11,764 research outputs found
Zero curvature conditions and conformal covariance
Two-dimensional zero curvature conditions with special emphasis on conformal properties are investigated in detail and the appearance of covariant higher order differential operators constructed in terms of a projective connection is elucidated. The analysis is based on the Kostant decomposition of simple Lie algebras in terms of representations with respect to their ``principal'' SL(2) subalgebra. Journal of Mathematical Physics is copyrighted by The American Institute of Physics
The GENGA Code: Gravitational Encounters in N-body simulations with GPU Acceleration
We describe an open source GPU implementation of a hybrid symplectic N-body
integrator, GENGA (Gravitational ENcounters with Gpu Acceleration), designed to
integrate planet and planetesimal dynamics in the late stage of planet
formation and stability analyses of planetary systems. GENGA uses a hybrid
symplectic integrator to handle close encounters with very good energy
conservation, which is essential in long-term planetary system integration. We
extended the second order hybrid integration scheme to higher orders. The GENGA
code supports three simulation modes: Integration of up to 2048 massive bodies,
integration with up to a million test particles, or parallel integration of a
large number of individual planetary systems. We compare the results of GENGA
to Mercury and pkdgrav2 in respect of energy conservation and performance, and
find that the energy conservation of GENGA is comparable to Mercury and around
two orders of magnitude better than pkdgrav2. GENGA runs up to 30 times faster
than Mercury and up to eight times faster than pkdgrav2. GENGA is written in
CUDA C and runs on all NVIDIA GPUs with compute capability of at least 2.0.Comment: Accepted by ApJ. 18 pages, 17 figures, 4 table
Spectrum of a duality-twisted Ising quantum chain
The Ising quantum chain with a peculiar twisted boundary condition is
considered. This boundary condition, first introduced in the framework of the
spin-1/2 XXZ Heisenberg quantum chain, is related to the duality
transformation, which becomes a symmetry of the model at the critical point.
Thus, at the critical point, the Ising quantum chain with the duality-twisted
boundary is translationally invariant, similar as in the case of the usual
periodic or antiperiodic boundary conditions. The complete energy spectrum of
the Ising quantum chain is calculated analytically for finite systems, and the
conformal properties of the scaling limit are investigated. This provides an
explicit example of a conformal twisted boundary condition and a corresponding
generalised twisted partition function.Comment: LaTeX, 7 pages, using IOP style
The effective action of warped M-theory reductions with higher-derivative terms - Part II
We study the three-dimensional effective action obtained by reducing
eleven-dimensional supergravity with higher-derivative terms on a background
solution including a warp-factor, an eight-dimensional compact manifold, and
fluxes. The dynamical fields are K\"ahler deformations and vectors from the
M-theory three-form. We show that the potential is only induced by fluxes and
the naive contributions obtained from higher-curvature terms on a Calabi-Yau
background vanish once the back-reaction to the full solution is taken into
account. For the resulting three-dimensional action we analyse the K\"ahler
potential and complex coordinates and show compatibility with N=2
supersymmetry. We argue that the higher-order result is also compatible with a
no-scale condition. We find that the complex coordinates should be formulated
as divisor integrals for which a non-trivial interplay between the warp-factor
terms and the higher-curvature terms allow a derivation of the moduli space
metric. This leads us to discuss higher-derivative corrections to the M5-brane
action.Comment: 26 page
On M-theory fourfold vacua with higher curvature terms
We study solutions to the eleven-dimensional supergravity action, including
terms quartic and cubic in the Riemann curvature, that admit an
eight-dimensional compact space. The internal background is found to be a
conformally Kahler manifold with vanishing first Chern class. The metric
solution, however, is non-Ricci-flat even when allowing for a conformal
rescaling including the warp factor. This deviation is due to the possible
non-harmonicity of the third Chern-form in the leading order Ricci-flat metric.
We present a systematic derivation of the background solution by solving the
Killing spinor conditions including higher curvature terms. These are
translated into first-order differential equations for a globally defined real
two-form and complex four-form on the fourfold. We comment on the supersymmetry
properties of the described solutions.Comment: 14 page
Non-Supersymmetric F-Theory Compactifications on Spin(7) Manifolds
We propose a novel approach to obtain non-supersymmetric four-dimensional
effective actions by considering F-theory on manifolds with special holonomy
Spin(7). To perform such studies we suggest that a duality relating M-theory on
a certain class of Spin(7) manifolds with F-theory on the same manifolds times
an interval exists. The Spin(7) geometries under consideration are constructed
as quotients of elliptically fibered Calabi-Yau fourfolds by an
anti-holomorphic and isometric involution. The three-dimensional minimally
supersymmetric effective action of M-theory on a general Spin(7) manifold with
fluxes is determined and specialized to the aforementioned geometries. This
effective theory is compared with an interval Kaluza-Klein reduction of a
non-supersymmetric four-dimensional theory with definite boundary conditions
for all fields. Using this strategy a minimal set of couplings of the
four-dimensional low-energy effective actions is obtained in terms of the
Spin(7) geometric data. We also discuss briefly the string interpretation in
the Type IIB weak coupling limit.Comment: 39 pages, 4 figures, v2: improvements and clarifications on the 4d
interpretation and weak coupling limit; typos correcte
Low Price Equilibrium in Multi-Unit Auctions: The GSM Spectrum Auction in Germany
The second-generation GSM spectrum auction in Germany is probably the most clear cut example of a low price outcome in a simultaneous ascending-bid auction.The present paper gives an account of the events, describes the auction rules and market conditions, and provides a theoretical explanation of low price equilibria in simultaneous, ascending-bid auctions.In particular it is shown that the low price equilibrium that implements the efficient allocation is the unique perfect equilibrium of that game.Multi-unit auctions, spectrum auctions, telecomm-unications, industrial organization, game theory
Implementing Efficient Market Structure
This article studies the design of optimal mechanisms to regulate entry in natural oligopoly markets, assuming the regulator is unable to control the behavior of firms once they are in the market. We adapt the Clark-Groves mechanism, characterize the optimal mechanism that maximizes the weighted sum of expected social surplus and expected tax revenue, and show that these mechanisms generally avoid budget deficits and prevent excessive entry.Mechanism design, natural oligopoly, auctions, entry
- âŠ