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

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

Coulomb Branch Operators and Mirror Symmetry in Three Dimensions

We develop new techniques for computing exact correlation functions of a class of local operators, including certain monopole operators, in three-dimensional $\mathcal{N} = 4$ abelian gauge theories that have superconformal infrared limits. These operators are position-dependent linear combinations of Coulomb branch operators. They form a one-dimensional topological sector that encodes a deformation quantization of the Coulomb branch chiral ring, and their correlation functions completely fix the ($n\leq 3$)-point functions of all half-BPS Coulomb branch operators. Using these results, we provide new derivations of the conformal dimension of half-BPS monopole operators as well as new and detailed tests of mirror symmetry. Our main approach involves supersymmetric localization on a hemisphere $HS^3$ with half-BPS boundary conditions, where operator insertions within the hemisphere are represented by certain shift operators acting on the $HS^3$ wavefunction. By gluing a pair of such wavefunctions, we obtain correlators on $S^3$ with an arbitrary number of operator insertions. Finally, we show that our results can be recovered by dimensionally reducing the Schur index of 4D $\mathcal{N} = 2$ theories decorated by BPS 't Hooft-Wilson loops.Comment: 92 pages plus appendices, two figures; v2 and v3: typos corrected, references adde

Transition behavior of k-surface from hyperbola to ellipse

The transition behavior of the k-surface of a lossy anisotropic indefinite slab is investigated. It is found that, if the material loss is taken into account, the k-surface does not show a sudden change from hyperbola to the ellipse when one principle element of the permittivity tensor changes from negative to positive. In fact, after introducing a small material loss, the shape of the k-surface can be a combination of a hyperbola and an ellipse, and a selective high directional transmission can be obtained in such a slab

Regional reserve pooling arrangements

Recently, several emerging market countries in East Asia and Latin America have initiated intra-regional reserve pooling mechanisms. This is puzzling from a traditional risk-diversification perspective, because country-level shocks are more correlated within rather than across regions. This paper provides a novel rationale for intra-regional pooling: if non-contingent reserve assets can be used to support production during a crisis, then a country's reserve accumulation decision affects not only its own production and consumption, but also its trading partners. If consumption through terms of trade effects. These terms of trade adjustments can be fully internalized only by a reserve pool among trading partners. If trade linkages are stronger within rather than across regions, then intra-regional reserve pooling may dominate inter-regional pooling, even if shocks are more correlated within regions.

The N=8{\cal N} = 8 Superconformal Bootstrap in Three Dimensions

We analyze the constraints imposed by unitarity and crossing symmetry on the four-point function of the stress-tensor multiplet of ${\cal N}=8$ superconformal field theories in three dimensions. We first derive the superconformal blocks by analyzing the superconformal Ward identity. Our results imply that the OPE of the primary operator of the stress-tensor multiplet with itself must have parity symmetry. We then analyze the relations between the crossing equations, and we find that these equations are mostly redundant. We implement the independent crossing constraints numerically and find bounds on OPE coefficients and operator dimensions as a function of the stress-tensor central charge. To make contact with known ${\cal N}=8$ superconformal field theories, we compute this central charge in a few particular cases using supersymmetric localization. For limiting values of the central charge, our numerical bounds are nearly saturated by the large $N$ limit of ABJM theory and also by the free $U(1)\times U(1)$ ABJM theory.Comment: 74 pages, 7 figures; v2 refs added, minor improvements; v3 typos fixe

The Korean system of innovation and the semiconductor industry

노트 : This paper is written as part of the Science Policy Research Unit/Sussex European Institute-joint project ‘‘Innovation Dynamics of Pacific Asia: Implications for Europe’’

Bootstrapping O(N)O(N) Vector Models with Four Supercharges in 3≤d≤43 \leq d \leq4

We analyze the conformal bootstrap constraints in theories with four supercharges and a global $O(N) \times U(1)$ flavor symmetry in $3 \leq d \leq 4$ dimensions. In particular, we consider the 4-point function of $O(N)$-fundamental chiral operators $Z_i$ that have no chiral primary in the $O(N)$-singlet sector of their OPE. We find features in our numerical bounds that nearly coincide with the theory of $N+1$ chiral super-fields with superpotential $W = X \sum_{i=1}^N Z_i^2$, as well as general bounds on SCFTs where $\sum_{i=1}^N Z_i^2$ vanishes in the chiral ring.Comment: 25 pages, 8 figure

Monopoles and Solitons in Fuzzy Physics

Monopoles and solitons have important topological aspects like quantized fluxes, winding numbers and curved target spaces. Naive discretizations which substitute a lattice of points for the underlying manifolds are incapable of retaining these features in a precise way. We study these problems of discrete physics and matrix models and discuss mathematically coherent discretizations of monopoles and solitons using fuzzy physics and noncommutative geometry. A fuzzy sigma-model action for the two-sphere fulfilling a fuzzy Belavin-Polyakov bound is also put forth.Comment: 17 pages, Latex. Uses amstex, amssymb.Spelling of the name of one Author corrected. To appear in Commun.Math.Phy