Localization of supersymmetric field theories on non-compact hyperbolic three-manifolds

We study supersymmetric gauge theories with an R-symmetry, defined on non-compact, hyperbolic, Riemannian three-manifolds, focusing on the case of a supersymmetry-preserving quotient of Euclidean AdS$_3$. We compute the exact partition function in these theories, using the method of localization, thus reducing the problem to the computation of one-loop determinants around a supersymmetric locus. We evaluate the one-loop determinants employing three different techniques: an index theorem, the method of pairing of eigenvalues, and the heat kernel method. Along the way, we discuss aspects of supersymmetry in manifolds with a conformal boundary, including supersymmetric actions and boundary conditions.Comment: v3:79p, minor clarifications and references adde

Controls on Dissolved Silicon Isotopes along the US GEOTRACES Eastern Pacific Zonal Transect (GP16)

The distribution of dissolved silicon isotopes (δ30Si) was examined along the US GEOTRACES East Pacific Zonal Transect (GP16) extending from Peru to Tahiti (10°S and 15°S latitude). Surface waters in the subtropical gyre displayed high δ30Si due to strong utilization of silicic acid (DSi). In contrast, surface waters close to the Peruvian coast where upwelling prevailed were less depleted and only moderately fractionated. δ30Si of water masses along the transect were compared with the results of an Optimum Multiparameter Analysis that quantified the fractional contributions of endmember water masses in each sample. Strong admixture of intermediate waters obscured the expected heavy isotopic signatures of Subantarctic Mode Water and Antarctic Intermediate Water. Isotope values were nearly homogenous below 2000 m (Average: +1.3 ± 0.1 ‰, 1 s.d.) despite the 25 μmol kg‐1 range in the DSi content among water masses. This homogeneity confirms prior observations and model results that predict nearly constant δ30Si values of +1.0 to +1.2 ‰ for Pacific deep waters with [DSi] > 100 μmol kg‐1. Waters above the East Pacific Rise (EPR) influenced by hydrothermal activity showed a small increase in [DSi] together with dissolved iron, but overall stations close to the EPR were slightly depleted in [DSi] (3 to 6 μmol kg‐1) with no significant shift in δ30Si compared to adjacent waters. Hydrothermal [DSi] appears to precipitate within the conduit of the EPR or upon contact with cold seawater resulting in a negligible influence of hydrothermal fluids on δ30Si in deep water. Key Points Surface waters have a large range in dissolved silicon isotopes covering nutrient‐rich coastal upwelling to oligotrophic waters Deep water masses with DSi concentrations > 100 μmol kg‐1 show homogenous silicon isotope signatures despite up to 25 μmol kg‐1 differences in [DSi] Hydrothermal fluids have a negligible effect on Si isotope distributions in the deep Pacifi

Holographic renormalization and supersymmetry

Holographic renormalization is a systematic procedure for regulating divergences in observables in asymptotically locally AdS spacetimes. For dual boundary field theories which are supersymmetric it is natural to ask whether this defines a supersymmetric renormalization scheme. Recent results in localization have brought this question into sharp focus: rigid supersymmetry on a curved boundary requires specific geometric structures, and general arguments imply that BPS observables, such as the partition function, are invariant under certain deformations of these structures. One can then ask if the dual holographic observables are similarly invariant. We study this question in minimal N = 2 gauged supergravity in four and five dimensions. In four dimensions we show that holographic renormalization precisely reproduces the expected field theory results. In five dimensions we find that no choice of standard holographic counterterms is compatible with supersymmetry, which leads us to introduce novel finite boundary terms. For a class of solutions satisfying certain topological assumptions we provide some independent tests of these new boundary terms, in particular showing that they reproduce the expected VEVs of conserved charges.Comment: 70 pages; corrected typo

Effect of Phosphorus and Strontium Additions on Formation Temperature and Nucleation Density of Primary Silicon in Al-19 Wt Pct Si Alloy and Their Effect on Eutectic Temperature

The influence of P and Sr additions on the formation temperature and nucleation density of primary silicon in Al-19 wt pct Si alloy has been determined, for small volumes of melt solidified at cooling rates _T of ~0.3 and 1 K/s. The proportion of ingot featuring primary silicon decreased progressively with increased Sr addition, which also markedly reduced the temperature for first formation of primary silicon and the number of primary silicon particles per unit volume �Nv: When combined with previously published results, the effects of amount of P addition and cooling rate on �Nv are in reasonable accord with �Nv� _T ¼ ðp=6fÞ1=2 109 [250 � 215 (wt pct P)0.17]�3, where �Nv is in mm�3, _T is in K/s, and f is volume fraction of primary silicon. Increased P addition reduces the eutectic temperature, while increased Sr appears to generate a minimum in eutectic temperature at about 100 ppmw Sr

A topologically twisted index for three-dimensional supersymmetric theories

We provide a general formula for the partition function of three-dimensional (formula presented) gauge theories placed on S2 7S1 with a topological twist along S2, which can be interpreted as an index for chiral states of the theories immersed in background magnetic fields. The result is expressed as a sum over magnetic fluxes of the residues of a meromorphic form which is a function of the scalar zero-modes. The partition function depends on a collection of background magnetic fluxes and fugacities for the global symmetries. We illustrate our formula in many examples of 3d Yang-Mills-Chern-Simons theories with matter, including Aharony and Giveon-Kutasov dualities. Finally, our formula generalizes to \u3a9-backgrounds, as well as two-dimensional theories on S2 and four-dimensional theories on S2 7 T2. In particular this provides an alternative way to compute genus-zero A-model topological amplitudes and Gromov-Witten invariants