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We consider the Cartan subalgebra of any very extended algebra G+++ where G is a simple Lie algebra and let the parameters be space-time fields. These are identified with diagonal metrics and dilatons. Using the properties of the algebra,…
We study the supersymmetric solutions of 11-dimensional supergravity with a factor of $AdS_2$ made of M2-branes. Such solutions can provide gravity duals of superconformal quantum mechanics, or through double Wick rotation, the generic…
Reconsidering the M2-brane solutions of d=11 supergravity with a transverse Englert flux introduced by one of us in 2016, we present a new purely group theoretical algorithm to solve Englert equation based on a specific embedding of the…
Synopsis: (i) how superstring theories are unified by M-theory; (ii) how superstring and supermembrane properties follow from the D=10 and D=11 supersymmetry algebras; (iii) how D=10 and D=11 supergravity theories determine the strong…
A duality relationship between certain brane configurations in type IIA and type IIB string theory is explored by exploiting the geometrical origins of each theory in M-theory. The configurations are dual ways of realising the…
We construct two-dimensional N=(2,2) supersymmetric gauge theories with orthogonal and symplectic groups using branes and orientifold planes in Type IIA string theory. A number of puzzles regarding the construction, including the effect of…
Among $T^7/\Gamma$ orbifold compactifications of $M$-theory, we examine models containing the particle physics Standard Model in four-dimensional spacetimes, which appear as fixed subspaces of the ten-dimensional spacetimes at each end of…
We construct M-theory on the orbifold C^2/Z_N by coupling 11-dimensional supergravity to a seven-dimensional Yang-Mills theory located on the orbifold fixed plane. It is shown that the resulting action is supersymmetric to leading…
We study the M-theory five-brane wrapped around the Seiberg-Witten curves for pure classical and exceptional groups given by an integrable system. Generically, the D4-branes arise as cuts that collapse to points after compactifying the…
We study the 6d N=(0,2) superconformal field theory, which describes multiple M5-branes, on the product space S^2 x M_4, and suggest a correspondence between a 2d N=(0,2) half-twisted gauge theory on S^2 and a topological sigma-model on the…
The bosonic content of string theory in curved background of multidimensional structure with p-branes has a systematic geometrical description as an effective sigma-model of gravity in lower dimension (say 3+1) with additional interacting…
We generalise the electric-magnetic duality in standard Maxwell theory to its non-commutative version. Both space-space and space-time non-commutativity are necessary. The duality symmetry is then extended to a general class of…
We construct new M-theory solutions of M5 branes that are a realization of the fully localized ten dimensional NS5/D6 and NS5/D5 brane intersections. These solutions are obtained by embedding self-dual geometries lifted to M-theory. We…
In this paper, an overview is presented of the recent construction of fully back-reacted half-BPS solutions in 11-dimensional supergravity which correspond to near-horizon geometries of M2 branes ending on, or intersecting with, M5 and…
We analyze properties of the Sp(2M) conformally invariant field equations in the recently proposed generalized $\half M(M+1)$-dimensional space-time $\M_M$ with matrix coordinates. It is shown that classical solutions of these field…
In this paper we discuss compactifications of M-theory to four dimensions on X \times S^1/Z_2, in which nonstandard embeddings in the E_8 \times E_8 vacuum gauge bundle are considered. At the level of the effective field theory description…
We review the evidence for the various dualities amongst the five D=10 superstring theories and for the existence of M-theory using the associated effective supergravity theories. We also summarise the combinatorial technics developed for…
We analyze a broad class of stationary solutions with residual N=1 supersymmetry of four-dimensional N=2 supergravity theories with terms quadratic in the Weyl tensor. These terms are encoded in a holomorphic function, which determines the…
The theory of generalized Weyl algebras is used to study the $2\times 2$ reflection equation algebra $\mathcal{A}=\mathcal{A}_q(\operatorname{M}_2)$ in the case that $q$ is not a root of unity, where the $R$-matrix used to define…
We construct time-dependent S-brane solutions to the supergravity field equations in various dimensions which (unlike most such geometries) do not contain curvature singularities. The configurations we consider are less symmetric than are…