We give a brief overview how to couple general relativity to the Standard Model of elementary particles, within the higher gauge theory framework, suitable for the spinfoam quantization procedure. We begin by providing a short review of all relevant mathematical concepts, most notably the idea of a categorical ladder, 3-groups and generalized parallel transport. Then, we give an explicit construction of the algebraic structure which describes the full Standard Model coupled to Einstein-Cartan gravity, along with the classical action, written in the form suitable for the spinfoam quantization procedure. We emphasize the usefulness of the 3-group concept as a superior tool to describe gauge symmetry, compared to an ordinary Lie group, as well as the possibility to employ this new structure to classify matter fields and study their spectrum, including the origin of fermion families.
We formulate and explore the physical implications of a new translation gauge theory of gravity in flat space-time with a new Yang-Mills action, which involves quadratic gauge curvature and fermions. The theory shows that the presence of an "effective Riemann metric tensor" for the motions of classical particles and light rays is probably the manifestation of the translation gauge symmetry. In the post-Newtonian approximation of the tensor gauge field produced by the energy-momentum tensor, the results are shown to be consistent with classical tests of gravity and with the quadrupole radiation…
A unified field theory of all known basic forces and elementary particles is built based on the postulates of gauge invariance and coordinate independence along with general conformal scaling symmetry. The hyper-spin charge of a unified hyper-spinor field is conjectured to correlate with the dimension of hyper-spacetime. The minimal dimension of hyper-spacetime for the unity of quarks and leptons in the standard model is found to be $D_h=19$ with a bimaximal symmetry. A unified fundamental interaction is governed by hyper-spin gauge symmetry SP(1,$D_h$-1). We show gravitational origin of gauge…
This paper explains the Unimodular gauge fixing of gravity and supergravity in the framework of a perturbative BRST construction. The unphysical sector contains additional BRST-exact quartets to suppress possible ambiguities and impose both the Unimodular gauge fixing condition on the metric and a gauge condition for the reparametrization symmetry of the unimodular part of the metric. The Unimodular gauge choice of the metric must be completed by a $γ$-Traceless gauge condition for the Rarita--Schwinger field in the case of supergravity. This gives an interesting new class of gauges for gravit…
Gravitation theory is formulated as gauge theory on natural bundles with spontaneous symmetry breaking where gauge symmetries are general covariant transformations, gauge fields are general linear connections, and Higgs fields are pseudo-Riemannian metrics.
We consider the model of minimally interacting electromagnetic, gravitational and massive scalar fields free of any additional nonlinearities. In the dimensionless form, the Lagranginan contains only one parameter γ= Gm^2/e^2 which corresponds to the ratio of gravitational and electromagnetic interactions and, for a typical elementary particle, is about 10^-40. However, regular (soliton-like) solutions can exist only for γ\ne 0 so that gravity would be necessary to form the structure of an (extended) elementary particle. Unfortunately (in the stationary spherically symmetrical case), the numer…
A definition of a convolution of tensor fields on group manifolds is given, which is then generalised to generic homogeneous spaces. This is applied to the product of gauge fields in the context of `gravity $=$ gauge $\times$ gauge'. In particular, it is shown that the linear Becchi-Rouet-Stora-Tyutin (BRST) gauge transformations of two Yang-Mills gauge fields generate the linear BRST diffeomorphism transformations of the graviton. This facilitates the definition of the `gauge $\times$ gauge' convolution product on, for example, the static Einstein universe, and more generally for ultrastatic …
When gravity is quantum, the point structure of space-time should be replaced by a non-commutative geometry. This is true even for quantum gravity in the infrared. Using the octonions as space-time coordinates, we construct a pre-spacetime, pre-quantum Lagrangian dynamics. We show that the symmetries of this non-commutative space unify the standard model of particle physics with $SU(2)_R$ chiral gravity. The algebra of the octonionic space yields spinor states which can be identified with three generations of quarks and leptons. The geometry of the space implies quantisation of electric charge…
Previous works (by Almiehri, Dong, Harlow, Pastakawski, Preskill, Yoshida and others) have established that quantum error correction plays an important role in understanding how the bulk degrees of freedom of an Anti-deSitter spacetime are encoded in the degrees of freedom of the boundary Conformal Field Theory. In previous work \cite{Vaid2013Elementary} I have argued that the Bilson-Thompson model \cite{Bilson-Thompson2006Quantum,Vaid2010Embedding} of elementary particles allows us to view elementary particles as gates for universal quantum computation. In the present work I show that the Bil…
Static quark-antiquark states in QCD, at finite quark separation, have a spectrum of metastable states corresponding to string-like excitations of the gauge field. In this article I suggest that there may also exist an excitation spectrum of heavy fermions in some gauge Higgs theories deep in the Higgs phase. In this situation there are no color electric flux tubes connecting quarks with antiquarks. There may, nonetheless, exist stable excitations of the bosonic fields surrounding an isolated fermion, below the particle production threshold. I present numerical evidence indicating the existenc…
We present the geometric formulation of gravity based on the mathematical structure of a Lie Algebroid. We show that this framework provides the geometrical setting to describe the gauge propriety of gravity.
