Higher Derivative Corrections to Eleven Dimensional Supergravity via Local Supersymmetry

In this paper we derive higher derivative corrections to the eleven dimensional supergravity by applying the Noether method with respect to the N=1 local supersymmetry. An ansatz for the higher derivative effective action, which includes quartic terms of the Riemann tensor, is parametrized by 132 parameters. Then we show that by the requirement of the local supersymmetry, the higher derivative effective action is essentially described by two parameters. The bosonic parts of these two superinvariants completely match with the known results obtained by the perturbative calculations in the type IIA superstring theory. Since the calculations are long and systematic, we build the computer programming to check the cancellation of the variations under the local supersymmetry. This is an extended version of our previous paper hep-th/0508204.Comment: 67 pages, no figure, references added, typos correcte

Fuzzy Sphere Dynamics and Non-Abelian DBI in Curved Backgrounds

We consider the non-Abelian action for the dynamics of $N Dp'$-branes in the background of $M Dp$-branes, which parameterises a fuzzy sphere using the SU(2) algebra. We find that the curved background leads to collapsing solutions for the fuzzy sphere except when we have $D0$ branes in the $D6$ background, which is a realisation of the gravitational Myers effect. Furthermore we find the equations of motion in the Abelian and non-Abelian theories are identical in the large $N$ limit. By picking a specific ansatz we find that we can incorporate angular momentum into the action, although this imposes restriction upon the dimensionality of the background solutions. We also consider the case of non-Abelian non-BPS branes, and examine the resultant dynamics using world-volume symmetry transformations. We find that the fuzzy sphere always collapses but the solutions are sensitive to the combination of the two conserved charges and we can find expanding solutions with turning points. We go on to consider the coincident $NS$5-brane background, and again construct the non-Abelian theory for both BPS and non-BPS branes. In the latter case we must use symmetry arguments to find additional conserved charges on the world-volumes to solve the equations of motion. We find that in the Non-BPS case there is a turning solution for specific regions of the tachyon and radion fields. Finally we investigate the more general dynamics of fuzzy $\mathbb{S}^{2k}$ in the $Dp$-brane background, and find collapsing solutions in all cases.Comment: 49 pages, 3 figures, Latex; Version to appear in JHE

Fate of the Black String Instability

Gregory and Laflamme showed that certain nonextremal black strings (and p-branes) are unstable to linearized perturbations. It is widely believed that this instability will cause the black string horizon to classically pinch off and then quantum mechanically separate, resulting in higher dimensional black holes. We argue that this cannot happen. Under very mild assumptions, classical event horizons cannot pinch off. Instead, they settle down to new static black string solutions which are not translationally invariant along the string.Comment: 11 pages, v2: few clarifications and references adde

Anomalies and O-plane charges in orientifolded brane tilings

We investigate orientifold of brane tilings. We clarify how the cancellations of gauge anomaly and Witten's anomaly are guaranteed by the conservation of the D5-brane charge. We also discuss the relation between brane tilings and the dual Calabi-Yau cones realized as the moduli spaces of gauge theories. Two types of flavor D5-branes in brane tilings and corresponding superpotentials of fundamental quark fields are proposed, and it is shown that the massless loci of these quarks in the moduli space correctly reproduce the worldvolume of flavor D7-branes in the Calabi-Yau cone dual to the fivebrane system.Comment: 46 pages, 19 figure

Aspects of higher curvature terms and U-duality

We discuss various aspects of dimensional reduction of gravity with the Einstein-Hilbert action supplemented by a lowest order deformation formed as the Riemann tensor raised to powers two, three or four. In the case of R^2 we give an explicit expression, and discuss the possibility of extended coset symmetries, especially SL(n+1,Z) for reduction on an n-torus to three dimensions. Then we start an investigation of the dimensional reduction of R^3 and R^4 by calculating some terms relevant for the coset formulation, aiming in particular towards E_8(8)/(Spin(16)/Z_2) in three dimensions and an investigation of the derivative structure. We emphasise some issues concerning the need for the introduction of non-scalar automorphic forms in order to realise certain expected enhanced symmetries.Comment: 26 pp., 15 figs., plain te

Electrified Fuzzy Spheres and Funnels in Curved Backgrounds

We use the non-Abelian DBI action to study the dynamics of $N$ coincident $Dp$-branes in an arbitrary curved background, with the presence of a homogenous world-volume electric field. The solutions are natural extensions of those without electric fields, and imply that the spheres will collapse toward zero size. We then go on to consider the $D1-D3$ intersection in a curved background and find various dualities and automorphisms of the general equations of motion. It is possible to map the dynamical equation of motion to the static one via Wick rotation, however the additional spatial dependence of the metric prevents this mapping from being invertible. Instead we find that a double Wick rotation leaves the static equation invariant. This is very different from the behaviour in Minkowski space. We go on to construct the most general static fuzzy funnel solutions for an arbitrary metric either by solving the static equations of motion, or by finding configurations which minimise the energy. As a consistency check we construct the Abelian $D3$-brane world-volume theory in the same generic background and find solutions consistent with energy minimisation. In the $NS$5-brane background we find time dependent solutions to the equations of motion, representing a time dependent fuzzy funnel. These solutions match those obtained from the $D$-string picture to leading order suggesting that the action in the large $N$ limit does not need corrections. We conclude by generalising our solutions to higher dimensional fuzzy funnels.Comment: 38 pages, Latex; references adde

Dirichlet Branes on Orientifolds

We consider the classification of BPS and non-BPS D-branes in orientifold models. In particular we construct all stable BPS and non-BPS D-branes in the Gimon-Polchinski (GP) and Dabholkar-Park-Blum-Zaffaroni (DPBZ) orientifolds and determine their stability regions in moduli space as well as decay products. We find several kinds of integrally and torsion charged non-BPS D-branes. Certain of these are found to have projective representations of the orientifold $\times$ GSO group on the Chan-Paton factors. It is found that the GP orientifold is not described by equivariant orthogonal K-theory as may have been at first expected. Instead a twisted version of this K-theory is expected to be relevant.Comment: 33 pages, LaTeX, 5 figures. v2 typos corrected, references included, (4,s)-branes re-examine