Unlike the fundamental forces of the Standard Model, such as electromagnetic, weak and strong forces, the quantum effects of gravity are still experimentally inaccessible. The weak coupling of gravity with matter makes it significant only for large m
asses where quantum effects are too subtle to be measured with current technology. Nevertheless, insight into quantum aspects of gravity is key to understanding unification theories, cosmology or the physics of black holes. Here we propose the simulation of quantum gravity with optical lattices which allows us to arbitrarily control coupling strengths. More concretely, we consider $(2+1)$-dimensional Dirac fermions, simulated by ultra-cold fermionic atoms arranged in a honeycomb lattice, coupled to massive quantum gravity, simulated by bosonic atoms positioned at the links of the lattice. The quantum effects of gravity induce interactions between the Dirac fermions that can be witnessed, for example, through the violation of Wicks theorem. The similarity of our approach to current experimental simulations of gauge theories suggests that quantum gravity models can be simulated in the laboratory in the near future.
We consider Carroll-invariant limits of Lorentz-invariant field theories. We show that just as in the case of electromagnetism, there are two inequivalent limits, one electric and the other magnetic. Each can be obtained from the corresponding Lorent
z-invariant theory written in Hamiltonian form through the same contraction procedure of taking the ultrarelativistic limit $c rightarrow 0$ where $c$ is the speed of light, but with two different consistent rescalings of the canonical variables. This procedure can be applied to general Lorentz-invariant theories ($p$-form gauge fields, higher spin free theories etc) and has the advantage of providing explicitly an action principle from which the electrically-contracted or magnetically-contracted dynamics follow (and not just the equations of motion). Even though not manifestly so, this Hamiltonian action principle is shown to be Carroll invariant. In the case of $p$-forms, we construct explicitly an equivalent manifestly Carroll-invariant action principle for each Carroll contraction. While the manifestly covariant variational description of the electric contraction is rather direct, the one for the magnetic contraction is more subtle and involves an additional pure gauge field, whose elimination modifies the Carroll transformations of the fields. We also treat gravity, which constitutes one of the main motivations of our study, and for which we provide the two different contractions in Hamiltonian form.
Motivated by the recent progresses in the formulation of geometric theories for the fractional quantum Hall states, we propose a novel non-relativistic geometric model for the Laughlin states based on an extension of the Nappi-Witten geometry. We sho
w that the U(1) gauge sector responsible for the fractional Hall conductance, the gravitational Chern-Simons action and Wen-Zee term associated to the Hall viscosity can be derived from a single Chern-Simons theory with a gauge connection that takes values in the extended Nappi-Witten algebra. We then provide a new derivation of the chiral boson associated to the gapless edge states from the Wess-Zumino-Witten model that is induced by the Chern-Simons theory on the boundary.
We construct the non-relativistic and Carrolli
Here, we analyse two Dirac fermion species in two spatial dimensions in the presence of general quartic contact interactions. By employing functional bosonisation techniques, we demonstrate that depending on the couplings of the fermion interactions
the system can be effectively described by a rich variety of topologically massive gauge theories. Among these effective theories, we obtain an extended Chern-Simons theory with higher order derivatives as well as two coupled Chern-Simons theories. Our formalism allows for a general description of interacting fermions emerging, for example, at the gapped boundary of three-dimensional topological crystalline insulators.
We show that gravitating Merons in $D$-dimensional massive Yang-Mills theory can be mapped to solutions of the Einstein-Skyrme model. The identification of the solutions relies on the fact that, when considering the Meron ansatz for the gauge connect
ion $A=lambda U^{-1}dU$, the massive Yang-Mills equations reduce to the Skyrme equations for the corresponding group element $U$. In the same way, the energy-momentum tensors of both theories can be identified and therefore lead to the same Einstein equations. Subsequently, we focus on the $SU(2)$ case and show that introducing a mass for the Yang-Mills field restricts Merons to live on geometries given by the direct product of $S^3$ (or $S^2$) and Lorentzian manifolds with constant Ricci scalar. We construct explicit examples for $D=4$ and $D=5$. Finally, we comment on possible generalizations.
We show that a recently proposed action for three-dimensional non-relativistic gravity can be obtained by taking the limit of a relativistic Lagrangian that involves the co-adjoint Poincare algebra. We point out the similarity of our construction wit
h the way that three-dimensional Galilei Gravity and Extended Bargmann Gravity can be obtained by taking the limit of a relativistic Lagrangian that involves the Poincare algebra. We extend our results to the AdS case and we will see that there is a chiral decomposition both at the relativistic and non-relativistic level. We comment on possible further generalizations.
We show that the Extended Bargmann and Newton-Hooke algebras in 2+1 dimensions can be obtained as expansions of the Nappi-Witten algebra. The result can be generalized to obtain two infinite families of non-relativistic symmetries, which include the
Maxwellian Exotic Bargmann symmetry, its generalized Newton-Hooke counterpart, and its Hietarinta dual. In each case, the invariant bilinear form on the Nappi-Witten algebra leads to the invariant tensor on the expanded algebra, allowing one to construct the corresponding Chern-Simons gravity theory.
The Maxwell group in 2+1 dimensions is given by a particular extension of a semi-direct product. This mathematical structure provides a sound framework to study different generalizations of the Maxwell symmetry in three space-time dimensions. By givi
ng a general definition of extended semi-direct products, we construct infinite-dimensional enhancements of the Maxwell group that enlarge the ${rm ISL}(2,mathbb{R})$ Kac-Moody group and the ${rm BMS}_3$ group by including non-commutative supertranslations. The coadjoint representation in each case is defined, and the corresponding geometric actions on coadjoint orbits are presented. These actions lead to novel Wess-Zumino terms that naturally realize the aforementioned infinite-dimensional symmetries. We briefly elaborate on potential applications in the contexts of three-dimensional gravity, higher-spin symmetries, and quantum Hall systems.
In this paper the arising of Gribov copies both in Landau and Coulomb gauges in regions with non-trivial topologies but flat metric, (such as closed tubes S1XD2, or RXT2) will be analyzed. Using a novel generalization of the hedgehog ansatz beyond sp
herical symmetry, analytic examples of Gribov copies of the vacuum will be constructed. Using such ansatz, we will also construct the elliptic Gribov pendulum. The requirement of absence of Gribov copies of the vacuum satisfying the strong boundary conditions implies geometrical constraints on the shapes and sizes of the regions with non-trivial topologies.