On the gauge invariant boundary condition in open XXZ chains: SoV bases, elementary blocks and overlaps
Univ Lyon, Ens de Lyon, Univ Claude Bernard, CNRS, Laboratoire de Physique（里昂大学，巴黎高等师范学院，克劳德·贝尔纳大学，法国国家科学研究中心，物理实验室）；Université Paris-Saclay, CNRS, LPTMS（巴黎萨克雷大学，法国国家科学研究中心，理论与模型物理实验室）
We start by briefly reviewing the description of gravity theories as gauge theories in four dimensions. More specifically we recall the procedure leading to the results of General Relativity and Weyl Gravity in a gauge-theoretic manner. Then, after a brief reminder of the formulation of gauge theories on noncommutative spaces, we review our recent work, where gravity is constructed as a gauge theory on the fuzzy $dS_4$.
The infinite group of deformed diffeomorphisms of the spacetime continuum is put into the basis of the gauge theory of gravity. This gives rise to some new ways for unification of gravity with other gauge interactions.
We study the gravity action built from two gauge fields corresponding to the generators of the conformal group. Starting with the action from which one can obtain Einstein gravity and conformal gravity upon imposing suitable constraints, we keep two independent gauge fields and integrate out the field corresponding to the generator of Lorentz transformations. We identify the two gauge fields with two vierbeins and perturb them around an Anti--de Sitter space. This gives the linearized equations that differ from both, Einstein gravity and conformal gravity linearized equations. We also study th…
Using gauge/gravity duality, we deduce several nontrivial consequences of quantum gravity from simple properties of the dual field theory. These include: (1) a version of cosmic censorship, (2) restrictions on evolution through black hole singularities, and (3) the exclusion of certain cosmological bounces. In the classical limit, the latter implies a new singularity theorem.
We review the basics and the current status of the Poincaré gauge theory of gravity. The general dynamical scheme of Poincaré gauge gravity (PG) is formulated, and its physical consequences are outlined. In particular, we discuss exact solutions with and without torsion, highlight the cosmological aspects, and consider the probing of the spacetime geometry.
