Tinkertoys for Gaiotto Duality

We describe a procedure for classifying N=2 superconformal theories of the type introduced by Davide Gaiotto. Any curve, C, on which the 6D A_{N-1} SCFT is compactified, can be decomposed into 3-punctured spheres, connected by cylinders. We classify the spheres, and the cylinders that connect them. The classification is carried out explicitly, up through N=5, and for several families of SCFTs for arbitrary N. These lead to a wealth of new S-dualities between Lagrangian and non-Lagrangian N=2 SCFTs.Comment: 61 pages, 136 figures (a veritable comic book). V2: Grotty bitmapped figures replaced with PDF versions; a couple of references fixe

Gauge/gravity duality and the interplay of various fractional branes

We consider different types of fractional branes on a Z_2 orbifold of the conifold and analyze in detail the corresponding gauge/gravity duality. The gauge theory possesses a rich and varied dynamics, both in the UV and in the IR. We find the dual supergravity solution which contains both untwisted and twisted 3-form fluxes, related to what are known as deformation and N=2 fractional branes respectively. We analyze the resulting RG flow from the supergravity perspective, by developing an algorithm to easily extract it. We find hints of a generalization of the familiar cascade of Seiberg dualities due to a non-trivial interplay between the different types of fractional branes. We finally consider the IR behavior in several limits, where the dominant effective dynamics is either confining, in a Coulomb phase or runaway, and discuss the resolution of singularities in the dual geometric background.Comment: 38 pages + appendices, 15 figures; v2: refs added and typos correcte

Gravity duals of 2d supersymmetric gauge theories

We find new supergravity solutions generated by D5-branes wrapping a four-cycle and preserving four and two supersymmetries. We first consider the configuration in which the fivebranes wrap a four-cycle in a Calabi-Yau threefold, which preserves four supersymmetries and is a gravity dual to the Coulomb branch of two-dimensional gauge theories with N=(2,2) supersymmetry. We also study the case of fivebranes wrapping a co-associative four-cycle in a manifold of G_2-holonomy, which provides a gravity dual of N=(1,1) supersymmetric Yang-Mills theory in two dimensions. We also discuss the addition of unquenched fundamental matter fields to these backgrounds and find the corresponding gravity solutions with flavor brane sources.Comment: 34 pages + appendices; v2: minor improvement

N=2 Generalized Superconformal Quiver Gauge Theory

Four dimensional N=2 generalized superconformal field theory can be defined by compactifying six dimensional (0,2) theory on a Riemann surface with regular punctures. In previous studies, gauge coupling constant space is identified with the moduli space of punctured Riemann surface M_{g,n}. We show that the weakly coupled gauge group description corresponds to a stable nodal curve, and the coupling space is actually the Deligne-Mumford compactification \bar{M}_{g,n}. We also give an algorithm to determine the weakly coupled gauge group and matter content in any duality frame.Comment: v2, reorganizing the materials, discussions on 2d CFT is remove

Conceptual-level evaluation of a variable stiffness skin for a morphing wing leading edge

A morphing leading edge produces a continuous aerodynamic surface that has no gaps between the moving and fixed parts. The continuous seamless shape has the potential to reduce drag, compared to conventional devices, such as slats that produce a discrete aerofoil shape change. However, the morphing leading edge has to achieve the required target shape by deforming from the baseline shape under the aerodynamic loads. In this paper, a conceptual-level method is proposed to evaluate the morphing leading edge structure. The feasibility of the skin design is validated by checking the failure index of the composite when the morphing leading edge undergoes the shape change. The stiffness of the morphing leading edge skin is spatially varied using variable lamina angles, and comparisons to the skin with constant stiffness are made to highlight its potential to reduce the actuation forces. The structural analysis is performed using a two-level structural optimisation scheme. The first level optimisation is applied to find the optimised structural proper- ties of the leading edge skin and the associated actuation forces. The structural properties of the skin are given as a stiffness distribution, which is controlled by a B spline interpolation function. In the second level, the design solution of the skin is investigated. The skin is assumed to be made of variable stiffness composite. The stack sequence of the composite is optimised element-by-element to match the target stiffness. A failure criterion is employed to obtain the failure index when the leading edge is actuated from the baseline shape to the target shape. Test cases are given to demonstrate that the optimisation scheme is able to provide the stiffness distribution of the leading edge skin and the actuation forces can be reduced by using a spatially variable stiffness skin

More Three Dimensional Mirror Pairs

We found a lot of new three dimensional N = 4 mirror pairs generalizing previous considerations on three dimensional generalized quiver gauge theories. We recovered almost all previous discovered mirror pairs with these constructions. One side of these mirror pairs are always the conventional quiver gauge theories. One of our result can also be used to determine the matter content and weakly coupled gauge groups of four dimensional N = 2 generalized quiver gauge theories derived from six dimensional A_N and D_N theory, therefore we explicitly constructed four dimensional S-duality pairs.Comment: 33 pages, 18 figures version2 minor correction

A note on fermions in holographic QCD

We study the fermionic sector of a probe D8-brane in the supergravity background made of D4-branes compactified on a circle with supersymmetry broken explicitly by the boundary conditions. At low energies the dual field theory is effectively four-dimensional and has proved surprisingly successful in recovering qualitative and quantitative properties of QCD. We investigate fluctuations of the fermionic fields on the probe D8-brane and interpret these as mesinos (fermionic superpartners of mesons). We demonstrate that the masses of these modes are comparable to meson masses and show that their interactions with ordinary mesons are not suppressed.Comment: 21+1 pp, 1 figure; v2: typos corrected, refs. adde

New Seiberg Dualities from N=2 Dualities

We propose a number of new Seiberg dualities of N=1 quiver gauge theories. The new Seiberg dualities originate in new S-dualities of N=2 superconformal field theories recently proposed by Gaiotto. N=2 S-dual theories deformed by suitable mass terms flow to our N=1 Seiberg dual theories. We show that the number of exactly marginal operators is universal for these Seiberg dual theories and the 't Hooft anomaly matching holds for these theories. These provide strong evidence for the new Seiberg dualities. Furthermore, we study in detail the Klebanov-Witten type theory and its dual as a concrete example. We show that chiral operators and their non-linear relations match between these theories. These arguments also give non-trivial consistency checks for our proposal.Comment: 31 pages, 7 figures. v2:version to appear in JHE

Nilpotent orbits and codimension-two defects of 6d N=(2,0) theories

We study the local properties of a class of codimension-2 defects of the 6d N=(2,0) theories of type J=A,D,E labeled by nilpotent orbits of a Lie algebra \mathfrak{g}, where \mathfrak{g} is determined by J and the outer-automorphism twist around the defect. This class is a natural generalisation of the defects of the 6d theory of type SU(N) labeled by a Young diagram with N boxes. For any of these defects, we determine its contribution to the dimension of the Higgs branch, to the Coulomb branch operators and their scaling dimensions, to the 4d central charges a and c, and to the flavour central charge k.Comment: 57 pages, LaTeX2