Critical and Non-Critical Einstein-Weyl Supergravity

We construct N=1 supersymmetrisations of some recently-proposed theories of critical gravity, conformal gravity, and extensions of critical gravity in four dimensions. The total action consists of the sum of three separately off-shell supersymmetric actions containing Einstein gravity, a cosmological term and the square of the Weyl tensor. For generic choices of the coefficients for these terms, the excitations of the resulting theory around an AdS_4 background describe massive spin-2 and massless spin-2 modes coming from the metric; massive spin-1 modes coming from a vector field in the theory; and massless and massive spin-3/2 modes (with two unequal masses) coming from the gravitino. These assemble into a massless and a massive N=1 spin-2 multiplet. In critical supergravity, the coefficients are tuned so that the spin-2 mode in the massive multiplet becomes massless. In the supersymmetrised extensions of critical gravity, the coefficients are chosen so that the massive modes lie in a "window" of lowest energies E_0 such that these ghostlike fields can be truncated by imposing appropriate boundary conditions at infinity, thus leaving just positive-norm massless supergravity modes.Comment: 29 page

Extra gauge symmetries in BHT gravity

We study the canonical structure of the Bergshoeff-Hohm-Townsend massive gravity, linearized around a maximally symmetric background. At the critical point in the space of parameters, defined by $\Lambda_0/m^2=-1$, we discover an extra gauge symmetry, which reflects the existence of the partially massless mode. The number of the Lagrangian degrees of freedom is found to be 1. We show that the canonical structure of the theory at the critical point is unstable under linearization.Comment: LATEX, 12 page

Nonlinear Dynamics of Parity-Even Tricritical Gravity in Three and Four Dimensions

Recently proposed "multicritical" higher-derivative gravities in Anti de Sitter space carry logarithmic representations of the Anti de Sitter isometry group. While generically non-unitary already at the quadratic, free-theory level, in special cases these theories admit a unitary subspace. The simplest example of such behavior is "tricritical" gravity. In this paper, we extend the study of parity-even tricritical gravity in d = 3, 4 to the first nonlinear order. We show that the would-be unitary subspace suffers from a linearization instability and is absent in the full non-linear theory.Comment: 22 pages; v2: references added, published versio

The general gaugings of maximal d=9 supergravity

We use the embedding tensor method to construct the most general maximal gauged/massive supergravity in d=9 dimensions and to determine its extended field content. Only the 8 independent deformation parameters (embedding tensor components, mass parameters etc.) identified by Bergshoeff \textit{et al.} (an SL(2,R) triplet, two doublets and a singlet can be consistently introduced in the theory, but their simultaneous use is subject to a number of quadratic constraints. These constraints have to be kept and enforced because they cannot be used to solve some deformation parameters in terms of the rest. The deformation parameters are associated to the possible 8-forms of the theory, and the constraints are associated to the 9-forms, all of them transforming in the conjugate representations. We also give the field strengths and the gauge and supersymmetry transformations for the electric fields in the most general case. We compare these results with the predictions of the E11 approach, finding that the latter predicts one additional doublet of 9-forms, analogously to what happens in N=2, d=4,5,6 theories.Comment: Latex file, 43 pages, reference adde

On fractionality of the path packing problem

In this paper, we study fractional multiflows in undirected graphs. A fractional multiflow in a graph G with a node subset T, called terminals, is a collection of weighted paths with ends in T such that the total weights of paths traversing each edge does not exceed 1. Well-known fractional path packing problem consists of maximizing the total weight of paths with ends in a subset S of TxT over all fractional multiflows. Together, G,T and S form a network. A network is an Eulerian network if all nodes in N\T have even degrees. A term "fractionality" was defined for the fractional path packing problem by A. Karzanov as the smallest natural number D so that there exists a solution to the problem that becomes integer-valued when multiplied by D. A. Karzanov has defined the class of Eulerian networks in terms of T and S, outside which D is infinite and proved that whithin this class D can be 1,2 or 4. He conjectured that D should be 1 or 2 for this class of networks. In this paper we prove this conjecture.Comment: 18 pages, 5 figures in .eps format, 2 latex files, main file is kc13.tex Resubmission due to incorrectly specified CS type of the article; no changes to the context have been mad

