Kazuyuki Furuuchi

“Topological” Charge of U(1) Instantons on Noncommutative R4

Non-singular instantons are shown to exist on noncommutative R^4 even with a U(1) gauge group. Their existence is primarily due to the noncommutativity of the space. The relation between U(1) instantons on noncommutative R^4 and the projection operators acting on the representation space of the noncommutative coordinates is reviewed. The integer number of instantons on the noncommutative R^4 can be understood as the winding number of the U(1) gauge field as well as the dimension of the projection on the representation space.Non-singular instantons are shown to exist on noncommutative R 4 even in U(1) gauge theory. Their existence is primarily due to the noncommutativity of the coordinates. The integer instanton number on the noncommutative R 4 can be understood as winding number of the U(1) gauge field as well as dimension of a certain projection operator acting on the representation space of the noncommutative coordinates.

M-theory superalgebra from multiple membranes

We investigate space-time supersymmetry of the model of multiple M2-branes proposed by Bagger-Lambert and Gustavsson. When there is a central element in Lie 3-algebra, the model possesses an extra symmetry shifting the fermions in the central element. Together with the original worldvolume supersymmetry transformation, we construct major part of the eleven dimensional space-time super-Poincare algebra with central extensions. Implications to transverse five-branes in the matrix model for M-theory are also discussed.

Equivalence of projections as gauge equivalence on noncommutative space

Abstract: Projections play crucial roles in the ADHM construction on noncommutative ℝ4. In this article a framework for the description of equivalence relations between projections is proposed. We treat the equivalence of projections as “gauge equivalence” on noncommutative space. We find an interesting application of this framework to the study of the U(2) instanton on noncommutative ℝ4: A zero winding number configuration with a hole at the origin is “gauge equivalent” to the noncommutative analog of the BPST instanton. Thus the “gauge transformation” in this case can be understood as a noncommutative resolution of the singular gauge transformation in ordinary ℝ4.

More on the Nambu-Poisson M5-brane theory: scaling limit, background independence and an all order solution to the Seiberg-Witten map

We continue our investigation on the Nambu-Poisson description of M5-brane in a large constant C-field background (NP M5-brane theory) constructed in refs. [1, 2]. In this paper, the low energy limit where the NP M5-brane theory is applicable is clarified. The background independence of the NP M5-brane theory is made manifest using the variables in the BLG model of multiple M2-branes. An all order solution to the Seiberg-Witten map is also constructed.

Supersymmetric reduced models with a symmetry based on Filippov algebra

Generalizations of the reduced model of super Yang-Mills theory obtained by replacing the Lie algebra structure to Filippov n-algebra structures are studied. Conditions for the reduced model actions to be supersymmetric are examined. These models are related with what we call min = 2 super p-brane actions.

Non-linearly extended self-dual relations from the Nambu-bracket description of M5-brane in a constant C-field background

The derivation of the self-dual relations for the two-form gauge field in the Nambu-bracket description of M5-brane in a constant C-field background initiated in ref. [1] is completed by including contributions from all the fields in the M5-brane action. The result is used to examine Seiberg-Witten map of the BPS conditions for the string solitons, up to the first order in the expansion by the parameter g which characterizes the strength of the interactions through the Nambu-bracket.

D-branes Wrapped on Fuzzy del Pezzo Surfaces

We construct classical solutions in quiver gauge theories on D0-branes probing toric del Pezzo singularities in Calabi-Yau manifolds. Our solutions represent D4-branes wrapped around fuzzy del Pezzo surfaces. We study the fluctuation spectrum around the fuzzy

Affleck-Dine baryogenesis in inflating curvaton scenario with (10–102 TeV) mass moduli curvaton

\mathbb{C}{\mathbb{P}^2}

Excursions through KK modes

solution in detail. We also comment on possible applications of our fuzzy del Pezzo surfaces to the fuzzy version of F-theory, dubbed F(uzz) theory.

Gauge-Higgs Unification In Spontaneously Created Fuzzy Extra Dimensions

We study the Affleck-Dine (AD) baryogenesis in the inflating curvaton scenario, when the curvaton is a moduli field with (10–102 TeV) mass. A moduli field with such mass is known to be free from the Polonyi problem, and furthermore its decay products can explain the present cold dark matter abundance. In our scenario, it further explains the primordial curvature perturbation and the present baryon density all together. The current observational bound on the baryon isocurvature perturbation, which severely constrains the AD baryogenesis with the original oscillating moduli curvaton scenario, is shown to put practically negligible constraint if we replace the oscillating curvaton with the inflating curvaton.