VOAs labelled by complex reflection groups and 4d SCFTs

We define and study a class of $\mathcal{N}=2$ vertex operator algebras $\mathcal{W}_{\mathcal{\mathsf{G}}}$ labelled by complex reflection groups. They are extensions of the $\mathcal{N}=2$ super Virasoro algebra obtained by introducing additional generators, in correspondence with the invariants of the complex reflection group $\mathcal{\mathsf{G}}$. If $\mathcal{\mathsf{G}}$ is a Coxeter group, the $\mathcal{N}=2$ super Virasoro algebra enhances to the (small) $\mathcal{N}=4$ superconformal algebra. With the exception of $\mathcal{\mathsf{G}} = \mathbb{Z}_2$, which corresponds to just the $\mathcal{N}=4$ algebra, these are non-deformable VOAs that exist only for a specific negative value of the central charge. We describe a free-field realization of $\mathcal{W}_{\mathcal{\mathsf{G}}}$ in terms of rank$(\mathcal{\mathsf{G}})$ $\beta \gamma bc$ ghost systems, generalizing a construction of Adamovic for the $\mathcal{N}=4$ algebra at $c = -9$. If $\mathcal{\mathsf{G}}$ is a Weyl group, $\mathcal{W}_{\mathcal{\mathsf{G}}}$ is believed to coincide with the $\mathcal{N}=4$ VOA that arises from the four-dimensional super Yang-Mills theory whose gauge algebra has Weyl group $\mathcal{\mathsf{G}}$. More generally, if $\mathcal{\mathsf{G}}$ is a crystallographic complex reflection group, $\mathcal{W}_{\mathcal{\mathsf{G}}}$ is conjecturally associated to an $\mathcal{N}=3$ $4d$ superconformal field theory. The free-field realization allows to determine the elusive `$R$-filtration' of $\mathcal{W}_{\mathcal{\mathsf{G}}}$, and thus to recover the full Macdonald index of the parent $4d$ theoryComment: 70 page

Effective actions for F-theory compactifications and tensor theories

In this thesis we study the low-energy effective dynamics emerging from a class of F-theory compactifications in four and six dimensions. We also investigate six-dimensional supersymmetric quantum field theories with self-dual tensors, motivated by the problem of describing the long-wavelength regime of a stack of M5-branes in M-theory. These setups share interesting common features. They both constitute examples of intrinsically non-perturbative physics. On the one hand, in the context of F-theory the non-perturbative character is encoded in the geometric formulation of this class of string vacua, which allows the complexified string coupling to vary in space. On the other hand, the dynamics of a stack of multiple M5-branes flows in the infrared to a novel kind of superconformal field theories in six dimensions - commonly referred to as (2,0) theories - that are expected to possess no perturbative weakly coupled regime and have resisted a complete understanding so far. In particular, no Lagrangian description is known for these models. The strategy we employ to address these two problems is also analogous. A recurring Leitmotif of our work is a transdimensional treatment of the system under examination: in order to extract information about dynamics in $d$ dimensions we consider a (d-1)-dimensional setup. As far as F-theory compactifications are concerned, this is a consequence of the duality between M-theory and F-theory, which constitutes our main tool in the derivation of the effective action of F-theory compactifications. We apply it to six-dimensional F-theory vacua, obtained by taking the internal space to be an elliptically fibered Calabi-Yau threefold, but we also employ it to explore a novel kind of F-theory constructions in four dimensions based on manifolds with Spin(7) holonomy. With reference to six-dimensional (2,0) theories, the transdimensional character of our approach relies in the idea of studying these theories in five dimensions. Indeed, we propose a Lagrangian that is formulated in five dimensions but has the potential to capture the six-dimensional interactions of (2,0) theories. This investigation leads us to explore in closer detail the relation between physics in five and in six dimensions. One of the outcomes of our exploration is a general result for one-loop corrections to Chern-Simons couplings in five dimensions

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

Spinorial geometry, off-shell Killing spinor identities and higher derivative 5D supergravities

Killing spinor identities relate components of equations of motion to each other for supersymmetric backgrounds. The only input required is the field content and the supersymmetry transformations of the fields, as long as an on-shell supersymmetrization of the action without additional fields exists. If we consider off-shell supersymmetry it is clear that the same relations will occur between components of the equations of motion independently of the specific action considered, in particular the Killing spinor identities can be derived for arbitrary, including higher derivative, supergravities, with a specified matter content. We give the Killing spinor identities for five-dimensional $\mathcal{N}=2$ ungauged supergravities coupled to Abelian vector multiplets, and then using spinorial geometry techniques so that we have explicit representatives for the spinors, we discuss the particular case of the time-like class of solutions to theories with perturbative corrections at the four derivative level. We also discuss the maximally supersymmetric solutions in the general off-shell case.Comment: 62 pages v2: fewer typos, and a few improvements in the text kindly suggested by a refere

An Analysis of Abusive Language Data Collected through a Game with a Purpose

In this work we present an analysis of abusive language annotations collected through a 3D video game. With this approach, we are able to involve in the annotation teenagers, i.e. typical targets of cyberbullying, whose data are usually not available for research purposes. Using the game in the framework of educational activities to empower teenagers against online abuse we are able to obtain insights into how teenagers communicate, and what kind of messages they consider more offensive. While players produced interesting annotations and the distributions of classes between players and experts are similar, we obtained a significant number of mismatching judgements between experts and players

