Geometric Construction of AdS Twistors

Time-like geodesics in AdS_4, AdS_5 and AdS_7 are constructed geometrically and independently of choice of AdS coordinates from division algebra spinors of the corresponding AdS groups, explaining and generalising the construction by Claus et al. of AdS_5 twistors.Comment: 11 pp, 1 figur

Superspace Methods in String Theory, Supergravity and Gauge Theory

In these two lectures, delivered at the XXXVII Karpacz Winter School, February 2001, I review some applications of superspace in various topics related to string theory and M-theory. The first lecture is mainly devoted to descriptions of brane dynamics formulated in supergravity backgrounds. The second lecture concerns the use of superspace techniques for determining consistent interactions in supersymmetric gauge theory and supergravity, e.g. alpha'-corrections from string/M-theory.Comment: 15 pp., latex, aippro

Non-gravitational exceptional supermultiplets

We examine non-gravitational minimal supermultiplets which are based on the tensor gauge fields appearing as matter fields in exceptional generalised geometry. When possible, off-shell multiplets are given. The fields in the multiplets describe non-gravitational parts of the internal dynamics of compactifications of M-theory. In flat backgrounds, they enjoy a global U-duality symmetry, but also provide multiplets with a possibility of coupling to a generalised exceptional geometry.Comment: 11 pp., plain te

Boundaries of 11-Dimensional Membranes

The action for an 11-dimensional supermembrane contains a chiral Wess-Zumino-Witten model coupling to the E8 super-Yang-Mills theory on the end-of-the-world 9-brane. It is demonstrated that this boundary string theory is dictated both by gauge invariance and by kappa-symmetry.Comment: plain tex, 6p

World-volume fields and background coupling of branes

This is the written version of an invited talk delivered at the workshop ``Quantum gravity in the Southern Cone'' held in San Carlos de Bariloche, Argentina, January 7-10, 1998. After giving a brief introduction to the concept of branes and their role in string theory, this talk describes a method for formulating the dynamics of branes, especially those containing non-scalar moduli. Emphasis is put on the coupling of branes to fields in the low-energy background supergravity theories, and on preservation of maximal amount of manifest symmetry. Due to the nature of the workshop, the presentation is aimed at physicists who are not experts in string theory.Comment: 12 pp, plain tex, talk presented at the workshop ``Quantum gravity in the Southern Cone'' held in San Carlos de Bariloche, Argentina, January 7-10, 199

M-branes on U-folds

We give a preliminary discussion of how the addition of extra coordinates in M-theory, which together with the original ones parametrise a U-fold, can serve as a tool for formulating brane dynamics with manifest U-duality. The redundant degrees of freedom are removed by generalised self-duality constraints or calibration conditions made possible by the algebraic structure of U-duality. This is the written version of an invited talk at the 7th International Workshop "Supersymmetries and Quantum Symmetries", Dubna, July 30-August 4, 2007.Comment: 8 p

E7E_7 as D=10D=10 space-time symmetry --- Origin of the twistor transform

Massless particle dynamics in $D=10$ Minkowski space is given an $E_7$-covariant formulation, including both space-time and twistor variables. $E_7$ contains the conformal algebra as a subalgebra. Analogous constructions apply to $D=3,4$ and 6.Comment: 4 page

Thoughts on Membranes, Matrices and Non-Commutativity

We review the passage from the supermembrane to matrix theory via a consistent truncation following a non-commutative deformation in light-cone gauge. Some indications are given that there should exist a generalisation of non-commutativity involving a three-index theta on the membrane, and we discuss some possible ways of investigating the corresponding algebraic structure.Comment: 11 pp, plain tex. Invited talk presented at the conference ``Non-Commutative Geometry and Representation Theory in Mathematical Physics'', Karlstad, Sweden, July 5-10, 200

Problems with Duality in N=2 Super-Yang-Mills Theory

Actual calculations of monopole and dyon spectra have previously been performed in N=4 SYM and in N=2 SYM with gauge group SU(2), and are in total agreement with duality conjectures for the finite theories. These calculations are extended to N=2 SYM with higher rank gauge groups, and it turns out that the SU(2) model with four fundamental hypermultiplet is an exception in that its soliton spectrum supports duality. This may be an indication that the other perturbatively finite N=2 theories have non-perturbative contributions to the beta-function. This talk contains a short summary of recent results.Comment: 5 pp., plain tex. Talk presented at the Second International Sakharov Conference on Physics, Moscow, May 199

Pure spinor superfields, with application to D=3 conformal models

I review and discuss the construction of supersymmetry multiplets and manifestly supersymmetric Batalin-Vilkovisky actions using pure spinors, with emphasis on models with maximal supersymmetry. The special cases of D=3, N=8 (Bagger-Lambert-Gustavsson) and N=6 (Aharony-Bergman-Jafferis-Maldacena) conformal models are treated in detail. Most of the material is covered by the papers arXiv:0808.3242 and arXiv:0809.0318. This is the written version of a talk given at 4th Baltic-Nordic workshop "Algebra, Geometry and Mathematical Physics", Tartu, Estonia, October 9-11, 2008, to appear in the Proceedings of the Estonian Academy of Sciences, vol 4, 2010.Comment: 13 p