We show that when graphene is only subject to strain, the spin connection gauge field that arises plays no measurable role, but when intrinsic curvature is present and strain is small, spin connection dictates most of the physics. We do so by showing that the Weyl field associated with strain is a pure gauge field and no constraint on the ($2+1$)-dimensional spacetime appears. On the other hand, for constant intrinsic curvature that also gives a pure gauge Weyl field, we find a classical manifestation of a quantum Weyl anomaly, descending from a constrained spacetime. We are in the position to do this because we find the equations that the conformal factor in ($2+1$) dimensions has to satisfy, which is a nontrivial generalization to ($2+1$) dimensions of the classic Liouville equation of the differential geometry of surfaces. Finally, we comment on the peculiarities of the only gauge field that can describe strain, the well-known pseudogauge field $A_1\sim u_{11}-u_{22}$ and $A_2\sim u_{12}$, and conclude by offering some scenarios in fundamental physics that this peculiar field could help to realize.

We investigate the structure of the gravity-induced generalized uncertainty principle in three dimensions. The subtleties of lower-dimensional gravity, and its important differences concerning four and higher dimensions, are duly taken into account, by considering different possible candidates for the gravitational radius, $R_g$, that is the minimal length/maximal resolution of the quantum mechanical localization process. We find that the event horizon of the $M\ne 0$ Bañados-Teitelboim-Zanelli micro-black-hole furnishes the most consistent $R_g$. This allows us to obtain a suitable formula for the generalized uncertainty principle in three dimensions, and also to estimate the corrections induced by the latter on the Hawking temperature and Bekenstein entropy. We also point to the extremal $M=0$ case, and its natural unit of length introduced by the cosmological constant, $\ell =1/\sqrt{-\mathrm{\Lambda }}$, as a possible alternative to $R_g$, and present a condensed matter analog realization of this scenario.

We consider finite-temperature SU(2) gauge theory in the continuum formulation, which necessitates the choice of a gauge fixing. Choosing the Landau gauge, the existing gauge copies are taken into...

An effective quantum field theory description of graphene in the ultrarelativistic regime is given by reduced quantum electrodynamics (QED) also known as pseudo QED also known as mixed-dimensional QED. It has been speculated in the literature that reduced QED constitutes an example of a specific class of hard-to-find theories: an interacting conformal field theories (CFT) in more than two dimensions. This speculation was based on two-loop perturbation theory. Here, we give a proof of this feature, namely the exact vanishing of the $\beta$-function, thereby showing that reduced QED can effectively be considered as an interacting (boundary) CFT, underpinning recent work in this area. The argument, valid for both two- and four-component spinors, also naturally extends to an exactly marginal deformation of reduced QED, thence resulting in a nonsupersymmetric conformal manifold. The latter corresponds to boundary layer fermions between two different dielectric half-spaces.