Related papers: Tensor Hierarchies of 5- and 6-Dimensional Field T…
This thesis focuses on renormalization of quantum field theories. Its first part considers three tensor models in three dimensions, a Fermionic quartic with tensors of rank-3 and two Bosonic sextic, of ranks 3 and 5. We rely upon the…
We study the dimensional reduction of five dimensional N=2 Yang-Mills-Einstein supergravity theories (YMESGT) coupled to tensor multiplets. The resulting 4D theories involve first order interactions among tensor and vector fields with mass…
This note supplements an earlier paper on conformal field theories. There it was shown how to construct tensor, spinor, and spinor-tensor primary fields in four dimensions from their counterparts in six dimensions, where conformal…
The main goal of this paper is to study the topological properties of tensors in tree-based Tucker format. These formats include the Tucker format and the Hierarchical Tucker format. A property of the so-called minimal subspaces is used for…
We treat random rank-$D$ tensor models as $D$-dimensional quantum field theories---tensor field theories (TFT)---and review some of their non-perturbative methods. We classify the correlation functions of complex tensor field theories by…
Tensor network states are capable of describing many-body systems with complex quantum entanglement, including systems with non-trivial topological order. In this paper, we study methods to calculate the topological properties of a tensor…
In this paper, first we introduce the notion of an embedding tensor on a 3-Lie algebra, which naturally induces a 3-Leibniz algebra. Using the derived bracket, we construct a Lie 3-algebra, whose Maurer-Cartan elements are embedding…
This thesis consists of an introductory text, which is divided into two parts, and six appended research papers. The first part contains a general discussion on conformal and superconformal symmetry in six dimensions, and treats how the…
Deformations of maximal supergravity theories induced by gauging non-abelian subgroups of the duality group reveal the presence of charged M-theory degrees of freedom that are not necessarily contained in supergravity. The relation with…
Third-order tensors are widely used as a mathematical tool for modeling physical properties of media in solid state physics. In most cases, they arise as constitutive tensors of proportionality between basic physics quantities. The…
We develop the embedding formalism for conformal field theories, aimed at doing computations with symmetric traceless operators of arbitrary spin. We use an index-free notation where tensors are encoded by polynomials in auxiliary…
We consider the theory of a symmetric tensor field in 4D, invariant under a subclass of infinitesimal diffeomorphism transformations, where the vector diff parameter is the 4-divergence of a scalar parameter. The resulting gauge symmetry…
We consider several diffeomorphism invariant field theories of 2- and 3-forms in six dimensions. They all share the same kinetic term $BdC$, but differ in the potential term that is added. The theory $BdC$ with no potential term is…
We show how three-dimensional superconformal theories for any number N <= 8 of supersymmetries can be obtained by taking a conformal limit of the corresponding three-dimensional gauged supergravity models. The superconformal theories are…
IIB supergravity is reformulated with a manifest local USp(8) invariance that makes the embedding of five-dimensional maximal supergravities transparent. In this formulation the ten-dimensional theory exhibits all the 27 one-form fields and…
In this paper I shall consider field theories in a space of four-dimensions which have field variables consisting of the components of a metric tensor and scalar field. The field equations of these scalar-tensor field theories will be…
Consistent nontrivial interactions within a special class of covariant mixed-symmetry type tensor gauge fields of degree three are constructed from the deformation of the solution to the master equation combined with specific cohomological…
The Horndeski action is the most general one involving a metric and a scalar field that leads to second order field equations in four dimensions. Being the natural extension of the well known Scalar-Tensor theories, its structure and…
We consider discrete gauge symmetries in D dimensions arising as remnants of broken continuous gauge symmetries carried by general antisymmetric tensor fields, rather than by standard 1-forms. The lagrangian for such a general ${\bf Z}_p$…
We study a set of theories built on a ranked sequence of antisymmetric tensor fields in D dimensional space-time. These linear theories exhibit gauge invariances that are analogous to the local gauge invariance of a massless vector…