Holographic two-point functions for 4d log-gravity

We compute holographic one- and two-point functions of critical higher-curvature gravity in four dimensions. The two most important operators are the stress tensor and its logarithmic partner, sourced by ordinary massless and by logarithmic non-normalisable gravitons, respectively. In addition, the logarithmic gravitons source two ordinary operators, one with spin-one and one with spin-zero. The one-point function of the stress tensor vanishes for all Einstein solutions, but has a non-zero contribution from logarithmic gravitons. The two-point functions of all operators match the expectations from a three-dimensional logarithmic conformal field theory.Comment: 35 pages; v2: typos corrected, added reference; v3: shorter introduction, minor changes in the text in section 3, added reference; published versio

Nonlinear Realization of Spontaneously Broken N=1 Supersymmetry Revisited

This paper revisits the nonlinear realization of spontaneously broken N=1 supersymmetry. It is shown that the constrained superfield formalism can be reinterpreted in the language of standard realization of nonlinear supersymmetry via a new and simpler route. Explicit formulas of actions are presented for general renormalizable theories with or without gauge interactions. The nonlinear Wess-Zumino gauge is discussed and relations are pointed out for different definitions of gauge fields. In addition, a general procedure is provided to deal with theories of arbitrary Kahler potentials.Comment: 1+18 pages, LaTe

Lyb-2 system of mouse B cells. Evidence for a role in the generation of antibody-forming cells

The Lyb-2 cell-surface alloantigens of the mouse are selectively and perhaps exclusively expressed in the B lymphocyte lineage, but not on antibody- forming cells. Thus if the Lyb-2 molecule is concerned in specific B cell function, it must participate in the generative phase of the antibody response. Accordingly, monoclonal Lyb-2 antibody was found to depress the plaque- forming cell (PFC) response to sheep erythrocytes in 5-d Mishell-Dutton assays when added within the first 3 d of culture, but not later. The rate of PFC generation was not affected, signifying an absolute reduction in the number of PFC generated. Because reduction of PFC counts by Lyb-2 antibody was not affected by exclusion of Lyt-2(+) T cells, it is unlikely that the reduction depends on augmented suppression by T cells. Augmented B cell- mediated suppression is also unlikely, because the PFC response of serial combinations of congenic Lyb-2.1 and Lyb-2.2 cells, in the presence of monoclonal Lyb-2.1 antibody, was reduced only in direct proportion to the number of Lyb-2.1 cells present. The PFC response of Lyb-2.1/Lyb-2.2 heterozygous cells was not reduced by Lyb-2.1 antibody, presumably because generation of PFC is impeded only if most Lyb-2 sites are blocked. Further evidence that the molecule identified by Lyb-2 plays a critical role in the generation of antibody-forming cells (AFC) in response to T-dependent antigen comes from the finding that Lyb-2 antibody does not reduce the PFC response to the T-independent antigens trinitrophenylated (TNP) Brucella abortus and TNP-FicolI, although elimination of Lyb-2(+) cells from the starting population by Lyb-2 antibody and complement reduces the PFC response to T- dependent and T-independent antigens alike

Aging Logarithmic Conformal Field Theory : a holographic view

We consider logarithmic extensions of the correlation and response functions of scalar operators for the systems with aging as well as Schr\"odinger symmetry. Aging is known to be the simplest nonequilibrium phenomena, and its physical significances can be understood by the two-time correlation and response functions. Their logarithmic part is completely fixed by the bulk geometry in terms of the conformal weight of the dual operator and the dual particle number. Motivated by recent experimental realizations of Kardar-Parisi-Zhang universality class in growth phenomena and its subsequent theoretical extension to aging, we investigate our two-time correlation functions out of equilibrium, which show several qualitatively different behaviors depending on the parameters in our theory. They exhibit either growing or aging, i.e. power-law decaying, behaviors for the entire range of our scaling time. Surprisingly, for some parameter ranges, they exhibit growing at early times as well as aging at later times.Comment: 1+26 pages, 15 figure