[en] Short introduction in NPD with several applications to (in)finit dimensional problems of mechanics, hydrodynamics, M-theory and quanputing is given.

[en] We deal with the problem of diffeomorphism anomaly in theories with branes. In particular we thoroughly analyze the problem of the residual chiral anomaly of a five-brane immersed in M-theory, paying attention to its global formulation in the five-brane world-volume. We conclude that the anomaly can be canceled by a local counterterm in the five-brane world-volume.

[en] In a recent paper (J M Hoff da Silva and da Rocha R 2009 Class. Quantum Grav. 26 055007) it is concluded that the Darmois-Israel junction conditions in the presence of torsion are not modified. We point out that this conclusion is invalid. (comments and replies)

[en] In this brief reply, we elucidate some missing points in the comment (Khakshournia S 2009 Class. Quantum Grav. 26 178001) on our original paper (Hoff da Silva J M and da Rocha R 2009 Class. Quantum Grav. 26 055007), explicitly showing that the comment is unfounded in this context. We show that the term proposed equals zero, since the brane discontinuity is correctly defined in the torsion. (comments and replies)

[en] We revisit the duality between ALE singularities in M-theory and 7-branes on a circle in F-theory. We see that a frozen M-theory singularity maps to a circle compactification involving a rotation of the plane transverse to the 7-brane, showing an interesting correspondence between commuting triples in simply-laced groups and Kodaira’s classification of singular elliptic fibrations. Our analysis strongly suggests that the O7"+ plane is the only completely frozen F-theory singularity.

[en] It is pointed out that the equations ∑_i=1^d[Xⁱ,[X_i,X_j]]=0 (and its super-symmetrizations, playing a central role in M-theory matrix models) describe non-commutative minimal surfaces – and can be solved as such

[en] We show how the theory of invariant principal bundle connections for reductive homogeneous spaces can be applied to determine the holonomy of generalised Killing spinor covariant derivatives of the form D = ∇ + Ω in a purely algebraic and algorithmic way, where Ω : TM → Λ"∗(TM) is a left-invariant homomorphism. Specialising this to the case of symmetric M-theory backgrounds (i.e., (M, g, F) with (M, g) an eleven-dimensional Lorentzian (locally) symmetric space and F an invariant closed 4-form), we derive several criteria for such a background to preserve some supersymmetry and consequently find all supersymmetric symmetric M-theory backgrounds

[en] We describe the collection of finite simple groups, with a view to physical applications. We recall first the prime cyclic groups Z_p and the alternating groups Alt_n>4. After a quick revision of finite fields F_q, q = p^f, with p prime, we consider the 16 families of finite simple groups of Lie type. There are also 26 extra ‘sporadic’ groups, which gather in three interconnected ‘generations’ (with 5+7+8 groups) plus the pariah groups (6). We point out a couple of physical applications, including constructing the biggest sporadic group, the ‘Monster’ group, with close to 10⁵⁴ elements from arguments of physics, and also the relation of some Mathieu groups with compactification in string and M-theory. (topical review)

[en] Motivated by the desire to do proper model building with D7-branes and fluxes, we study the motion of D7-branes on a Calabi-Yau orientifold from the perspective of F-theory. We consider this approach promising since, by working effectively with an elliptically fibred M-theory compactification, the explicit positioning of D7-branes by (M-theory) fluxes is straightforward. The locations of D7-branes are encoded in the periods of certain M-theory cycles, which allows for a very explicit understanding of the moduli space of D7-brane motion. The picture of moving D7-branes on a fixed underlying space relies on negligible backreaction, which can be ensured in Sen's weak coupling limit. However, even in this limit we find certain 'physics obstructions' which reduce the freedom of the D7-brane motion as compared to the motion of holomorphic submanifolds in the orientifold background. These obstructions originate in the intersections of D7-branes and O7-planes, where the type IIB coupling cannot remain weak. We illustrate this effect for D7-brane models on CP¹xCP¹ (the Bianchi-Sagnotti-Gimon-Polchinski model) and on CP². Furthermore, in the simple example of 16 D7-branes and 4 O7-planes on CP¹ (F-theory on K3), we obtain a completely explicit parameterization of the moduli space in terms of periods of integral M-theory cycles. In the weak coupling limit, D7-brane motion factorizes from the geometric deformations of the base space

[en] We consider the compactification of M-theory on X⁷ with Betti numbers (b₀, b₁, b₂, b₃, b₃, b₂, b₁, b₀) and define a generalized mirror symmetry (b₀, b₁, b₂, b₃) → (b₀, b₁, b₂ - ρ/2, b₃ + ρ/2) under which ρ ≡ 7b₀ - 5b₁ + 3b₂ - b₃ changes sign. Generalized self-mirror theories with ρ = 0 have massless sectors with vanishing trace anomaly (before dualization). Examples include pure supergravity with N≥4 and supergravity plus matter with N≤4.