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Sum rules in effective field theories, predicated upon causality, place restrictions on scattering amplitudes mediated by effective contact interactions. Through unitarity of the $S$-matrix, these imply that the size of higher dimensional…
We investigate linear maps between matrix algebras that remain positive under tensor powers, i.e., under tensoring with $n$ copies of themselves. Completely positive and completely co-positive maps are trivial examples of this kind. We show…
The methods of effective field theory are used to explore the theoretical and phenomenological aspects of the torsion field. Spinor action coupled to electromagnetic field and torsion possesses an additional softly broken gauge symmetry.…
We continue our constructive study of tensor field theory through the next natural model, namely the rank four tensor theory with quartic melonic interactions and propagator inverse of the Laplacian on $U(1)^4$. This superrenormalizable…
This paper provides an extension of the constructive loop vertex expansion to stable matrix models with interactions of arbitrarily high order. We introduce a new representation for such models, then perform a forest expansion on this…
This paper studies a high-dimensional inference problem involving the matrix tensor product of random matrices. This problem generalizes a number of contemporary data science problems including the spiked matrix models used in sparse…
We study the renormalization of dimension four composite operators and the energy-momentum tensor in noncommutative complex scalar field theory. The proper operator basis is defined and it is proved that the bare composite operators are…
Under the hypotheses of analyticity in the coupling constant, locality, Lorentz covariance, and Poincare invariance of the deformations, combined with the preservation of the number of derivatives on each field, the consistent interactions…
A tensorial representation of $\phi^4$ field theory introduced in Phys. Rev. D. 93, 085005 (2016) is studied close to six dimensions, with an eye towards a possible realization of an interacting conformal field theory in five dimensions. We…
Under the hypotheses of analyticity, locality, Lorentz covariance, and Poincare invariance of the deformations, combined with the requirement that the interaction vertices contain at most two space-time derivatives of the fields, we…
Tensor models are measures for random tensors. They generalise matrix models and were developed to study random geometry in arbitrary dimension. Moreover, they are strongly connected to quantum gravity theories as additionally to the…
Resummed-Range Effective Field Theory is the consistent non-relativistic Effective Field Theory of point interactions in systems with large two-body scattering length $a$ and an effective range $r_0$ large in magnitude but negative. Its…
In a recently proposed model in which a vector non-Abelian gauge field interacts with an antisymmetric tensor field, it has been shown that the tensor field possesses no physical degrees of freedom. This formal demonstration is tested by…
Consistent couplings between a massless tensor field with the mixed symmetry of the Riemann tensor and a massless vector field are analyzed in the framework of Lagrangian BRST cohomology. Under the assumptions on smoothness, locality,…
We complete the first stage of constructing a theory of fields not investigated before; these fields transform according to Lorentz group representations decomposable into an infinite direct sum of finite-dimensional irreducible…
Effective field theory provides a way of parameterizing strong-field deviations from General Relativity that might be observable in the gravitational waves emitted in a black hole merger. To perform numerical simulations of mergers in such…
Recent advances in {matrix-mimetic} tensor frameworks have made it possible to preserve linear algebraic properties for multilinear data analysis and, as a result, to obtain optimal representations of multiway data. Matrix mimeticity arises…
Random tensors are the natural generalization of random matrices to higher order objects. They provide generating functions for random geometries and, assuming some familiarity with random matrix theory and quantum field theory, we discuss…
The 3-dimensional coherence matrix is interpreted by emphasising its invariance with respect to spatial rotations. Under these transformations, it naturally decomposes into a real symmetric positive definite matrix, interpreted as the…
The equivalence between rank-2 anti-symmetric tensor fields, considered as gauge potentials, and torsionless non-linear $\sigma$-models suggests us to study the possibility of coupling tensorial matter with Yang-Mills fields, through the…