New BPS Objects in N=2 Supersymmetric Gauge Theories

We explore BPS soliton configurations in N=2 supersymmetric Yang-Mills theory with matter fields arising from parallel D3 branes on D7 branes. Especially we focus on two parameter family of 1/8 BPS equations, dyonic objects, and 1/8 BPS objects and raise a possibility of absence of BPS vortices when the number of D3 branes is larger than that of D7 branes.Comment: 28 pages, LaTeX, no figur

Quantum SUSY Algebra of QQ-lumps in the Massive Grassmannian Sigma Model

We compute the $\mathcal{N}=2$ SUSY algebra of the massive Grassmannian sigma model in 2+1 dimensions. We first rederive the action of the model by using the Scherk-Schwarz dimensional reduction from $\mathcal{N}=1$ theory in 3+1 dimensions. Then, we perform the canonical quantization by using the Dirac method. We find that a particular choice of the operator ordering yields the quantum SUSY algebra of the $Q$-lumps with cental extension.Comment: 7 pages, references adde

Instantons in the Higgs Phase

When instantons are put into the Higgs phase, vortices are attached to instantons. We construct such composite solitons as 1/4 BPS states in five-dimensional supersymmetric U(Nc) gauge theory with Nf(>=Nc) fundamental hypermultiplets. We solve the hypermultiplet BPS equation and show that all 1/4 BPS solutions are generated by an Nc x Nf matrix which is holomorphic in two complex variables, assuming the vector multiplet BPS equation does not give additional moduli. We determine the total moduli space formed by topological sectors patched together and work out the multi-instanton solution inside a single vortex with complete moduli. Small instanton singularities are interpreted as small sigma-model lump singularities inside the vortex. The relation between monopoles and instantons in the Higgs phase is also clarified as limits of calorons in the Higgs phase. Another type of instantons stuck at an intersection of two vortices and dyonic instantons in the Higgs phase are also discussed.Comment: 32 pages, 6 figures, typos corrected, comments and references adde

Characterization of bacteria associated with lichens found in cold environment

第6回極域科学シンポジウム分野横断セッション：[IB2] 地球環境変動の解析と地球生命システム学の構築11月19日（木）　統計数理研究所 セミナー室1（D305

Sigma-model soliton intersections from exceptional calibrations

A first-order `BPS' equation is obtained for 1/8 supersymmetric intersections of soliton-membranes (lumps) of supersymmetric (4+1)-dimensional massless sigma models, and a special non-singular solution is found that preserves 1/4 supersymmetry. For 4-dimensional hyper-K\"ahler target spaces ($HK_4$) the BPS equation is shown to be the low-energy limit of the equation for a Cayley-calibrated 4-surface in \bE^4\times HK_4. Similar first-order equations are found for stationary intersections of Q-lump-membranes of the massive sigma model, but now generic solutions preserve either 1/8 supersymmetry or no supersymmetry, depending on the time orientation.Comment: 21 pages. Version 3: Minor corrections and one further reference: version published in JHE

Global Structure of Moduli Space for BPS Walls

We study the global structure of the moduli space of BPS walls in the Higgs branch of supersymmetric theories with eight supercharges. We examine the structure in the neighborhood of a special Lagrangian submanifold M, and find that the dimension of the moduli space can be larger than that naively suggested by the index theorem, contrary to previous examples of BPS solitons. We investigate BPS wall solutions in an explicit example of M using Abelian gauge theory. Its Higgs branch turns out to contain several special Lagrangian submanifolds including M. We show that the total moduli space of BPS walls is the union of these submanifolds. We also find interesting dynamics between BPS walls as a byproduct of the analysis. Namely, mutual repulsion and attraction between BPS walls sometimes forbid a movement of a wall and lock it in a certain position; we also find that a pair of walls can transmute to another pair of walls with different tension after they pass through.Comment: 42 pages, 11 figures; a few comments adde