Hamiltonian formulation of higher rank symmetric gauge theories

Recent discussions of fractons have evolved around higher rank symmetric gauge theories with emphasis on the role of Gauss constraints. This has prompted the present study where a detailed hamiltonian analysis of such theories is presented. Besides a general treatment, the traceless scalar charge theory is considered in details. A new form for the action is given which, in $$2+1$$ 2 + 1 dimensions, yields area preserving diffeomorphisms. Investigation of global symmetries reveals that this diffeomorphism invariance induces a noncommuting charge algebra that gets exactly mapped to the algebra of coordinates in the lowest Landau level problem. Connections of this charge algebra to noncommutative fluid dynamics and magnetohydrodynamics are shown.

Symmetries and conformal bridge in Schwarschild-(A)dS black hole mechanics

We show that the Schwarzschild-(A)dS black hole mechanics possesses a hidden symmetry under the three-dimensional Poincaré group. This symmetry shows up after having gauge-fixed the diffeomorphism invariance in the symmetry-reduced homogeneous Einstein-Λ model and stands as a physical symmetry of the system. It dictates the geometry both in the black hole interior and exterior regions, as well as beyond the cosmological horizon in the Schwarzschild-dS case. It follows that one can associate a set of non-trivial conserved charges to the Schwarzschild-(A)dS black hole which act in each causally disconnected regions. In T-region, they act on fields living on spacelike hypersurface of constant time, while in R-regions, they act on time-like hypersurface of constant radius. We find that while the expression of the charges depend explicitly on the location of the hypersurface, the charge algebra remains the same at any radius in R-regions (or time in T-regions). Finally, the analysis of the Casimirs of the charge algebra reveals a new solution-generating map. The $$ \mathfrak{sl}\left(2,\mathrm{\mathbb{R}}\right) $$ sl 2 ℝ Casimir is shown to generate a one-parameter family of deformation of the black hole geometry labelled by the cosmological constant. This gives rise to a new conformal bridge allowing one to continuously deform the Schwarzschild-AdS geometry to the Schwarzschild and the Schwarzschild-dS solutions.

Shape Dynamics of the TT¯ Deformation

I will show how the flow triggered by deforming two-dimensional conformal field theories on a torus by the TT¯ operator is identical to the evolution generated by the (radial) quantum Shape Hamiltonian in 2 + 1 dimensions. I will discuss how the gauge invariances of the Shape Dynamics, i.e., volume-preserving conformal invariance and diffeomorphism invariance along slices of constant radius are realized as Ward identities of the deformed quantum field theory. I will also comment about the relationship between the reduction to shape space on the gravity side and the solvability of the irrelevant operator deformation of the conformal field theory

Confinement in 4D: An Attempt at Classical Understanding

In this review, we revisit our approach to constructing an effective theory for Abelian and Non-Abelian gauge theories in 4D. Our goal is to have an effective theory that provides a simple classical picture of the main qualitatively important features of these theories. We set out to ensure the presence of the massless photons—Goldstone bosons in Abelian theory and their disappearance in the Non-Abelian case—accompanied by the formation of confining strings between charged states. Our formulation avoids using vector fields and instead operates with the basic degrees of freedom that are the scalar fields of a nonlinear σ-model. The Mark 1 model we study turns out to have a large global symmetry group-the 2D diffeomorphism invariance in the Abelian limit, which is isomorphic to the group of all canonical transformations in the classical two dimensional phase space. This symmetry is not present in QED, and we eliminate it by “gauging” this infinite dimensional global group. Introducing additional modifications to the model (Mark 2), we are able to prove that the “Abelian” version is equivalent to the theory of a free photon. Achieving the desired property in the “Non-Abelian” regime turns out to be tricky. We are able to introduce a perturbation that leads to the formation of confining strings in our Mark 1 model. These strings have somewhat unusual properties, in that their profile does not decay exponentially away from the center of the string. In addition, the perturbation explicitly breaks the diffeomorphism invariance. Preserving this invariance in the gauged model as well as achieving confining strings in Mark 2 model remains an open question.

Perturbative and Non-Pertrubative Trace Anomalies

We study the definition of trace anomalies for models of Dirac and Weyl fermions coupled to a metric and a gauge potential. While in the non-perturbative case the trace anomaly is the response of the effective action to a Weyl transformation, the definition in a perturbative approach is more involved. In the latter case, we use a specific formula proposed by M.Duff, of which we present a physical interpretation. The main body of the paper consists in deriving trace anomalies with the above formula and comparing them with the corresponding non-perturbative results. We show that they coincide and stress the basic role of diffeomorphism invariance for the validity of the approach.