Unimodular gravity can be formulated so that transverse diffeomorphisms and Weyl transformations are symmetries of the theory. For this formulation of unimodular gravity, we work out the two-point and three-point $h_{μν}$ contributions to the on-shell classical gravity action in the leading approximation and for an Euclidean AdS background. We conclude that these contributions do not agree with those obtained by using General Relativity due to IR divergent contact terms. The subtraction of these IR divergent terms yields the same IR finite result for both unimodular gravity and General Relativ…
We compute the one-loop divergences in a higher-derivative theory of gravity including Ricci tensor squared and Ricci scalar squared terms, in addition to the Hilbert and cosmological terms, on an (generally off-shell) Einstein background. We work with a two-parameter family of parametrizations of the graviton field, and a two-parameter family of gauges. We find that there are some choices of gauge or parametrization that reduce the dependence on the remaining parameters. The results are invariant under a recently discovered "duality" that involves the replacement of the densitized metric by a…
We consider the harmonic gauge condition in linearized gravity, seen as a gauge theory for a symmetric tensor field. Once the harmonic gauge condition is implemented, as customary, according to the Faddeev-Popov procedure, the gauge fixed action still depends on one gauge parameter. Consequently, the harmonic gauge appears to be a class of conditions, rather than a particular one. This allows to give a physical motivation for the covariant harmonic gauge(s), which emerges when the gravitational perturbation is given a mass term. In fact, for a particular choice of harmonic gauge, we find a the…
The weak-gravity bound has been discovered in asymptotically safe gravity-matter systems, where it limits the maximum strength of gravitational fluctuations. In the present paper, we explore it for the first time in systems with more than one gauge field, to discover whether systems with 12 gauge fields (like the Standard Model) exhibit a weak-gravity bound and whether the gravitational fixed point evades it. Further, we test the robustness of the present and previous results on the weak-gravity bound by exploring their dependence on a gravitational gauge parameter. Finally, the existence of t…
We demonstrate that Einstein's general relativity theory arises as a special case in the framework of the Poincaré gauge theory of gravity under the assumption of a suitable nonminimal coupling of matter to the Riemann-Cartan geometry of spacetime.
Following the Hamiltonian structure of bi-gravity and multi-gravity models in the full phase space, we have constructed the generating functional of diffeomorphism gauge symmetry. As is expected, this generator is constructed from the first class constraints of the system. We show that this gauge generator works well in giving the gauge transformations of the canonical variables.
Conformal and Noncommutative Gravity from Gauge Symmetry Breaking and SO(2,16) Unification
National Technical University of Athens（雅典国立技术大学）；Max-Planck-Institut für Physik（马克斯·普朗克物理研究所）；Universität Hamburg（汉堡大学）；Deutsches Elektronen-Synchrotron DESY（德国电子同步加速器中心）
After reviewing how Albert Einstein's general relativity (GR) can be viewed as a gauge theory of the Poincaré algebra, we show how Élie Cartan's geometric formulation of Newtonian gravity (Newton-Cartan gravity) can be viewed as a gauge theory of the Bargmann algebra following the construction of [R. Andringa, E. Bergshoeff, S. Panda, and M. de Roo, "Newtonian Gravity and the Bargmann Algebra," Class. Quant. Grav. 28 (2011) 105011, arXiv:1011.1145 [hep-th]]. In doing so, we will touch on the following auxiliary topics: the extension of Yang-Mills gauge theory to a more generic formalism of gau…
In this paper, we discuss the gravitational waves in the context of gauge theory gravity with a negative cosmological constant. The gauge theory gravity is a gravity theory under gauge formulation in the language of geometric algebra. In contrast to general relativity, the background spacetime in gauge theory gravity is flat, the gauge freedom comes from the fact that equations in terms of physical quantities should be kept in a covariant form under spacetime displacement and rotation. Similar to the electromagnetism, the gauge formulation enables us to interpret the gravitational force as a g…
In this paper, we base on the formalism of Symbolic Gauge Theory in the case of General relativity; we calculate the Feynman diagrams for the interaction between harmonic gravitational connections in the topological field theory. These calculations provide insights to interactions between gravity and dark energy. They could, therefore, have important repercussions for current cosmological problems.
We deduce, in a general background gauge, the counter-term Lagrangian for pure quantum gravity to one-loop order. As an application, we evaluate the leading quantum correction to the classical gravitational potential, generated by the vacuum polarization. We find that, in specific background gauges, this yields the complete result for the one-loop quantum corrections to the Newtonian potential. This approach is also applied to calculate the $\ln(T)$ contributions in quantum gravity at high-temperature.
In three-dimensional gravity, we discuss the relation between the Fefferman--Graham gauge, the Bondi gauge and the Eddington--Finkelstein type of gauge, often referred to as the derivative expansion, involved in the fluid/gravity correspondence. Starting with a negative cosmological constant, for each gauge, we derive the solution space and the residual gauge diffeomorphisms. We construct explicitly the diffeomorphisms that relate the various gauges, and establish the precise matching of their boundary data. We show that Bondi and Fefferman--Graham gauges are equivalent, while the fluid/gravit…
