3,270 research outputs found
1/8 BPS black hole composites
We show that the 1/8 BPS condition for composite stationary black holes can
be rewritten as a first order system of differential equations associated to
the nilpotent orbit in which lie the Noether charges of the black holes.
Solving these equations, we prove that the most general 1/8 BPS black hole
composites are solutions of the N=2 truncation of the theory associated to the
quaternions. This system of first order differential equations generalises to
the non-BPS solutions with a vanishing central charge at the horizon in N=2, 4
supergravity theories with a symmetric moduli space. We solve these equations
for the exceptional N=2 supergravity associated to the octonions.Comment: 19 page
Extremal black holes and nilpotent orbits
The stationary solutions of a large variety of (super)gravity theories can be
described within a non-linear sigma model G / H* coupled to Euclidean gravity
in three-dimensions, for which G is a simple group and H* a non-compact real
form of its maximal compact subgroup. The absence of naked singularities in
four dimensions requires the G Noether charge in 3D to satisfy a characteristic
equation that determines it in function of the mass, the NUT charge and the
electro-magnetic charges of the solution. It follows that the Noether charge
associated to extremal black holes must lie in a certain Lagrangian submanifold
of a nilpotent orbit of G. Constructing a suitable parameterisation of this
Lagrangian, we are able to determine the so-called `fake superpotential' that
governs the radial dependency of the scalar fields.Comment: Invited talk at the XVI International Congress on Mathematical
Physics, Prague, 3-8 August 200
Shadows and Twisted Variables
We explain how a new type of fields called shadows and the use of twisted
variables allow for a better description of Yang-Mills supersymmetric theories.
(Based on lectures given in Cargese, June 2006.)Comment: Cargese Jun 200
non-BPS walls of marginal stability
We explore the properties of non-BPS multi-centre extremal black holes in
ungauged N=2 supergravity coupled to n_v vector multiplets, as described by
solutions to the composite non-BPS linear system. After setting up an explicit
description that allows for arbitrary non-BPS charges to be realised at each
centre, we study the structure of the resulting solutions. Using these results,
we prove that the binding energy of the composite is always positive and we
show explicitly the existence of walls of marginal stability for generic
choices of charges. The two-centre solutions only exist on a hypersurface of
dimension n_v+1 in moduli space, with an n_v-dimensional boundary, where the
distance between the centres diverges and the binding energy vanishes.Comment: 54 pages, 1 figur
The two D6R4 type invariants and their higher order generalisation
We show that there are two distinct classes of D6R4 type supersymmetry
invariants in maximal supergravity. The second class includes a coupling in
F2D4R4 that generalises to 1/8 BPS protected F2kD4R4 couplings. We work out the
supersymmetry constraints on the corresponding threshold functions, and argue
that the functions in the second class satisfy to homogeneous differential
equations for arbitrary k>0, such that the corresponding exact threshold
functions in type II string theory should be proportional to Eisenstein series,
which we identify. This analysis explains in particular that the exact D6R4
threshold function is the sum of an Eisenstein function and a solution to an
inhomogeneous Poisson equation in string theory.Comment: 53 page
Loops in exceptional field theory
We study certain four-graviton amplitudes in exceptional field theory in
dimensions up to two loops. As the formulation is manifestly
invariant under the U-duality group , our resulting
expressions can be expressed in terms of automorphic forms. In the low energy
expansion, we find terms in the M-theory effective action of type ,
and with automorphic coefficient functions in
agreement with independent derivations from string theory. This provides in
particular an explicit integral formula for the exact string theory threshold function. We exhibit moreover that the usual supergravity
logarithmic divergences cancel out in the full exceptional field theory
amplitude, within an appropriately defined dimensional regularisation scheme.
We also comment on terms of higher derivative order and the role of the section
constraint for possible counterterms.Comment: 1+78 pages: v2: Added references and typos corrected. Version
accepted by JHEP. v3: corrected discussion of associativity in EFT and other
typo
Minimal unitary representations from supersymmetry
We compute the supersymmetry constraints on the R^4 type corrections in
maximal supergravity in dimension 8, 6, 4 and 3, and determine the tensorial
differential equations satisfied by the function of the scalar fields
multiplying the R^4 term in the corresponding invariants. The second order
derivative of this function restricted to the Joseph ideal vanishes in
dimension lower than six. These results are extended to the d^4 R^4 and the d^6
R^4 corrections, based on the harmonic superspace construction of these
invariants in the linearised approximation. We discuss the solutions of these
differential equations and analysis the consequences on the non-perturbative
type II low energy string theory effective action.Comment: 84 pages, Corrected version for publication in JHEP, additional
comment on d^6 R^4 in four dimension
Supergravity divergences, supersymmetry and automorphic forms
We investigate the occurrence of divergences in maximal supergravity in
various dimensions from the point of view of supersymmetry constraints on the
U-duality invariant threshold functions defining the higher derivative
couplings in the effective action. Our method makes use of tensorial
differential equations that constrain these couplings. We study in detail the
Fourier modes and wave-front sets of the associated automorphic functions and
find that they are always associated to special nilpotent orbits.Comment: 45 pages, 2 figures. v2: JHEP version with small correction
A bubbling bolt
We present a new solvable system, solving the equations of five-dimensional
ungauged N=1 supergravity coupled to vector multiplets, that allows for
non-extremal solutions and reduces to a known system when restricted to the
floating brane Ansatz. A two-centre globally hyperbolic smooth geometry is
obtained as a solution to this system, describing a bubble linking a
Gibbons--Hawking centre to a charged bolt. However this solution turns out to
violate the BPS bound, and we show that its generalisation to an arbitrary
number of Gibbons--Hawking centres never admits a spin structure.Comment: 36 page
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