$G_2$ holonomy metrics and wrapped D6-branes

We consider type II backgrounds of the form R^{1,d-1} x M^{10-d} for even d, preserving 2^{d/2} real supercharges; for d = 4, 6, 8 this is minimal supersymmetry in d dimensions, while for d = 2 it is N = (2,0) supersymmetry in two dimensions. For d = 6 we prove, by explicitly solving the Killing-spinor equations, that there is a one-to-one correspondence between background supersymmetry equations in pure-spinor form and D-brane generalized calibrations; this correspondence ha...

We obtain regular deformed D2-brane solutions with fractional D2-branes arising as wrapped D4-branes. The space transverse to the D2-brane is a complete Ricci-flat 7-manifold of G_2 holonomy, which is asymptotically conical with principal orbits that are topologically CP^3 or the flag manifold SU(3)/(U(1) x U(1)). We obtain the solution by first constructing an L^2 normalisable harmonic 3-form. We also review a previously-obtained regular deformed D2-brane whose transverse sp...

We study wrapped brane configurations via possible maximally supersymmetric gauged supergravities. First, we construct various supersymmetric wrapped D3 brane configurations from D=5 N=8 SO(6) gauged supergravity. This procedure provides certain new examples of wrapped D3 branes around supersymmetric cycles inside non-compact special holonomy manifolds. We analyze their behaviors numerically in order to discuss a correspondence to Higgs and Coulomb branches of sigma models on...

Calibration technology provides us with a fast and elegant way to find the supergravity solutions for BPS wrapped M-branes. Its true potential had however remained untapped due to the absence of a classification of calibrations in spacetimes with non-trivial flux. The applications of this method were thus limited in practise to M-branes wrapping Kahler calibrated cycles. In this paper, we catagorize a type of generalised calibrations which exist in supergravity backgrounds an...

We systematically analyse the necessary and sufficient conditions for the preservation of supersymmetry for bosonic geometries of the form R^{1,9-d} \times M_d, in the common NS-NS sector of type II string theory and also type I/heterotic string theory. The results are phrased in terms of the intrinsic torsion of G-structures and provide a comprehensive classification of static supersymmetric backgrounds in these theories. Generalised calibrations naturally appear since the g...

We construct D=11 supergravity solutions dual to the twisted field theories arising when M-theory fivebranes wrap supersymmetric cycles. The cases considered are M-fivebranes wrapped on (i) a complex Lagrangian four-cycle in a D=8 hyper-Kaehler manifold corresponding to a D=2 field theory with (2,1) supersymmetry (ii) a product of two holomorphic two-cycles in a product of two Calabi-Yau two-folds corresponding to a D=2 field theory with (2,2) supersymmetry and (iii) a produc...

We study supergravity solutions representing D3-branes with transverse 6-space having R x S^2 x S^3 topology. We consider regular and fractional D3-branes on a natural one-parameter extensions of the standard Calabi-Yau metrics on the singular and resolved conifolds. After imposing a Z_2 identification on an angular coordinate these generalized "6-d conifolds" are nonsingular spaces. The backreaction of D3-branes creates a curvature singularity that coincides with a horizon. ...

We classify 7-dimensional cocalibrated $\G_2$-manifolds with parallel characteristic torsion and non-abelian holonomy. All these spaces admit a metric connection $\nabla^{\mathrm{c}}$ with totally skew-symmetric torsion and a spinor field $\Psi_1$ solving the equations in the common sector of type II superstring theory. There exist $\G_2$-structures with parallel characteristic torsion that are not naturally reductive.

We study the flow from the theory of D2-branes in a G2 holonomy background to M2-branes in a Spin(7) holonomy background. We consider in detail the UV and IR regimes, and the effect of topology change of the background on the field theory. We conjecture a non-Abelian N=1 mirror symmetry.

We present new solutions of 8d gauged supergravity which, upon uplift to type IIA, represent D6 branes wrapped on spindles. A further circle uplift gives 11d supergravity on a Calabi-Yau three-fold which is the cone over five-dimensional $Y^{p,q}$ manifolds. This highlights a connection between co-homogeneity one Sasaki-Einstein metrics in general dimension and the recently introduced spindle solutions in gauged supergravity. We find that a similar connection also exists for ...