Bargaining among Groups: An Axiomatic Viewpoint

We introduce a model of bargaining among groups, and characterize a family of solutions using a Consistency axiom and a few other invariance and monotonicity properties. For each solution in the family, there exists some constant alpha >= 0 such that the "bargaining power" of a group is proportional to calpha where c is the cardinality of the group.

Bent BPS domain walls of D=5 N=2 gauged supergravity coupled to hypermultiplets

Within D=5 N=2 gauged supergravity coupled to hypermultiplets we derive consistency conditions for BPS domain walls with constant negative curvature on the wall. For such wall solutions to exist, the covariant derivative of the projector, governing the constraint on the Killing spinor, has to be non-zero and proportional to the cosmological constant on the domain walls. We also prove that in this case solutions of the Killing spinor equations are solutions of the equations of motion. We present explicit, analytically solved examples of such domain walls, employing the universal hypermultiplet fields. These examples involve the running of two scalar fields and the space-time in the transverse direction that is cut off at a critical distance, governed by the magnitude of the negative cosmological constant on the wall.Comment: 18 pages, Late

Junction conditions in General Relativity with spin sources

The junction conditions for General Relativity in the presence of domain walls with intrinsic spin are derived in three and higher dimensions. A stress tensor and a spin current can be defined just by requiring the existence of a well defined volume element instead of an induced metric, so as to allow for generic torsion sources. In general, when the torsion is localized on the domain wall, it is necessary to relax the continuity of the tangential components of the vielbein. In fact it is found that the spin current is proportional to the jump in the vielbein and the stress-energy tensor is proportional to the jump in the spin connection. The consistency of the junction conditions implies a constraint between the direction of flow of energy and the orientation of the spin. As an application, we derive the circularly symmetric solutions for both the rotating string with tension and the spinning dust string in three dimensions. The rotating string with tension generates a rotating truncated cone outside and a flat space-time with inevitable frame dragging inside. In the case of a string made of spinning dust, in opposition to the previous case no frame dragging is present inside, so that in this sense, the dragging effect can be "shielded" by considering spinning instead of rotating sources. Both solutions are consistently lifted as cylinders in the four-dimensional case.Comment: 24 pages, no figures, CECS style. References added and misprints corrected. Published Versio

On the Reduction in Accuracy of Finite Difference Schemes on Manifolds without Boundary

We investigate error bounds for numerical solutions of divergence structure linear elliptic PDEs on compact manifolds without boundary. Our focus is on a class of monotone finite difference approximations, which provide a strong form of stability that guarantees the existence of a bounded solution. In many settings including the Dirichlet problem, it is easy to show that the resulting solution error is proportional to the formal consistency error of the scheme. We make the surprising observation that this need not be true for PDEs posed on compact manifolds without boundary. By carefully constructing barrier functions, we prove that the solution error achieved by a scheme with consistency error $\mathcal{O}(h^\alpha)$ is bounded by $\mathcal{O}(h^{\alpha/(d+1)})$ in dimension $d$. We also provide a specific example where this predicted convergence rate is observed numerically. Using these error bounds, we further design a family of provably convergent approximations to the solution gradient.Comment: 28 pages, 7 figure

Against Chaos in Temperature in Mean-Field Spin-Glass Models

We study the problem of chaos in temperature in some mean-field spin-glass models by means of a replica computation over a model of coupled systems. We propose a set of solutions of the saddle point equations which are intrinsically non-chaotic and solve a general problem regarding the consistency of their structure. These solutions are relevant in the case of uncoupled systems too, therefore they imply a non-trivial overlap distribution $P(q_{T1T2})$ between systems at different temperatures. The existence of such solutions is checked to fifth order in an expansion near the critical temperature through highly non-trivial cancellations, while it is proved that a dangerous set of such cancellations holds exactly at all orders in the Sherrington-Kirkpatrick (SK) model. The SK model with soft-spin distribution is also considered obtaining analogous results. Previous analytical results are discussed.Comment: 20 pages, submitted to J.Phys.

Four-point correlator constraints on electromagnetic chiral parameters and resonance effective Lagrangians

We pursue the analysis of a set of generalized DGMLY sum rules for the electromagnetic chiral parameters at order $e^2p^2$ and discuss implications for effective Lagrangians with resonances. We exploit a formalism in which charge spurions are introduced and treated as sources. We show that no inconsistency arises from anomalies up to quadratic order in the spurions. We focus on the sum rules associated with QCD 4-point correlators which were not analyzed in detail before. Convergence properties of the sum rules are deduced from a general analysis of the form of the counterterms in the presence of electromagnetic spurions. Following the approach in which vector and axial-vector resonances are described with antisymmetric tensor fields and have a chiral order, we show that the convergence constraints are violated at chiral order four and can be satisfied by introducing a set of terms of order six. The relevant couplings get completely and uniquely determined from a set of generalized Weinberg sum-rule relations. An update on the corrections to Dashen's low-energy theorem is given.Comment: 42 pages, 1 figure. v2: references adde

Recent developments in bimetric theory

This review is dedicated to recent progress in the field of classical, interacting, massive spin-2 theories, with a focus on ghost-free bimetric theory. We will outline its history and its development as a nontrivial extension and generalisation of nonlinear massive gravity. We present a detailed discussion of the consistency proofs of both theories, before we review Einstein solutions to the bimetric equations of motion in vacuum as well as the resulting mass spectrum. We introduce couplings to matter and then discuss the general relativity and massive gravity limits of bimetric theory, which correspond to decoupling the massive or the massless spin-2 field from the matter sector, respectively. More general classical solutions are reviewed and the present status of bimetric cosmology is summarised. An interesting corner in the bimetric parameter space which could potentially give rise to a nonlinear theory for partially massless spin-2 fields is also discussed. Relations to higher-curvature theories of gravity are explained and finally we give an overview of possible extensions of the theory and review its formulation in terms of vielbeins.Comment: 124 pages, 4 figures; minor changes, corrected typos; matches published versio

Loop Corrections to Supergravity on AdS5×S5AdS_5 \times S^5

We consider the four-point correlator of the stress-energy tensor multiplet in ${\cal N}=4$ SYM. In the planar limit and at large 't Hooft coupling such correlator is given by the corresponding holographic correlation function in IIB supergravity on $AdS_5 \times S^5$. We consider subleading corrections in the number of colours, i.e. order $1/N^4$, at large 't Hooft coupling. This corresponds to loop corrections to the supergravity result. Consistency conditions, most notably crossing symmetry, constrain the form of such corrections and lead to a complete determination of the spectrum of leading twist intermediate operators.Comment: 6 pages, minor changes, added reference