On Newton-Cartan trace anomalies

We classify the trace anomaly for parity-invariant non-relativistic Schr\"odinger theories in 2+1 dimensions coupled to background Newton-Cartan gravity. The general anomaly structure looks very different from the one in the z=2 Lifshitz theories. The type A content of the anomaly is remarkably identical to that of the relativistic 3+1 dimensional case, suggesting the conjecture that an a-theorem should exist also in the Newton-Cartan context. Erratum: due to an overcounting of the number of linearly-independent terms in the basis, the type A anomaly disappears if Frobenius condition is imposed. See appended erratum for details. This crucial mistake was pointed out to us in arXiv:1601.06795.Comment: 16 pages, V2:few equations corrected (final results unchanged), references added, typos, V3: erratum include

The Tensor Track, III

We provide an informal up-to-date review of the tensor track approach to quantum gravity. In a long introduction we describe in simple terms the motivations for this approach. Then the many recent advances are summarized, with emphasis on some points (Gromov-Hausdorff limit, Loop vertex expansion, Osterwalder-Schrader positivity...) which, while important for the tensor track program, are not detailed in the usual quantum gravity literature. We list open questions in the conclusion and provide a rather extended bibliography.Comment: 53 pages, 6 figure

Twistors, special relativity, conformal symmetry and minimal coupling - a review

An approach to special relativistic dynamics using the language of spinors and twistors is presented. Exploiting the natural conformally invariant symplectic structure of the twistor space, a model is constructed which describes a relativistic massive, spinning and charged particle, minimally coupled to an external electro-magnetic field. On the two-twistor phase space the relativistic Hamiltonian dynamics is generated by a Poincare scalar function obtained from the classical limit (appropriately defined by us) of the second order, to an external electro-magnetic field minimally coupled, Dirac operator. In the so defined relativistic classical limit there are no Grassman variables. Besides, the arising equation that describes dynamics of the relativistic spin differs significantly from the so called Thomas Bergman Michel Telegdi equation.Comment: 39 pages, no figures, few erronous statements (not affecting anything else in the papper) on page 23 delete

Systematic Study of Theories with Quantum Modified Moduli

We begin the process of classifying all supersymmetric theories with quantum modified moduli. We determine all theories based on a single SU or Sp gauge group with quantum modified moduli. By flowing among theories we have calculated the precise modifications to the algebraic constraints that determine the moduli at the quantum level. We find a class of theories, those with a classical constraint that is covariant but not invariant under global symmetries, that have a singular modification to the moduli, which consists of a new branch.Comment: 21 pages, ReVTeX (or Latex, etc), corrected typos and cQMM discusio

Quantum Gravity and Random Tensors

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 in the first part of this note the applications of such models to quantum gravity. In a second part we review tensor field theories, that is standard field theories in $\mathbb{R}^d$ but with tensor fields, which lead to a new family of large $N$ conformal field theories relevant for the study of the $AdS/CFT$ correspondence.Comment: Contribution to the Poincar\'e Seminar, December 16th 2023 (second version, some references added

Group field theory condensate cosmology: An appetizer

This contribution is an appetizer to the relatively young and fast evolving approach to quantum cosmology based on group field theory condensate states. We summarize the main assumptions and pillars of this approach which has revealed new perspectives on the long-standing question of how to recover the continuum from discrete geometric building blocks. Among others, we give a snapshot of recent work on isotropic cosmological solutions exhibiting an accelerated expansion, a bounce where anisotropies are shown to be under control and inhomogeneities with an approximately scale-invariant power spectrum. Finally, we point to open issues in the condensate cosmology approach.Comment: Review article as an invited contribution for the special issue "Progress in Group Field Theory and Related Quantum Gravity Formalisms", Universe journa