Examples of N=2 to N=1 supersymmetry breaking

In this paper we consider gauged N=2 supergravities which arise in the low-energy limit of type II string theories and study examples which exhibit spontaneous partial supersymmetry breaking. For the quantum STU model we derive the scalar field space and the scalar potential of the N=1 supersymmetric low-energy effective action. We also study the properties of the Minkowskian N=1 supersymmetricground states for a broader class of supergravities including the quantum STU model.Comment: 22 pages, added references, version to appear in JHE

Conformal correlators of mixed-symmetry tensors

We generalize the embedding formalism for conformal field theories to the case of general operators with mixed symmetry. The index-free notation encoding symmetric tensors as polynomials in an auxiliary polarization vector is extended to mixed-symmetry tensors by introducing a new commuting or anticommuting polarization vector for each row or column in the Young diagram that describes the index symmetries of the tensor. We determine the tensor structures that are allowed in n-point conformal correlation functions and give an algorithm for counting them in terms of tensor product coefficients. A simple derivation of the unitarity bound for arbitrary mixed-symmetry tensors is obtained by considering the conservation condition in embedding space. We show, with an example, how the new formalism can be used to compute conformal blocks of arbitrary external fields for the exchange of any conformal primary and its descendants. The matching between the number of tensor structures in conformal field theory correlators of operators in d dimensions and massive scattering amplitudes in d+1 dimensions is also seen to carry over to mixed-symmetry tensors.Comment: 46 pages, many figures, v2: Reformulated the counting of tensor structures, new section on conserved operators, v3: fixed typo

String theory in target space

It is argued that the complete S-matrix of string theory at tree level in a flat background can be obtained from a small set of target space properties, without recourse to the worldsheet description. The main non-standard inputs are (generalised) Britto-Cachazo-Feng-Witten shifts, as well as the monodromy relations for open string theory and the Kawai-Lewellen-Tye relations for closed string theory. The roots of the scattering amplitudes and especially their appearance in the residues at the kinematic poles are central to the story. These residues determine the amplitudes through on-shell recursion relations. Several checks of the formalism are presented, including a computation of the Koba-Nielsen amplitude in the bosonic string. Furthermore the question of target space unitarity is (re-)investigated. For the Veneziano amplitude this question is reduced by Poincare invariance, unitarity and locality to that of positivity of a particular numerical sum. Interestingly, this analysis produces the main conditions of the no-ghost theorem on dimension and intercept from the first three poles of this amplitude.Comment: 66 pages, many figure

From Entanglement Witness to Generalized Catalan Numbers

The problem of entanglement detection for arbitrary spin systems is analyzed. We demonstrate how a single measurement of the squared total spin can probabilistically discern separable from entangled many-particle states. For achieving this goal, we construct a tripartite analogy between the degeneracy of entanglement witness eigenstates, tensor products of $SO(3)$ representations and classical lattice walks with special constraints. Within this framework, degeneracies are naturally given by generalized Catalan numbers and determine the fraction of states that are decidedly entangled and also known to be somewhat protected against decoherence. In addition, we introduce the concept of a "sterile entanglement witness", which for large enough systems detects entanglement without affecting much the system's state. We discuss when our proposed entanglement witness can be regarded as a sterile one.Comment: v2 includes a few addition

Applying a potential across a biomembrane: electrostatic contribution to the bending rigidity and membrane instability

We investigate the effect on biomembrane mechanical properties due to the presence an external potential for a non-conductive non-compressible membrane surrounded by different electrolytes. By solving the Debye-Huckel and Laplace equations for the electrostatic potential and using the relevant stress-tensor we find: in (1.) the small screening length limit, where the Debye screening length is smaller than the distance between the electrodes, the screening certifies that all electrostatic interactions are short-range and the major effect of the applied potential is to decrease the membrane tension and increase the bending rigidity; explicit expressions for electrostatic contribution to the tension and bending rigidity are derived as a function of the applied potential, the Debye screening lengths and the dielectric constants of the membrane and the solvents. For sufficiently large voltages the negative contribution to the tension is expected to cause a membrane stretching instability. For (2.) the dielectric limit, i.e. no salt (and small wavevectors compared to the distance between the electrodes), when the dielectric constant on the two sides are different the applied potential induces an effective (unscreened) membrane charge density, whose long-range interaction is expected to lead to a membrane undulation instability.Comment: 16 pages, 3 figures, some revisio

Radial expansion for spinning conformal blocks

This paper develops a method to compute any bosonic conformal block as a series expansion in the optimal radial coordinate introduced by Hogervorst and Rychkov. The method reduces to the known result when the external operators are all the same scalar operator, but it allows to compute conformal blocks for external operators with spin. Moreover, we explain how to write closed form recursion relations for the coefficients of the expansions. We study three examples of four point functions in detail: one vector and three scalars; two vectors and two scalars; two spin 2 tensors and two scalars. Finally, for the case of two external vectors, we also provide a more efficient way to generate the series expansion using the analytic structure of the blocks as a function of the scaling dimension of the exchanged operator.Comment: 42 pages, 17 figures, 7 Mathematica files, v2: minor changes in the text, typos correcte

Projectors and seed conformal blocks for traceless mixed-symmetry tensors

In this paper we derive the projectors to all irreducible SO(d) representations (traceless mixed-symmetry tensors) that appear in the partial wave decomposition of a conformal correlator of four stress-tensors in d dimensions. These projectors are given in a closed form for arbitrary length $l_1$ of the first row of the Young diagram. The appearance of Gegenbauer polynomials leads directly to recursion relations in $l_1$ for seed conformal blocks. Further results include a differential operator that generates the projectors to traceless mixed-symmetry tensors and the general normalization constant of the shadow operator.Comment: 49 pages, 1 Mathematica notebook, many figures, v2: add reference

Weathering the storm: Children’s resilience against bullying and harassment

Resilience is a concept of growing interest in the research field, as well as bullying and quality of life. Resilience has gained rising interest over the past decade because it has capacity for systematically informed prevention and intervention (Elbau et al. 2019). This study looks at data from a former study “Trivsel I Tromsø” with children and adolescence victims to bullying and harassment (N=237) and a control group (N=735). In total (N=952). The pupils that matched the criteria, were from 9 to 16 years, who bullied and/or harassed at the cut off-point 3 or more times a month. The aim of the study was to look for any evidence of resilience within the bullied and harassed group. To assess this The Strenghts and Difficulties Questionnaire (SDQ) were used, and resilience was defined within the children or adolescence who scored in the normal range of total difficulty. Furthermore, KINDLR and the SDQ Pro-social score was used in effort to map out trends of resilience within the dataset. This is followed by regression analyses to sort out which variables had the most resistance towards the negative impacts. Main result of this study shows that 176 (74%) of the pupils were resilient towards the bullying and harassment. A moderate resiliency was considered within the borderline N=35 (14,7%), the last group N=26 (10,9%) were associated with low resilience. Compared to the control group, the most important protective factors were friends, the school environment, and emotional well-being in reducing the negative impacts displayed by the SDQ (with some reservations during overlap issues). The also study notes that physical well-being and self-esteem, and pro-social factors has effects against bullying and suggests that family has an effect in lowering the negative impacts of the bulling and harassment