Abstract:We consider the correlation functions of Coulomb branch operators in fourdimensional N = 2 Superconformal Field Theories (SCFTs) involving exactly one antichiral operator. These extremal correlators are the "minimal" non-holomorphic local observables in the theory. We show that they can be expressed in terms of certain determinants of derivatives of the four-sphere partition function of an appropriate deformation of the SCFT. This relation between the extremal correlators and the deformed four-sphere partition function is non-trivial due to the presence of conformal anomalies, which lead to operator mixing on the sphere. Evaluating the deformed four-sphere partition function using supersymmetric localization, we compute the extremal correlators explicitly in many interesting examples. Additionally, the representation of the extremal correlators mentioned above leads to a system of integrable differential equations. We compare our exact results with previous perturbative computations and with the four-dimensional tt * equations. We also use our results to study some of the asymptotic properties of the perturbative series expansions we obtain in N = 2 SQCD.

We introduce a novel Skyrme-like conserved current in the effective theory of pions and vector mesons based on the idea of hidden local symmetry. The associated charge is equivalent to the skyrmion charge for any smooth configuration. In addition, there exist singular configurations that can be identified as N_f=1Nf=1 baryons charged under the new symmetry. Under this identification, the vector mesons play the role of the Chern-Simons vector fields living on the quantum Hall droplet that forms the N_f=1Nf=1 baryon. We propose that this current is the correct effective expression for the baryon current at low energies. This proposal gives a unified picture for the two types of baryons and allows them to continuously transform one to the other in a natural way. In addition, Chern-Simons dualities on the droplet can be interpreted as a result of Seiberg-like duality between gluons and vector mesons.

We study the phases of the SU (N 1 ) × SU (N 2 ) gauge theory with a bi-fundamental fermion in 3+1 dimensions. We show that the discrete anomalies and Berry phases associated to the one-form symmetry of the theory allow for several topologically distinct phase diagrams. We identify several limits of the theory where the phase diagram can be determined using various controlled approximations. When the two ranks are equal N 1 = N 2 , these limits all lead to the same topology for the phase diagram and provide a consistent global understanding of the phases of the theory. When N 1 = N 2 , different limits lead to distinct topologies of the phase diagram. This necessarily implies nontrivial physics at some intermediate regimes of parameter space. In the large N 1,2 limit, we argue that the topological transitions are accounted for by a (non-supersymmetric) duality cascade as one varies the parameters of the theory.

In the Norwegian-Greenland Sea and the Arctic Ocean the present-day North American plate boundary exhibits great variety in morphology and structural style. From the neovolcanic rift zone in Iceland the plate boundary extends into the Norwegian-Greenland Sea and the Eurasian Basin of the Arctic Ocean as a system of mid-oceanic ridge segments and transform faults, but becomes less distinct beneath the Siberian continental margin (Fig. 1). The asymmetry in the location of some of the active spreading axes, as well as the existence of extinct spreading centers, microcontinents, and volcanic plateaus and ridges imply a complex structural evolution of the surrounding ocean basins. It is reasonably well documented that the oldest oceanic crust formed by sea-floor spreading between Greenland, Lomonosov Ridge, and Eurasia dates back to the negative polarity interval between magnetic anomalies 24B and 25 (late Paleocene/early Eocene). In this chapter we focus on a description of the present plate boundary in terms of morphology, relative plate motion, variation in geological and geophysical parameters, and seismicity. For practical purposes we restrict ourselves to the youngest crust and primarily discuss the crust formed during the past 10 m.y. More comprehensive treatments of the ocean basins and their plate tectonic evolution are presented by Eldholm and others (this volume) and by Kristoffersen and others (this volume). Various aspects of the plate boundary north of Iceland have also been discussed in the Western North Atlantic synthesis volume of this series (Einarsson, 1986; Melson and O’Hearn, 1986; Schilling, 1986; Srivastava and Tapscottt, 1986; Vogt, 1986).

In this paper we study supersymmetric field theories on an AdS p × S q spacetime that preserves their full supersymmetry. This is an interesting example of supersymmetry on a non-compact curved space. The supersymmetry algebra on such a space is a (p − 1)-dimensional superconformal algebra, and we classify all possible algebras that can arise for p ≥ 3. In some AdS 3 cases more than one superconformal algebra can arise from the same field theory. We discuss in detail the special case of four dimensional field theories with N = 1 and N = 2 supersymmetry on AdS 3 × S 1 .