121181228
WZW fusion rules, quantum groups, and the modular matrix S
A simple algorithm, due to Walton, for calculating the fusion rules of WZW theories is proved and applied to several nontrivial examples. The results are used to gain new insight in the structure of non-fully reducible modules of the quantum groups Uqg, and to find the explicit form of the modular transformation matrix S for some cases where it had not yet been worked out before.
118981675
Higher level WZW sectors from free fermions
We introduce a gauge group of internal symmetries of an ambient algebra as a new tool for investigating the superselection structure of WZW theories and the representation theory of the corresponding affine Lie algebras. The relevant ambient algebra arises from the description of these conformal field theories in terms of free fermions. As an illustration we analyze in detail the so(N) WZW theories at level two, which allows us in particular to construct explicit bases for the level-two irreducible highest weight modules. In this case there is actually a homomorphism from the representation ring of the gauge group to the subring of the WZW fusion ring that corresponds to the Neveu–Schwarz sector, even though the level-two observable algebra is smaller than the gauge invariant subalgebra of the field algebra.
119511581
Conformal embeddings and hidden symmetries of free fermion theories
It is shown that the conformal field theory of free complex fermions transforming in the (anti)symmetric tensor representation R of u(N) is characterized by a nontrivial operator algebra. However, this theory can be naturally embedded into the theory of free Dirac fermions in the defining representation of u(dimR); the latter theory corresponds to an operator algebra which is trivial in the sense that e.g. φ×φ+ = 1. We argue that these observations can be generalized to any system of free fermions possessing an energy-momentum tensor of the Sugawara form. As a consequence, there exist no further cases where a free fermion theory is quantum equivalent to a WZW theory, besides the ones already well known (i.e. those based on the current algebras so(N) and u(N) with unit central charge).
121251376
Thermal and superthermal properties of supersymmetric field theories
Abstract We discuss the finite-temperature behaviour of supersymmetric field theories. We show that their “superthermal” properties which concern the question of susy breaking at finite temperature and their thermal properties must be considered separately. Susy breaking is determined by the so-called superthermal ensemble, whereas thermodynamical properties follow from the conventional thermal ensemble, leading to the usual statistics for the bosonic and fermionic components of a superfield. We show that superspace techniques can be used in a straightforward way only for superthermal Green functions but not for thermal ones. We also discuss the possibility of finite-temperature susy restoration and the implications of Goldstone's theorem at finite temperature.
119750730
Level 1 WZW superselection sectors
AbstractThe superselection structure of the Wess-Zumino-Witten theory based on the affine Lie algebra
$$\widehat{so}(N)$$
 at level one is investigated for arbitraryN. By making use of the free fermion representation of the affine algebra, the endomorphisms which represent the superselection sectors on the observable algebra can be constructed as endomorphisms of the underlying Majorana algebra. These endomorphisms do not close on the chiral algebra of the theory, but we are able to obtain a larger algebra on which the endomorphisms close. The composition of equivalence classes of the endomorphisms reproduces the WZW fusion rules.
122072743
A Supersymmetric Instanton Calculus for SU($N$) Gauge Theories
We extend a previously formulated instanton superfield method from SU(2) to SU(N) gauge theories without classical vacuum expectation values of scalar fields. We consider supersymmetric Yang-Mills, supersymmetric QCD, and a class of chiral theories with matter in the fundamental and antisymmetric tensor representation. Via cluster decomposition, our results provide non-trivial consistency checks; in particular they enable us to conclude that for most of the chiral theories the approach without classical scalar VEV's is inconsistent.
118685069
Klein tunneling in graphene: optics with massless electrons
Abstract
This article provides a pedagogical review on Klein tunneling in graphene, i.e. the
peculiar tunneling properties of two-dimensional massless Dirac electrons. We consider two
simple situations in detail: a massless Dirac electron incident either on a potential step
or on a potential barrier and use elementary quantum wave mechanics to obtain the
transmission probability. We emphasize the connection to related phenomena in optics, such
as the Snell-Descartes law of refraction, total internal reflection, Fabry-Pérot
resonances, negative refraction index materials (the so called meta-materials), etc. We
also stress that Klein tunneling is not a genuine quantum tunneling effect as it does not
necessarily involve passing through a classically forbidden region via evanescent waves. A
crucial role in Klein tunneling is played by the conservation of (sublattice) pseudo-spin,
which is discussed in detail. A major consequence is the absence of backscattering at
normal incidence, of which we give a new shorten proof. The current experimental status is
also thoroughly reviewed. The Appendix contains the discussion of a one-dimensional toy
model that clearly illustrates the difference in Klein tunneling between mono- and
bi-layer graphene.

119325012
RCFT with defects: Factorization and fundamental world sheets
It is known that for any full rational conformal field theory, the correlation functions that are obtained by the TFT construction satisfy all locality, modular invariance and factorization conditi ...