We demonstrate theoretically that the topology of energy bands and Fermi
surface in bilayer graphene undergoes a very sensitive transition when
extremely tiny lateral interlayer shift occurs in arbitrary directions. The
phenomenon originates from a generation of effective non-Abelian vector
potential in Dirac Hamiltonian by the sliding motions. The characteristics of
the transition such as pair annihilations of massless Dirac fermions are
dictated by the sliding direction owing to a unique interplay between the
effective non-Abelian gauge fields and Berry's phases associated with massless
electrons. The transition manifests itself in various measurable quantities
such as anomalous density of states, minimal conductivity, and distinct Landau
level spectrum.Comment: title changed, an extended version for regular article format, 10
pages, 5 figure
We study the low-energy limit of a compactification of N = 4 U(n) super YangMills theory on S 1 with boundary conditions modified by an S-duality and R-symmetry twist. This theory has N = 6 supersymmetry in 2+1D. We analyze the T 2 compactification of this 2+1D theory by identifying a dual weakly coupled type-IIA background. The Hilbert space of normalizable ground states is finite-dimensional and appears to exhibit a rich structure of sectors. We identify most of them with Hilbert spaces of Chern-Simons theory (with appropriate gauge groups and levels). We also discuss a realization of a related twisted compactification in terms of the (2, 0)-theory, where the recent solution by Gaiotto and Witten of the boundary conditions describing D3-branes ending on a (p, q) 5-brane plays a crucial role.
We propose various ways of adding mass terms to three-dimensional twistor string theory. We begin with a review of mini-twistor space-the reduction of D = 4 twistor space to D = 3. We adapt the two proposals for twistor string theory, Witten's and Berkovits's, to D = 3 super Yang-Mills theory. In Berkovits's model, we identify the enhanced R-symmetry. We then construct B-model topological string theories that, we propose, correspond to D = 3 Yang-Mills theory with massive spinors and massive and massless scalars in the adjoint representation of the gauge group. We also analyze the counterparts of these constructions in Berkovits's model. Some of our constructions can be lifted to D = 4, where infinitesimal mass terms correspond to VEVs of certain superconformal gravity fields.
We continue the study of the low-energy limit of N = 4 super Yang-Mills theory compactified on a circle with S-duality and R-symmetry twists that preserve N = 6 supersymmetry in 2+1D. We introduce external static supersymmetric quark and antiquark sources into the theory and calculate the Witten Index of the resulting Hilbert space of ground states on T 2 . Using these results we compute the action of simple Wilson loops on the Hilbert space of ground states without sources. In some cases we find disagreement between our results for the Wilson loop eigenvalues and previous conjectures about a connection with Chern-Simons theory.
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