4d Index to 3d Index and 2d TQFT

We compute the 4d superconformal index for N=1,2 gauge theories on S^1 x L(p,1), where L(p,1) is a lens space. We find that the 4d N=1,2 index on S^1 x L(p,1) reduces to a 3d N=2,4 index on S^1 x S^2 in the large p limit, and to a 3d partition function on a squashed L(p,1) when the size of temporal S^1 shrinks to zero. As an application of our index, we study 4d N=2 superconformal field theories arising from the 6d N=(2,0) A_1 theory on a punctured Riemann surface, and conjecture the existence of a 2d Topological Quantum Field Theory on the Riemann surface whose correlation function coincides with the 4d N=2 index on S^1 x L(p,1).Comment: 24 pages, 2 figures; v2: typos corrected, refs added, discussion of L(p,q) remove

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

Gravity interpretation for the Bethe Ansatz expansion of the N=4 SYM index

The superconformal index of the N=4 SU(N) supersymmetric Yang-Mills theory counts the 1/16-BPS (Bogomol'nyi-Prasad-Sommerfield) states in this theory, and has been used via the AdS/CFT correspondence to count black hole microstates of 1/16-BPS black holes. On one hand, this index may be related to the Euclidean partition function of the theory on S3×S1 with complex chemical potentials, which maps by the AdS/CFT correspondence to a sum over Euclidean gravity solutions. On the other hand, the index may be expressed as a sum over solutions to Bethe Ansatz (BA) equations. We show that the solutions to the BA equations that are known to have a good large N limit, for the case of equal chemical potentials for the two angular momenta, have a one-to-one mapping to (complex) Euclidean black hole solutions on the gravity side. This mapping captures both the leading contribution from the classical gravity action (of order N2), as well as nonperturbative corrections in 1/N, which on the gravity side are related to wrapped D3-branes. Some of the BA solutions map to orbifolds of the standard Euclidean black hole solutions (which obey exactly the same boundary conditions as the other solutions). A priori there are many more gravitational solutions than Bethe Ansatz solutions, but we show that, by considering the nonperturbative effects, the extra solutions are ruled out, leading to a precise match between the solutions on both sides

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

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

Seiberg duality for Chern-Simons quivers and D-brane mutations

Chern-Simons quivers for M2-branes at Calabi-Yau singularities are best understood as the low energy theory of D2-branes on a dual type IIA background. We show how the D2-brane point of view naturally leads to three dimensional Seiberg dualities for Chern-Simons quivers with chiral matter content: They arise from a change of brane basis (or mutation), in complete analogy with the better known Seiberg dualities for D3-brane quivers. This perspective reproduces the known rules for Seiberg dualities in Chern-Simons-Yang-Mills theories with unitary gauge groups. We provide explicit examples of dual theories for the quiver dual to the Y^{p,q}(CP^2) geometries. We also comment on the string theory derivation of CS quivers dual to massive type IIA geometries.Comment: 32 pages+appendix; v2: added a referenc

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

Webs of five-branes and N=2 superconformal field theories

We describe configurations of 5-branes and 7-branes which realize, when compactified on a circle, new isolated four-dimensional N=2 superconformal field theories recently constructed by Gaiotto. Our diagrammatic method allows to easily count the dimensions of Coulomb and Higgs branches, with the help of a generalized s-rule. We furthermore show that superconformal field theories with E6,7,8 flavor symmetry can be analyzed in a uniform manner in this framework; in particular we realize these theories at infinitely strongly-coupled limits of quiver theories with SU gauge groups

Biochemical survey on episodic localized darkening in Turkey deboned thigh meat packaged in modified atmosphere

Abstract The color of food, especially meat and meat products, is a parameter that strongly influences consumer choice. In Italy, repeated cases of darkening in deboned thigh meat of male turkeys packaged in modified atmosphere (MAP; 80% 02, 20% CO2) have been reported. The pH, lipid oxidation (TBARS), heme proteins, and iron content were investigated in MAP samples of turkey males, females, and in oxygen-permeable film-packaged males. Furthermore, the absorbance spectrum (400 to 700 nm) of the meat extracts was analyzed to better delineate the evolution and characteristics of the darkening process. Results showed that darkening occurred only in males with higher content of total iron, independently of the content of heme proteins, which differs only between males and females. Furthermore, pH was higher in muscles taken as controls, with respect to muscles involved in the darkening, as well as in females. Finally, TBARS values were found to be higher in darkened regions than in not darkened ones, as well as in MAP samples with respect to oxygen-permeable film-packaged samples. These findings suggest that darkening occurrence might depend on kind of muscle, sex, and individual characteristics of the animals raised under the same breeding conditions

Three-dimensional dualities with bosons and fermions

We propose new infinite families of non-supersymmetric IR dualities in three space-time dimensions, between Chern-Simons gauge theories (with classical gauge groups) with both scalars and fermions in the fundamental representation. In all cases we study the phase diagram as we vary two relevant couplings, finding interesting lines of phase transitions. In various cases the dualities lead to predictions about multi-critical fixed points and the emergence of IR quantum symmetries. For unitary groups we also discuss the coupling to background gauge fields and the map of simple monopole operators. \ua9 2018, The Author(s)