18/07/2016, 16:20 — 17:00 — Amphitheatre Ea1, North Tower, IST
Tatsuhiro Misumi, Akita & Keio University

Non-BPS Exact Solutions and their Relations to Bions

We discuss non-BPS exact solutions in $\mathbb{C}\mathbb{P}^N$ and Grassmann sigma models on $\mathbb{R}^1 \times \mathbb{S}^1$ with twisted boundary conditions. We focus on the relation of the non-BPS solutions to the ansatz of multi-instanton (bion) configurations and discuss their significance in the context of the resurgence theory. We find that the transition between seemingly distinct configurations of multi-instantons occur as moduli changes in the non-BPS solutions, and the simplest non-BPS exact solution corresponds to multi-bion configurations with fully-compressed double fractional instantons in the middle. It indicates that the non-BPS solutions make small but nonzero contribution to the resurgent trans-series as special cases of the multi-bion configurations. We observe a generic pattern of transitions between distinct multi-bion configurations (flipping partners), leading to the three essential properties of the non-BPS exact solution: (i) opposite sign for terms corresponding to the left and right infinities, (ii) symmetric location of fractional instantons, and (iii) the transition between distinct bion configurations. By studying the balance of forces, we show that the relative phases between the instanton constituents play decisive roles in stability and instability of the muli-instanton configurations.

See also

R-misumi.pdf