A proposal for a two-step sampling design to oversample units responding to prescribed characteristics

We introduce a novel method to extract a sample from a finite population where units with desired characteristics are over-represented. The approach is both sequential and adaptive and allows, via suitable compositions of predictive and objective functions, to target specific subsets of the population. We consider the problem of estimation and conjecture the validity of a modified Horvitz–Thompson estimator capable to account for the imbalance induced by the targeting procedure. After discussing how to apply the method to the sampling of geographically distributed units, we investigate its potential via simulations.Online publication date: 19 Jan 201

A 3D Role-Playing Game for Abusive Language Annotation

Gamification has been applied to many linguistic annotation tasks, as an alternative to crowdsourcing platforms to collect annotated data in an inexpensive way. However, we think that still much has to be explored. Games with a Purpose (GWAPs) tend to lack important elements that we commonly see in commercial games, such as 2D and 3D worlds or a story. Making GWAPs more similar to full-fledged video games in order to involve users more easily and increase dissemination is a demanding yet interesting ground to explore. In this paper we present a 3D role-playing game for abusive language annotation that is currently under development

F-Theory on Spin(7) Manifolds: Weak-Coupling Limit

F-theory on appropriately fibered Spin(7) holonomy manifolds is defined to arise as the dual of M-theory on the same space in the limit of a shrinking fiber. A class of Spin(7) orbifolds can be constructed as quotients of elliptically fibered Calabi-Yau fourfolds by an anti-holomorphic involution. The F-theory dual then exhibits one macroscopic dimension that has the topology of an interval. In this work we study the weak-coupling limit of a subclass of such constructions and identify the objects that arise in this limit. On the Type IIB side we find space-time filling O7-planes as well as O5-planes and orbifold five-planes with a (-1)^{F_L} factor localised on the interval boundaries. These orbifold planes are referred to as X5-planes and are S-dual to a D5-O5 system. For other involutions exotic O3-planes and X3-planes on top of a six-dimensional orbifold singularity can appear. We show that the objects present preserve a mutual supersymmetry of four supercharges in the bulk of the interval and two supercharges on the boundary. It follows that in the infinite-interval and weak-coupling limit full four-dimensional N=1 supersymmetry is restored, which on the Type IIA side corresponds to an enhancement of supersymmetry by winding modes in the vanishing interval limit.Comment: 23 page

A Kaluza-Klein inspired action for chiral p-forms and their anomalies

The dynamics of chiral p-forms can be captured by a lower-dimensional parity-violating action motivated by a Kaluza-Klein reduction on a circle. The massless modes are (p-1)-forms with standard kinetic terms and Chern-Simons couplings to the Kaluza-Klein vector of the background metric. The massive modes are p-forms charged under the Kaluza-Klein vector and admit parity-odd first-order kinetic terms. Gauge invariance is implemented by a Stueckelberg-like mechanism using (p-1)-forms. A Chern-Simons term for the Kaluza-Klein vector is generated at one loop by massive p-form modes. These findings are shown to be consistent with anomalies and supersymmetry for six-dimensional supergravity theories with chiral tensor multiplets.Comment: 4 pages, 1 figur

Effective actions for F-theory compactifications and tensor theories

In this thesis we study the low-energy effective dynamics emerging from a class of F-theory compactifications in four and six dimensions. We also investigate six-dimensional supersymmetric quantum field theories with self-dual tensors, motivated by the problem of describing the long-wavelength regime of a stack of M5-branes in M-theory. These setups share interesting common features. They both constitute examples of intrinsically non-perturbative physics. On the one hand, in the context of F-theory the non-perturbative character is encoded in the geometric formulation of this class of string vacua, which allows the complexified string coupling to vary in space. On the other hand, the dynamics of a stack of multiple M5-branes flows in the infrared to a novel kind of superconformal field theories in six dimensions - commonly referred to as (2,0) theories - that are expected to possess no perturbative weakly coupled regime and have resisted a complete understanding so far. In particular, no Lagrangian description is known for these models. The strategy we employ to address these two problems is also analogous. A recurring Leitmotif of our work is a transdimensional treatment of the system under examination: in order to extract information about dynamics in $d$ dimensions we consider a (d-1)-dimensional setup. As far as F-theory compactifications are concerned, this is a consequence of the duality between M-theory and F-theory, which constitutes our main tool in the derivation of the effective action of F-theory compactifications. We apply it to six-dimensional F-theory vacua, obtained by taking the internal space to be an elliptically fibered Calabi-Yau threefold, but we also employ it to explore a novel kind of F-theory constructions in four dimensions based on manifolds with Spin(7) holonomy. With reference to six-dimensional (2,0) theories, the transdimensional character of our approach relies in the idea of studying these theories in five dimensions. Indeed, we propose a Lagrangian that is formulated in five dimensions but has the potential to capture the six-dimensional interactions of (2,0) theories. This investigation leads us to explore in closer detail the relation between physics in five and in six dimensions. One of the outcomes of our exploration is a general result for one-loop corrections to Chern-Simons couplings in five dimensions