Supersymmetric solutions on SU(4)-structure deformed Stenzel space

The Stenzel space fourfold is a non-compact Calabi-Yau which is a higher dimensional analogue of the deformed conifold. We consider N = (1,1) type IIA, N = 1 M-theory and N = (2,0) type IIB compactifications on this Stenzel space, thus examining the gravity side of potentially higher dimensional analogues of Klebanov-Strassler-like compactifications. We construct families of SU(4)-structures and solve associated moduli spaces, of complex and symplectic structures amongst others. By making use of these, we can construct IIA compactifications on manifolds homeomorphic to the Stenzel space fourfold, but with complex non-CY SU(4)-structures. Such compactifications are sourced by a distribution of NS5-branes. The external metric is asymptotically conformal AdS_3 and should thus be suitable for holography applications.Comment: 55 pages, 2 figures. v3: minor clarifications added, published versio

3d N=1 effective supergravity and F-theory from M-theory on fourfolds

We consider 3d N=1 M-theory compactifications on Calabi-Yau fourfolds, and the effective 3d theory of light modes obtained by reduction from eleven dimensions. We study in detail the mass spectrum at the vacuum and, by decoupling the massive multiplets, we derive the effective 3d N=1 theory in the large-volume limit up to quartic fermion terms. We show that in general it is an ungauged N=1 supergravity of the form expected from 3d supersymmetry. In particular the massless bosonic fields consist of the volume modulus and the axions originating from the eleven-dimensional three-form, while the moduli-space metric is locally isometric to hyperbolic space. We consider the F-theory interpretation of the 3d N=1 M-theory vacua in the light of the F-theory effective action approach. We show that these vacua generally have F-theory duals with circle fluxes, thus breaking 4d Poincar\'e invariance.Comment: 37 pages. Published version, minor change

IIB supergravity on manifolds with SU(4) structure and generalized geometry

We consider N=(2,0) backgrounds of IIB supergravity on eight-manifolds M_8 with strict SU(4) structure. We give the explicit solution to the Killing spinor equations as a set of algebraic relations between irreducible su(4) modules of the fluxes and the torsion classes of M_8. One consequence of supersymmetry is that M_8 must be complex. We show that the conjecture of arxiv:1010.5789 concerning the correspondence between background supersymmetry equations in terms of generalized pure spinors and generalized calibrations for admissible static, magnetic D-branes, does not capture the full set of supersymmetry equations. We identify the missing constraints and express them in the form of a single pure-spinor equation which is well defined for generic SU(4)\times SU(4) backgrounds. This additional equation is given in terms of a certain analytic continuation of the generalized calibration form for codimension-2 static, magnetic D-branes.Comment: 23 pages. V2: added references, including to spinorial geometr

Mirror symmetry & supersymmetry on SU(4)-structure backgrounds

We revisit the backgrounds of type IIB on manifolds with $SU(4)$-structure and discuss two sets of solutions arising from internal geometries that are complex and symplectic respectively. Both can be realized in terms of generalized complex geometry. We identify a map which relates the complex and symplectic supersymmetric systems. In the semi-flat torus bundle setting this map corresponds to T-duality and suggest a way of extending the mirror transform to non-K\"ahler geometries.Comment: 40 page

IIA supergravity and M-theory on manifolds with SU(4) structure

We give the general form of supersymmetric backgrounds with two real supercharges of M-theory and type IIA supergravity (with non-zero Romans mass in general) of the form \mathbb{R}^{1,d} \times \M_8, d=1,2, on eight-dimensional manifolds with SU(4) structure. We point out a subtlety in the integrability theorems for low-dimensional supersymmetric compactifications. As a special case we examine Calabi-Yau flux vacua and we show that unbroken supersymmetry does not in general require the four-form flux to be (2,2) or primitive. Our results could be used to construct novel higher-dimensional analogues of the Klebanov-Strassler geometry. In the case of M-theory large-volume Calabi-Yau flux vacua our results are in agreement with partial supersymmetry breaking in three-dimensional N=2 supergravity. Alternatively, the conditions for supersymmetry can be expressed in terms of a real `superpotential' in accordance with three-dimensional N=1 supergravity. We present explicit examples of M-theory flux vacua on K3 \times K3, which however do not appear to possess F-theory duals with four-dimensional Poincar\'e invariance.Comment: 41 pages. V2: the K3xK3 examples of section 3.2.2 have been generalized to manifestly admit a large-volume limit. Published versio

Generalized complex geometry of pure backgrounds in ten and eleven dimensions

Pure backgrounds are a natural generalization of supersymmetric Calabi-Yau compactifications in the presence of flux. They are described in the language of generalized SU(d) x SU(d) structures and generalized complex geometry, and they exhibit some interesting general patterns: the internal manifold is generalized Calabi-Yau, while the Ramond-Ramond flux is exact in a precise sense discussed in this paper. We have shown that although these two characteristics do persist in the case of generic ten-dimensional Euclidean type II pure backgrounds, they do not capture the full content of supersymmetry. We also discuss the uplift of real Euclidean type IIA pure backgrounds to supersymmetric backgrounds of Lorentzian eleven-dimensional supergravity.Comment: 26 pages. Typos fixed, references adde

Application of ultrasound to monitor in vivo residual bone movement within transtibial prosthetic sockets

Transtibial prosthetic users do often struggle to achieve an optimal prosthetic fit, leading to residual limb pain and stump-socket instability. Prosthetists face challenges in objectively assessing the impact of prosthetic adjustments on residual limb loading. Understanding the mechanical behaviour of the pseudo-joint formed by the residual bone and prosthesis may facilitate prosthetic adjustments and achieving optimal fit. This study aimed to assess the feasibility of using B-mode ultrasound to monitor in vivo residual bone movement within a transtibial prosthetic socket during different stepping tasks. Five transtibial prosthesis users participated, and ultrasound images were captured using a Samsung HM70A system during five dynamic conditions. Bone movement relative to the socket was quantified by tracking the bone contour using Adobe After-Effect. During the study a methodological adjustment was made to improve data quality, and the first two participants were excluded from analysis. The remaining three participants exhibited consistent range of motion, with a signal to noise ratio ranging from 1.12 to 2.59. Medial–lateral and anterior–posterior absolute range of motion varied between 0.03 to 0.88 cm and 0.14 to 0.87 cm, respectively. This study demonstrated that it is feasible to use B-mode ultrasound to monitor in vivo residual bone movement inside an intact prosthetic socket during stepping tasks