Interacting Preformed Cooper Pairs in Resonant Fermi Gases

We consider the normal phase of a strongly interacting Fermi gas, which can have either an equal or an unequal number of atoms in its two accessible spin states. Due to the unitarity-limited attractive interaction between particles with different spin, noncondensed Cooper pairs are formed. The starting point in treating preformed pairs is the Nozi\`{e}res-Schmitt-Rink (NSR) theory, which approximates the pairs as being noninteracting. Here, we consider the effects of the interactions between the Cooper pairs in a Wilsonian renormalization-group scheme. Starting from the exact bosonic action for the pairs, we calculate the Cooper-pair self-energy by combining the NSR formalism with the Wilsonian approach. We compare our findings with the recent experiments by Harikoshi {\it et al.} [Science {\bf 327}, 442 (2010)] and Nascimb\`{e}ne {\it et al.} [Nature {\bf 463}, 1057 (2010)], and find very good agreement. We also make predictions for the population-imbalanced case, that can be tested in experiments.Comment: 10 pages, 6 figures, accepted version for PRA, discussion of the imbalanced Fermi gas added, new figure and references adde

Matter and singularities

We analyze the structure of matter representations arising from codimension two singularities in F-theory, focusing on gauge groups SU(N). We give a detailed local description of the geometry associated with several types of singularities and the associated matter representations. We also construct global F-theory models for 6D and 4D theories containing these matter representations. The codimension two singularities encountered include examples where the apparent Kodaira singularity type does not need to be completely resolved to produce a smooth Calabi-Yau, examples with rank enhancement by more than one, and examples where the 7-brane configuration is singular. We identify novel phase transitions, in some of which the gauge group remains fixed but the singularity type and associated matter content change along a continuous family of theories. Global analysis of 6D theories on P^2 with 7-branes wrapped on curves of small degree reproduces the range of 6D supergravity theories identified through anomaly cancellation and other consistency conditions. Analogous 4D models are constructed through global F-theory compactifications on P^3, and have a similar pattern of SU(N) matter content. This leads to a constraint on the matter content of a limited class of 4D supergravity theories containing SU(N) as a local factor of the gauge group.Comment: 55 pages, 7 figures; v2: references added; v3: minor correctio

M2-Branes and Fano 3-folds

A class of supersymmetric gauge theories arising from M2-branes probing Calabi-Yau 4-folds which are cones over smooth toric Fano 3-folds is investigated. For each model, the toric data of the mesonic moduli space is derived using the forward algorithm. The generators of the mesonic moduli space are determined using Hilbert series. The spectrum of scaling dimensions for chiral operators is computed.Comment: 128 pages, 39 figures, 42 table