Three Dimensional Bosonization From Supersymmetry

Three dimensional bosonization is a conjectured duality between non-supersymmetric Chern-Simons theories coupled to matter fields in the fundamental representation of the gauge group. There is a well-established supersymmetric version of this duality, which involves Chern-Simons theories with ${\cal N} = 2$ supersymmetry coupled to fundamental chiral multiplets. Assuming that the supersymmetric duality is valid, we prove that non-supersymmetric bosonization holds for all planar correlators of single-trace operators. The main tool we employ is a double-trace flow from the supersymmetric theory to an IR fixed point, in which the scalars and fermions are effectively decoupled in the planar limit. A generalization of this technique can be used to derive the duality mapping of all renormalizable couplings, in non-supersymmetric theories with both a scalar and a fermion. Our results do not rely on an explicit computation of planar diagrams.Comment: 39 pages, 3 figures. v2: added reference

Relativistic photoemission theory for general nonlocal potentials

An improved formulation of the one-step model of photoemission from crystal surfaces is proposed which overcomes different limitations of the original theory. Considering the results of an electronic-structure calculation, the electronic (one-particle) potential and the (many-body) self-energy, as given quantities, we derive explicit expressions for the dipole transition-matrix elements. The theory is formulated within a spin-polarized, relativistic framework for general nonspherical and space-filling one-particle potentials and general nonlocal, complex and energy-dependent self-energies. It applies to semi-infinite lattices with perfect lateral translational invariance and arbitrary number of atoms per unit cell.Comment: LaTeX, 18 pages, no figur

Bounds on N=1\mathcal{N}=1 Superconformal Theories with Global Symmetries

Recently, the conformal-bootstrap has been successfully used to obtain generic bounds on the spectrum and OPE coefficients of unitary conformal field theories. In practice, these bounds are obtained by assuming the existence of a scalar operator in the theory and analyzing the crossing-symmetry constraints of its 4-point function. In $\mathcal{N}=1$ superconformal theories with a global symmetry there is always a scalar primary operator, which is the top of the current-multiplet. In this paper we analyze the crossing-symmetry constraints of the 4-point function of this operator for $\mathcal{N}=1$ theories with $SU(N)$ global symmetry. We analyze the current-current OPE, and derive the superconformal blocks, generalizing the work of Fortin, Intrilligator and Stergiou to the non-Abelian case and finding new superconformal blocks which appear in the Abelian case. We then use these results to obtain bounds on the coefficient of the current 2-point function.Comment: Corrected error in analysis for U(1) symmetr

A one-dimensional theory for Higgs branch operators

We use supersymmetric localization to calculate correlation functions of half-BPS local operators in 3d ${\cal N} = 4$ superconformal field theories whose Lagrangian descriptions consist of vectormultiplets coupled to hypermultiplets. The operators we primarily study are certain twisted linear combinations of Higgs branch operators that can be inserted anywhere along a given line. These operators are constructed from the hypermultiplet scalars. They form a one-dimensional non-commutative operator algebra with topological correlation functions. The 2- and 3-point functions of Higgs branch operators in the full 3d ${\cal N}=4$ theory can be simply inferred from the 1d topological algebra. After conformally mapping the 3d superconformal field theory from flat space to a round three-sphere, we preform supersymmetric localization using a supercharge that does not belong to any 3d ${\cal N} = 2$ subalgebra of the ${\cal N}=4$ algebra. The result is a simple model that can be used to calculate correlation functions in the 1d topological algebra mentioned above. This model is a 1d Gaussian theory coupled to a matrix model, and it can be viewed as a gauge-fixed version of a topological gauged quantum mechanics. Our results generalize to non-conformal theories on $S^3$ that contain real mass and Fayet-Iliopolous parameters. We also provide partial results in the 1d topological algebra associated with the Coulomb branch, where we calculate correlation functions of local operators built from the vectormultiplet scalars.Comment: 108 pages; v2: typos corrected, some statements clarifie

Gate Defined Quantum Confinement in Suspended Bilayer Graphene

Quantum confined devices that manipulate single electrons in graphene are emerging as attractive candidates for nanoelectronics applications. Previous experiments have employed etched graphene nanostructures, but edge and substrate disorder severely limit device functionality. Here we present a technique that builds quantum confined structures in suspended bilayer graphene with tunnel barriers defined by external electric fields that break layer inversion symmetry, thereby eliminating both edge and substrate disorder. We report clean quantum dot formation in two regimes: at zero magnetic field B using the single particle energy gap induced by a perpendicular electric field and at B > 0 using the quantum Hall ferromagnet {\nu} = 0 gap for confinement. Coulomb blockade oscillations exhibit periodicity consistent with electrostatic simulations based on local top gate geometry, a direct demonstration of local control over the band structure of graphene. This technology integrates single electron transport with high device quality and access to vibrational modes, enabling broad applications from electromechanical sensors to quantum bits.Comment: 22 pages, 9 figures, includes supplementary informatio

Local Spin Susceptibilities of Low-Dimensional Electron Systems

We investigate, assess, and suggest possibilities for a measurement of the local spin susceptibility of a conducting low-dimensional electron system. The basic setup of the experiment we envisage is a source-probe one. Locally induced spin density (e.g. by a magnetized atomic force microscope tip) extends in the medium according to its spin susceptibility. The induced magnetization can be detected as a dipolar magnetic field, for instance, by an ultra-sensitive nitrogen-vacancy center based detector, from which the spatial structure of the spin susceptibility can be deduced. We find that one-dimensional systems, such as semiconducting nanowires or carbon nanotubes, are expected to yield a measurable signal. The signal in a two-dimensional electron gas is weaker, though materials with high enough $g$-factor (such as InGaAs) seem promising for successful measurements.Comment: 11 pages, 12 figure

Charge and spin addition energies of one dimensional quantumn dot

We derive the effective action for a one dimensional electron island formed between a double barrier in a single channel quantum wire including the electron spin. Current and energy addition terms corresponding to charge and spin are identified. The influence of the range and the strength of the electron interaction and other system parameters on the charge and spin addition energies, and on the excitation spectra of the modes confined within the island is studied. We find by comparison with experiment that spin excitations in addition to non-zero range of the interaction and inhomogeneity effects are important for understanding the electron transport through one dimensional quantum islands in cleaved-edge-overgrowth systems.Comment: 11 pages, 3 figures, to be published in Physical Review

Bootstrapping O(N)O(N) Vector Models in 4<d<64<d<6

We use the conformal bootstrap to study conformal field theories with $O(N)$ global symmetry in $d=5$ and $d=5.95$ spacetime dimensions that have a scalar operator $\phi_i$ transforming as an $O(N)$ vector. The crossing symmetry of the four-point function of this $O(N)$ vector operator, along with unitarity assumptions, determine constraints on the scaling dimensions of conformal primary operators in the $\phi_i \times \phi_j$ OPE. Imposing a lower bound on the second smallest scaling dimension of such an $O(N)$-singlet conformal primary, and varying the scaling dimension of the lowest one, we obtain an allowed region that exhibits a kink located very close to the interacting $O(N)$-symmetric CFT conjectured to exist recently by Fei, Giombi, and Klebanov. Under reasonable assumptions on the dimension of the second lowest $O(N)$ singlet in the $\phi_i \times \phi_j$ OPE, we observe that this kink disappears in $d =5$ for small enough $N$, suggesting that in this case an interacting $O(N)$ CFT may cease to exist for $N$ below a certain critical value.Comment: 24 pages, 5 figures; v2 minor improvement