Group Momentum Space and Hopf Algebra Symmetries of Point Particles Coupled to 2+1 Gravity

We present an in-depth investigation of the ${\rm SL}(2,\mathbb{R})$ momentum space describing point particles coupled to Einstein gravity in three space-time dimensions. We introduce different sets of coordinates on the group manifold and discuss their properties under Lorentz transformations. In particular we show how a certain set of coordinates exhibits an upper bound on the energy under deformed Lorentz boosts which saturate at the Planck energy. We discuss how this deformed symmetry framework is generally described by a quantum deformation of the Poincar\'e group: the quantum double of ${\rm SL}(2,\mathbb{R})$. We then illustrate how the space of functions on the group manifold momentum space has a dual representation on a non-commutative space of coordinates via a (quantum) group Fourier transform. In this context we explore the connection between Weyl maps and different notions of (quantum) group Fourier transform appeared in the literature in the past years and establish relations between them

An experimental inquiry into the nature of relational goods

Our experiment aims at studying the impact of two types of relational goods on the voluntary contributions to the production of a public good, i.e. acquaintance among the contributors and having performed a common work before the experiment. We implement two treatments with 128 participants from two different groups. In the first treatment the subjects are left talking in a room before the experiment (cheap talk treatment); they are not suggested any particular topic to talk about, nor are they requested to perform any activity in particular. The second treatment involves the performance of a common work (namely, the computation of some indices of economic performance of three companies, based on their balance sheets). The two groups of subjects are composed either by people with or without previous acquaintance. An equal number of subjects from each of these groups is then allocated to either treatment. After that the subjects played a standard 10-rounds public goods game in groups of 4. The groups were gender-homogeneous. This allows us also to inquire for the possible presence of a gender effect in our experiment. Our results show that: 1) both common work and previous acquaintance increase the average contribution to the public good, 2) there is a relevant gender effect with women contributing more or less than men, depending on the treatment. Therefore, we conclude that relational goods are important to enhance cooperation, that acquaintance and working together are rather complements than substitutes, and that different relational goods produce different effects on cooperation. Also, we find further evidence for women's behaviour to be more context-specific than men's.relational goods; public goods experiments; gender effect

Proving the Weak Gravity Conjecture in Perturbative String Theory, Part I: The Bosonic String

We present a complete proof of the Weak Gravity Conjecture in any perturbative bosonic string theory in spacetime dimension $D\ge6$. Our proof works by relating the black hole extremality bound to long range forces, which are more easily calculated on the worldsheet, closing the gaps in partial arguments in the existing literature. We simultaneously establish a strict, sublattice form of the conjecture in the same class of theories. We close by discussing the scope and limitations of our analysis, along with possible extensions including an upcoming generalization of our work to the superstring.Comment: 33 pages plus appendices, 6 figure

Twists of superconformal algebras

We develop the theory of ``conformal twists'' of superconformal field theories in dimensions 3 to 6, extending the well-known analysis of twists for supersymmetric theories. The conformal twists describe all possible inequivalent choices of a nilpotent element in the superconformal algebra. Such twists can give rise to interesting subalgebras and protected sectors of operators, with the Donaldson--Witten topological field theory and the vertex operator algebras of 4-dimensional N=2 SCFTs being prominent examples. We work mostly with the complexified superconformal algebras, unless explicitly stated otherwise; real forms of the superconformal algebra may have important physical implications, but we leave these subtleties to future work. To obtain mathematical precision, we explain how to extract vertex algebras and E_n algebras from a twisted superconformal field theory using factorization algebras

Competition and its effects on cooperation - An experimental test

This paper inquires experimentally whether competition has any impact on the individual disposition to contribute voluntarily to the provision of a public good. Participants perform a task and are remunerated according to two schemes, a non-competitive and a competitive one, then they play a standard public goods game. In the first scheme participants earn a flat remuneration, in the latter they are ranked according to their performance and remunerated consequently. Information about ranking and income before the game is played vary across three different treatments from no information, to information only about income, to full information about ranking and income. We find that competition per se does not affect the amount of contribution, and that there is a clear and strong negative income effect. Also, and in line with other studies, it emerges that the time spent to choose how much to contribute is negatively correlated with the decision of cooperating fully, suggesting that cooperation is more instinctive than non-cooperation. However, the main result is that information plays a crucial role: full information about the relative performance in the competitive environment enhances the cooperation, while partial information reduces it. This result is robust and the effects are large. We suggest a couple of tentative explanations, but further research is required