We study the large $N$ limit of some supersymmetric partition functions $\mathrm{U}(N)_{k}\times \mathrm{U}(N)_{-k}$ ABJM theory computed by localization. conjecture an explicit expression, valid to all orders in limit, for function on $\mathrm{U}(1)\times \mathrm{U}(1)$ invariant squashed sphere presence real masses terms Airy function. Several non-trivial tests this are presented. In addition...

There is an interesting relation between the quantum periods on a certain limit of local $\mathbb{P}^1\times \mathbb{P}^1$ Calabi-Yau space and TBA (Thermodynamic Bethe Ansatz) system appeared in studies ABJM (Aharony-Bergman-Jafferis-Maldacena) theory. We propose one-parameter generalization relation. Furthermore, we derive differential operators for TBA-like equation various limits generalized

We find a closed formula for the overlap of Bethe eigenstates an alternating SU(4) spin chain, describing scalar sector ABJM theory, and matrix product states any bond dimension representing 1/2 BPS co-dimension one domain walls in field theory. One point functions defect CFTs involved, being directly expressible terms these overlaps, are hence completely determined.