A note on supersymmetric AdS_6 solutions of massive type IIA supergravity

Motivated by the AdS_6/CFT_5 correspondence, we study general supersymmetric solutions of massive type IIA supergravity, consisting of a warped product of six-dimensional anti-de Sitter space AdS_6 with a four-dimensional Riemannian manifold M_4, and fluxes compatible with the SO(5,2) symmetry. We find that the only local solution of this form is the warped AdS_6 x_w S^4 solution, originally discovered by Brandhuber and Oz. We discuss the supersymmetric properties of this solution.Comment: 18 page

The gravity dual of supersymmetric gauge theories on a two-parameter deformed three-sphere

We present rigid supersymmetric backgrounds for three-dimensional N=2 supersymmetric gauge theories, comprising a two-parameter U(1)xU(1)-invariant deformed three-sphere, and their gravity duals. These are described by supersymmetric solutions of four-dimensional N=2 gauged supergravity with a self-dual metric on the ball and different instantons for the graviphoton field. We find two types of solutions, distinguished by their holographic free energies. In one type the holographic free energy is constant, whereas in another type it depends in a simple way on the parameters and is generically complex. This leads to a conjecture for the localized partition function of a class of N=2 supersymmetric gauge theories on these backgrounds.Comment: 27 pages, 1 figure; v2: typos fixed, minor changes, one reference adde

The supersymmetric NUTs and bolts of holography

We show that a given conformal boundary can have a rich and intricate space of supersymmetric supergravity solutions filling it, focusing on the case where this conformal boundary is a biaxially squashed Lens space. Generically we find that the biaxially squashed Lens space S^3/Z_p admits Taub-NUT-AdS fillings, with topology R^4/Z_p, as well as smooth Taub-Bolt-AdS fillings with non-trivial topology. We show that the Taub-NUT-AdS solutions always lift to solutions of M-theory, and correspondingly that the gravitational free energy then agrees with the large N limit of the dual field theory free energy, obtained from the localized partition function of a class of N=2 Chern-Simons-matter theories. However, the solutions of Taub-Bolt-AdS type only lift to M-theory for appropriate classes of internal manifold, meaning that these solutions exist only for corresponding classes of three-dimensional N=2 field theories.Comment: 54 pages plus 7 appendices; v2: discussion of global properties of gauge field A in eleven dimensions improved and some parts of the paper rewritten to reflect this, new subsections 6.4.1, 6.4.2 and appendix F added, references added; v3: final version published in Nuclear Physics

Universal consistent truncation for 6d/7d gauge/gravity duals

Recently, AdS_7 solutions of IIA supergravity have been classified; there are infinitely many of them, whose expression is known analytically, and with internal space of S^3 topology. Their field theory duals are six-dimensional (1,0) SCFT's. In this paper we show that for each of these AdS_7 solutions there exists a consistent truncation from massive IIA supergravity to minimal gauged supergravity in seven dimensions. This theory has an SU(2) gauge group, and a single scalar, whose value is related to a certain distortion of the internal S^3. This explains the universality observed in recent work on AdS_5 and AdS_4 solutions dual to compactifications of the (1,0) SCFT_6's. Thanks to previous work on the minimal gauged supergravity, the truncation also implies the existence of holographic RG-flows connecting those solutions to the AdS_7 vacuum, as well as new classes of IIA AdS_3 solutions.Comment: 23 pages; v2: references added, minor changes, additions and correction

Superstrings on Penrose limits of AdS7_7 solutions

We consider the Penrose limit of AdS$_7$ solutions of massive Type IIA supergravity. The resulting pp-wave geometry is supported by RR and NSNS fields. We quantize the Green--Schwarz superstring on the obtained pp-wave background, in the light-cone gauge

Supersymmetric AdS_5 solutions of massive IIA supergravity

Motivated by a recently found class of AdS_7 solutions, we classify AdS_5 solutions in massive IIA, finding infinitely many new analytical examples. We reduce the general problem to a set of PDEs, determining the local internal metric, which is a fibration over a surface. Under a certain simplifying assumption, we are then able to analytically solve the PDEs and give a complete list of all solutions. Among these, one class is new and regular. These spaces can be related to the AdS_7 solutions via a simple universal map for the metric, dilaton and fluxes. The natural interpretation of this map is that the dual CFT_6 and CFT_4 are related by twisted compactification on a Riemann surface $\Sigma_g$. The ratio of their free energy coefficients is proportional to the Euler characteristic of $\Sigma_g$. As a byproduct, we also find the analytic expression for the AdS_7 solutions, which were previously known only numerically. We determine the free energy for simple examples: it is a simple cubic function of the flux integers.Comment: 56 pages, 2 figures, LaTeX; v3: subsection 4.3.1 revised, minor correction

Meaning in Structure and the Structure of Meaning in La Modification and La Route des Flandres

Stream of consciousness novels employ a variety of narrative techniques to depict the flow of consciousness. This article examines narrative structures underlying the subjective frame created by a sole character/narrator in two French New Novels, Michel Butor\u27s La Modification and Claude Simon\u27s La Route des Flandres. There is a dynamic relationship between form and content. Conventional narrative syntax in Butor\u27s work reflects the evaluative and associative processes of the mind attempting to resolve an emotional conflict. In Simon\u27s work, narrative structures mirror the complex embedding of four main fables as the narrative process attempts to depict the uncontrolled thought patterns evoked in a half-asleep state. The rational and the illusory functions of the mental process that differentiate these novels are reflected not only in the narrative structures but also in their global form, theme and conception of the role of language in a work of art

AdS_6 solutions of type II supergravity

Very few AdS_6 x M_4 supersymmetric solutions are known: one in massive IIA, and two IIB solutions dual to it. The IIA solution is known to be unique; in this paper, we use the pure spinor approach to give a classification for IIB supergravity. We reduce the problem to two PDEs on a two-dimensional space Sigma. M_4 is then a fibration of S^2 over Sigma; the metric and fluxes are completely determined in terms of the solution to the PDEs. The results seem likely to accommodate near-horizon limits of (p,q)-fivebrane webs studied in the literature as a source of CFT_5's. We also show that there are no AdS_6 solutions in eleven-dimensional supergravity.Comment: 37 pages; v2: references and equations (5.1) added, version published in Journal of High Energy Physics; v3: equation (5.1b) correcte

Global spinal deformity from the upper cervical perspective. What is Abnormal in the upper cervical spine?

Hypothesis: Reciprocal changes in the upper cervical spine correlate with adult TL deformity modifiers. Design: This was a retrospective review. Introduction: The upper cervical spine has remarkable adaptability to wide ranges of thoracolumbar (TL) deformity. Methods: Patients \u3e18 years with adult spinal deformity (ASD) and complete radiographic data at baseline (BL) and 1 year were identified. Patients were grouped into component types of the Roussouly classification system (Type 1: Pelvic incidence [PI] Results: A total of 343 ASD patients were analyzed. When grouped by BL Schwab and Roussouly, Group Conclusions: Our study suggests that upper cervical alignment remains relatively stable through most broad variations of adult TL deformity. Changes in SVA correlated most with upper cervical changes