ABJM on ellipsoid and topological strings

It is known that the large N expansion of the partition function in ABJM theory on a three-sphere is completely determined by the topological string on local Hirzebruch surface F_0. In this note, we investigate the ABJM partition function on an ellipsoid, which has a conventional deformation parameter b. Using 3d mirror symmetry, we find a remarkable relation between the ellipsoid partition function for b^2=3 (or b^2=1/3) in ABJM theory at k=1 and a matrix model for the topological string on another Calabi-Yau threefold, known as local P^2. As in the case of b=1, we can compute the full large N expansion of the partition function in this case. This is the first example of the complete large N solution in ABJM theory on the squashed sphere. Using the obtained results, we also analyze the supersymmetric Renyi entropy.Comment: 29 page

Vector Mesons in Nuclear Medium

We summarize the current theoretical and experimental status of the spectral change of the vector mesons in dense matter.Comment: 4 pages, Latex, talk at Quark Matter '9

Adiabatic Effective Action for Vortices in Neutral and Charged Superfluids

Adiabatic effective action for vortices in neutral and charged superfluids at zero temperature are calculated using the topological Landau-Ginzburg theory recently proposed by Hatsuda, Yahikozawa, Ao and Thouless, and vortex dynamics are examined. The Berry phase term arising in the effective action naturally yields the Magnus force in both neutral and charged superfluids. It is shown that in neutral superfluid there is only one degree of freedom, namely the center of vorticities, and the vortex energy is proportinal to the sum of all vorticities so that it is finite only for the vanishing total vorticity of the system. On the other hand the effective mass and the vortex energy for a vortex in charged superfluids are defined individually as expected. The effects of the vortex core on these quantities are also estimated. The possible depinning scenario which is governed by the Magnus force and the inertial mass is also discussed.Comment: 26 page

Comments on Exact Quantization Conditions and Non-Perturbative Topological Strings

We give some remarks on exact quantization conditions associated with quantized mirror curves of local Calabi-Yau threefolds, conjectured in arXiv:1410.3382. It is shown that they characterize a non-perturbative completion of the refined topological strings in the Nekrasov-Shatashvili limit. We find that the quantization conditions enjoy an exact S-dual invariance. We also discuss Borel summability of the semi-classical spectrum.Comment: 15 pages, v2: minor corrections, references adde