We use the symmetries of monolayer graphene to write a set of constraints that must be satisfied by any electron-phonon interaction hamiltonian. The explicit solution as a series expansion in the momenta gives the most general, model-independent couplings between electrons and long wavelength acoustic and optical phonons. As an application, the possibility of describing elastic strains in terms of effective electromagnetic fields is considered in detail, with an emphasis on group theory conditions and the role of time reversal symmetry.

We revise the tight binding approach to strained or curved graphene in the presence of external probes such as Photoemission or Scanning Tunneling Microscopy experiments. We show that extra terms arise in the continuum limit of the tight binding Hamiltonian which can not be accounted for by changes in the hopping parameters due to lattice deformations, encoded in the parameter \beta. These material independent extra couplings are of the same order of magnitude as the standard ones and have a geometric origin. They include corrections to the position-dependent Fermi velocity and to a new vector field. We show that the new vector field does not couple to electrons like a standard gauge field and that no ? \beta-independent pseudomagnetic fields exist in strained graphene.Comment: Revised version as publishe

The algebraic structure of chiral anomalies is made globally valid on non-trivial bundles by the introduction of a fixed background connection. Some of the techniques used in the study of the anomaly are improved or generalized, including a systematic way of generating towers of "descent equations".

We consider the existence of bulk chiral fermions around points of symmetry in the Brillouin zone of nonmagnetic 3D crystals with negligible spin-orbit interactions. We use group theory to show that this is possible, but only for a reduced number of space groups and points of symmetry that we tabulate. Moreover, we show that for a handful of space groups the existence of bulk chiral fermions is not only possible but unavoidable, irrespective of the concrete crystal structure. Thus our tables can be used to look for bulk chiral fermions in a specific class of systems, namely that of nonmagnetic 3D crystals with sufficiently weak spin-orbit coupling. We also discuss the effects of spin-orbit interactions and possible extensions of our approach to Weyl semimetals, crystals with magnetic order, and systems with Dirac points with pseudospin 1 and 3/2. A simple tight-binding model is used to illustrate some of the issues.

No abstract

We propose a discrete model whose continuum limit reproduces the string susceptibility and the scaling dimensions of (2, 4m) minimal superconformal models coupled to 2D supergravity. The basic assumption in our presentation is a set of super-Virasoro constraints imposed on the partition function. We recover the Neveu-Schwarz and Ramond sectors of the theory, and we are also able to evaluate all planar loop correlation functions in the continuum limit. We find evidence to identify the integrable hierarchy of nonlinear equations describing the double scaling limit as a supersymmetric generalization of KP studied by Rabin.

We briefly review recent developments in the theory of supermembranes and su-permatrix models. In a second part we discuss their interaction with background fields. In particular, we present the full background field coupling for the bosonic case. This is a short summary of the talk at the workshop. A more extended version will appear elsewhere. 1 Supermembranes and matrix models It has been known for some time 1 that certain supersymmetric quantum-mechanical models characterized by the presence of zero-potential valleys and Gauss-type constraints 2 play an important role in the quantization of fundamental supermembranes 3. In the light-cone formulation with a flat target space 4,1 , the supermembrane theory exhibits a residual invariance under area-preserving diffeomorphisms of the membrane surface. This infinite-dimensional group can be truncated in many cases to a finite-dimensional group, e.g. to U(N), such as to lead to a quantum-mechanical model based on a finite number of degrees of freedom. The relevant Hamiltonian equals H = g −1 Tr 1 2 P 2 − 1 4 [X a , X b ] 2 + 1 2 g θ T γ a [X a , θ]. (1) Here, X, P and θ take values in the Lie algebra of the gauge group and are represented by matrices that span this Lie algebra. Furthermore, these mo-menta and coordinates transform as vectors and spinors under the 'transverse' a Talk presented at theVaì encia workshop Beyond the Standard Model; from Theory to Experiment, October 13-17, 1997.

We use a symmetry approach to construct a systematic derivative expansion of the low-energy effective Hamiltonian modifying the continuum Dirac description of graphene in the presence of nonuniform elastic deformations. We extract all experimentally relevant terms and describe their physical significance. Among them there is a new gap-opening term that describes the Zeeman coupling of the elastic pseudomagnetic field and the pseudospin. We determine the value of the couplings using a generalized tight-binding model.