Quantum gravity states, entanglement graphs and second-quantized tensor networks

In recent years, the import of quantum information techniques in quantum gravity opened new perspectives in the study of the microscopic structure of spacetime. We contribute to such a program by establishing a precise correspondence between the quantum information formalism of tensor networks (TN), in the case of projected entangled-pair states (PEPS) generalised to a second-quantized framework, and group field theory (GFT) states, and by showing how, in this quantum gravity approach, discrete spatial manifolds arise as entanglement patterns among quanta of space, having a dual representation in terms of graphs and simplicial complexes. We devote special attention to the implementation and consequences of the label independence of the graphs/networks, corresponding to the indistinguishability of the space quanta and representing a discrete counterpart of the diffeomorphism invariance of a consistent quantum gravity formalism. We also outline a relational setting to recover distinguishability of graph/network vertices at an effective and physical level, in a partial semi-classical limit of the theory.

Holographic DC conductivity for backreacted NLED in massive gravity

In this work a holographic model with the charge current dual to a general non-linear electrodynamics (NLED) is discussed in the framework of massive gravity. Massive graviton can break the diffeomorphism invariance in the bulk and generates momentum dissipation in the dual boundary theory. The expression of DC conductivities in a finite magnetic field are obtained, with the backreaction of NLED field on the background geometry. General transport properties in various limits are presented, and then we turn to the three of specific NLED models: the conventional Maxwell electrodynamics, the Maxwell-Chern-Simons electrodynamics, and the Born-Infeld electrodynamics, to study the parameter-dependence of in-plane resistivities. Two mechanisms leading to the Mott-insulating behaviors and negative magneto-resistivities are revealed at zero temperature, and the role played by the massive gravity coupling parameters are discussed.

Near-BPS baby Skyrmions with Gaussian tails

We consider the baby Skyrme model in a physically motivated limit of reaching the restricted or BPS baby Skyrme model, which is a model that enjoys area-preserving diffeomorphism invariance. The perturbation consists of the kinetic Dirichlet term with a small coefficient ϵ as well as the standard pion mass term, with coefficient $$ \upepsilon {m}_1^2 $$ ϵ m 1 2 . The pions remain lighter than the soliton for any ϵ and therefore the model is physically acceptable, even in the ϵ → 0 limit. The version of the BPS baby Skyrme model we use has BPS solutions with Gaussian tails. We perform full numerical computations in the ϵ → 0 limit and even reach the strict ϵ = 0 case, finding new nontrivial BPS solutions, for which we do not yet know the analytic form.

Gravity with Explicit Diffeomorphism Breaking

Modified theories of gravity that explicitly break diffeomorphism invariance have been used for over a decade to explore open issues related to quantum gravity, dark energy, and dark matter. At the same time, the Standard-Model Extension (SME) has been widely used as a phenomenological framework in investigations of spacetime symmetry breaking. Until recently, it was thought that the SME was suitable only for theories with spontaneous spacetime symmetry breaking due to consistency conditions stemming from the Bianchi identities. However, it has recently been shown that, particularly with matter couplings included, the consistency conditions can also be satisfied in theories with explicit breaking. An overview of how this is achieved is presented, and two examples are examined. The first is massive gravity, which includes a nondynamical background tensor. The second is a model based on a low-energy limit of Hořava gravity, where spacetime has a physically preferred foliation. In both cases, bounds on matter–gravity interactions that explicitly break diffeomorphisms are obtained using the SME.

Boosting GWs in supersolid inflation

Inflation driven by a generic self-gravitating medium is an interesting alternative to study the impact of spontaneous spacetime symmetry breaking during a quasi de-Sitter phase, in particular the 4-dimensional diffeomorphism invariance of GR is spontaneously broken down to I SO(3). The effective description is based on four scalar fields that describe the excitations of a supersolid. There are two phonon-like propagating scalar degrees of freedom that mix non-trivially both at early and late times and, after exiting the horizon, give rise to non-trivial correlations among the different scalar power spectra. The non-linear structure of the theory allows a secondary gravitational waves production during inflation, efficient enough to saturate the present experimental bound and with a blue-tilted spectral index.