Multivector Fields of Noether Symmetries in the Lagrangian Formalism and Belinfante Tensor

Elsewhere, we gave the explicit expressions of the multivectors fields associated to infinitesimal symmetries which gave rise to Noether currents for classical field theories and relativistic mechanic using the Second Order Partial Differential Equation SOPDE condition for the Poincar\'e-Cartan form.\\ The main objective of this paper is to reformulate the multivector fields associated to translational and rotational symmetries of the gauge fields in particular those of the electromagnetic field which gave rise to symmetrical and invariant gauge energy-momentum tensor and the orbital angular momentum. The spin angular momentum appears however because of the internal symmetry inside the fiber.

Ambitwistor strings in six and five dimensions

Ambitwistor strings are chiral (holomorphic) strings whose target is the space of complex null geodesics, ambitwistor space. We introduce twistor representations of ambitwistor space in 6 and 5 dimensions. In 6d the twistor representation is naturally conformally invariant. Anomaly cancellation leads to models that describe biadjoint scalar amplitudes and certain conformally invariant gauge and gravity theories, respectively of 4th and 6th order. There are three such models, reflecting triality for the conformal group SO(8) associated to these 6d models. On reduction to five dimensions, gauge anomaly cancellation requires supersymmetry and the resulting models describe maximally supersymmetric Yang-Mills and gravity. The twistor representation of these ambitwistor strings lead to formulæ for maximally supersymmetric gauge and gravity amplitudes based on the polarized scattering equations in 5d, found earlier by the first two authors.

A worldsheet perspective on heterotic T-duality orbifolds

Asymmetric heterotic orbifolds are discussed from the worldsheet perspective. Starting from Buscher’s gauging of a theory of D compact bosons the duality covariant description of Tseytlin is obtained after a non-Lorentz invariant gauge fixing. A left-over of the gauge symmetry can be used to removed the doubled constant zero modes so that D physical target space coordinate remain. This can be thought of as the worldsheet realization of the strong constraint of double field theory. The extension of this description to the heterotic theory is straightforward as all results are written in terms of the invariant and the generalized metrics. An explicit method is outline how to obtain a generalized metric which is invariant under T-duality orbifold actions. It is explicitly shown how shift orbifolds lead to redefinitions of the Narain moduli. Finally, a number of higher dimensional T-folds are constructed including a novel asymmetric ℤ6 orbifold.

Single extra dimension from κ-Poincaré and gauge invariance

We show that κ-Poincaré invariant gauge theories on κ-Minkowski space with physically acceptable commutative (low energy) limit must be 5-d. The gauge invariance requirement of the action fixes the dimension of the κ-Minkowski space to d = 5 and selects the unique twisted differential calculus with which the construction can be achieved. We characterize a BRST symmetry related to the 5-d noncommutative gauge invariance though the definition of a nilpotent operation, which is used to construct a gauge-fixed action. We also consider standard scenarios assuming (compactification of) flat extra dimension, for which the 5-d deformation parameter κ can be viewed as the bulk 5-d Planck mass. We study physical properties of the resulting 4-d effective theories. Recent data from collider experiments require κ ≳ $$ \mathcal{O} $$ O (1013) GeV. The use of standard test of in-vacuo dispersion relations of Gamma Ray Burst photons increases this lower bound by 4 orders of magnitude. The robustness of this bound is discussed in the light of possible new features of noncommutative causal structures.

Bundle geometry of the connection space, covariant Hamiltonian formalism, the problem of boundaries in gauge theories, and the dressing field method

We take advantage of the principal bundle geometry of the space of connections to obtain general results on the presymplectic structure of two classes of (pure) gauge theories: invariant theories, and non-invariant theories satisfying two restricting hypothesis. In particular, we derive the general field-dependent gauge transformations of the presymplectic potential and presymplectic 2-form in both cases. We point-out that a generalisation of the standard bundle geometry, called twisted geometry, arises naturally in the study of non-invariant gauge theories (e.g. non-Abelian Chern-Simons theory). These results prove that the well-known problem of associating a symplectic structure to a gauge theory over bounded regions is a generic feature of both classes. The edge modes strategy, recently introduced to address this issue, has been actively developed in various contexts by several authors. We draw attention to the dressing field method as the geometric framework underpinning, or rather encompassing, this strategy. The geometric insight afforded by the method both clarifies it and clearly delineates its potential shortcomings as well as its conditions of success. Applying our general framework to various examples allows to straightforwardly recover several results of the recent literature on edge modes and on the presymplectic structure of general relativity.

Holographic models of composite Higgs in the Veneziano limit. Part I. Bosonic sector

We study strongly-coupled, approximately scale-invariant gauge theories, which develop a mass gap in the infrared. We argue that a large number of fermion flavours is most suitable to provide an ultraviolet completion for the composite Higgs scenario. The holographic approach allows to describe the qualitative features of the non-perturbative dynamics in the Veneziano limit. We introduce new bottom-up holographic models, which incorporate the backreaction of flavour on the geometry, and show that this can correlate the mass gap to the scale of flavour-symmetry breaking. We compute the mass spectrum for the various composite bosonic states, and study its dependence on the scaling dimension of the symmetry-breaking operators, as well as on the number of flavours. The different regions with a light dilaton are critically surveyed. We carefully assess the domain of validity of the holographic approach, and compare it with lattice simulations and the Nambu-Jona-Lasinio model.

An E11 invariant gauge fixing

We consider the nonlinear realisation of the semi-direct product of [Formula: see text] and its vector representation which leads to a space-time with tangent group that is the Cartan involution invariant subalgebra of [Formula: see text]. We give an alternative derivation of the invariant tangent space metric that this space–time possesses and compute this metric at low levels in eleven, five and four dimensions. We show that one can gauge fix the nonlinear realisation in an [Formula: see text] invariant manner.

Invariant connections and invariant holomorphic bundles on homogeneous manifolds

Let X be a differentiable manifold endowed with a transitive action α: A×X→X of a Lie group A. Let K be a Lie group. Under suitable technical assumptions, we give explicit classification theorems, in terms of explicit finite dimensional quotients, of three classes of objects:equivalence classes of α-invariant K-connections on X α-invariant gauge classes of K-connections on X, andα-invariant isomorphism classes of pairs (Q,P) consisting of a holomorphic Kℂ-bundle Q → X and a K-reduction P of Q (when X has an α-invariant complex structure).