observations and many other astrophysical data sets