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We construct supersymmetric $AdS_5\times \Sigma$ solutions of $D=7$ gauged supergravity, where $\Sigma$ is a two-dimensional orbifold known as a spindle. These uplift on $S^4$ to solutions of $D=11$ supergravity which have orbifold singularites. We argue that the solutions are dual to $d=4$, $\mathcal{N}=1$ SCFTs that arise from $N$ M5-branes wrapped on a spindle, embedded as a holomorphic curve inside a Calabi-Yau three-fold. In contrast to the usual topological twist solutions, the superconformal R-symmetry mixes with the isometry of the spindle in the IR, and we verify this via a field theory calculation, as well as reproducing the gravity formula for the central charge., Comment: 25 pages. Very minor change, published version

We construct supersymmetric $AdS_3$ solutions of $D=11$ supergravity, dual to $d=2$, $\mathcal{N}=(0,2)$ SCFTs, that are associated with M5-branes wrapping two different four-dimensional orbifolds. In one case the orbifold is a spindle fibred over another spindle, while in the other it is a spindle fibred over a Riemann surface with genus $g>1$. We show that the central charges of the $d=2$ SCFTs calculated from the gravity solutions agree with field theory computations using anomaly polynomials. The new $D=11$ solutions are obtained after constructing a new consistent Kaluza-Klein truncation of maximal $D=7$ gauged supergravity reduced on a spindle down to $D=5$ minimal gauged supergravity., 37 pages. Very minor changes. Published version

We construct a family of multi-dyonically charged and rotating supersymmetric AdS$_2\times \Sigma$ solutions of $D=4$, $\mathcal{N}=4$ gauged supergravity, where $\Sigma$ is a sphere with two conical singularities known as a spindle. We argue that these arise as near horizon limits of extremal dyonically charged rotating and accelerating supersymmetric black holes in AdS$_4$, that we conjecture to exist. We demonstrate this in the non-rotating limit, constructing the accelerating black hole solutions and showing that the non-spinning spindle solutions arise as the near horizon limit of the supersymmetric and extremal sub-class of these black holes. From the near horizon solutions we compute the Bekenstein-Hawking entropy of the black holes as a function of the conserved charges, and show that this may equivalently be obtained by extremizing a simple entropy function. For appropriately quantized magnetic fluxes, the solutions uplift on $S^7$, or its ${\cal N}=4$ orbifolds $S^7/\Gamma$, to smooth supersymmetric solutions to $D=11$ supergravity, where the entropy is expected to count microstates of the theory on $N$ M2-branes wrapped on a spinning spindle, in the large $N$ limit., Comment: Minor changes, matches published version

We introduce an entropy function for supersymmetric accelerating black holes in $AdS_4$, that uplift on general Sasaki-Einstein manifolds $X_7$ to solutions of M-theory. This allows one to compute the black hole entropy without knowing the explicit solutions. A dual holographic microstate counting would follow from computing certain supersymmetric partition functions of Chern-Simons-matter theories compactified on a spindle. We make a general prediction for a class of such partition functions in terms of ``blocks'', with each block being constructed from the partition function on a three-sphere., Comment: 6 pages

We study the thermodynamics of $AdS_4$ black hole solutions of Einstein-Maxwell theory that are accelerating, rotating, and carry electric and magnetic charges. We focus on the class for which the black hole horizon is a spindle and can be uplifted on regular Sasaki-Einstein spaces to give solutions of $D=11$ supergravity that are free from conical singularities. We use holography to calculate the Euclidean on-shell action and to define a set of conserved charges which give rise to a first law. We identify a complex locus of supersymmetric and non-extremal solutions, defined through an analytic continuation of the parameters, upon which we obtain a simple expression for the on-shell action. A Legendre transform of this action combined with a reality constraint then leads to the Bekenstein-Hawking entropy for the class of supersymmetric and extremal black holes., Comment: 47 pages. Very minor changes; published version

We study solutions in the Pleba\'nski--Demia\'nski family which describe an accelerating, rotating and dyonically charged black hole in $AdS_4$. These are solutions of $D=4$ Einstein-Maxwell theory with a negative cosmological constant and hence minimal $D=4$ gauged supergravity. It is well known that when the acceleration is non-vanishing the $D=4$ black hole metrics have conical singularities. By uplifting the solutions to $D=11$ supergravity using a regular Sasaki-Einstein $7$-manifold, $SE_7$, we show how the free parameters can be chosen to eliminate the conical singularities. Topologically, the $D=11$ solutions incorporate an $SE_7$ fibration over a two-dimensional weighted projective space, $\mathbb{WCP}^1_{[n_-,n_+]}$, also known as a spindle, which is labelled by two integers that determine the conical singularities of the $D=4$ metrics. We also discuss the supersymmetric and extremal limit and show that the near horizon limit gives rise to a new family of regular supersymmetric $AdS_2\times Y_9$ solutions of $D=11$ supergravity, which generalise a known family by the addition of a rotation parameter. We calculate the entropy of these black holes and argue that it should be possible to derive this from certain ${\cal N}=2$, $d=3$ quiver gauge theories compactified on a spinning spindle with appropriate magnetic flux., Comment: 76 pages, 8 figures; v2: very minor changes, published version

We consider D3-brane gauge theories at an arbitrary toric Calabi-Yau 3-fold cone singularity that are then further compactified on a Riemann surface $\Sigma_g$, with an arbitrary partial topological twist for the global $U(1)$ symmetries. This constitutes a rich, infinite class of two-dimensional $(0,2)$ theories. Under the assumption that such a theory flows to a SCFT, we show that the supergravity formulas for the central charge and $R$-charges of BPS baryonic operators of the dual AdS$_3$ solution may be computed using only the toric data of the Calabi-Yau 3-fold and the topological twist parameters. We exemplify the procedure for both the $Y^{p,q}$ and $X^{p,q}$ 3-fold singularities, along with their associated dual quiver gauge theories, showing that the new supergravity results perfectly match the field theory results obtained using $c$-extremization, for arbitrary twist over $\Sigma_g$. We furthermore conjecture that the trial central charge $\mathscr{Z}$, which we define in gravity, matches the field theory trial $c$-function off-shell, and show this holds in non-trivial examples. Finally, we check our general geometric formulae against a number of explicitly known supergravity solutions., Comment: 62 pages. Typos corrected, published version

We construct families of supersymmetric AdS$_3\times Y_7$ and AdS$_3\times Y_8$ solutions to type IIB string theory and M-theory, respectively. Here $Y_7$ is an $S^5$ fibration over $\Sigma$, while $Y_8$ is an $S^4$ fibration over $\Sigma_g\times \Sigma$, where $\Sigma_g$ is a Riemann surface of genus $g>1$ and $\Sigma$ is a two-dimensional orbifold known as a spindle. We interpret the solutions as near-horizon limits of $N$ D3-branes wrapped on $\Sigma$ and $N$ M5-branes wrapped on $\Sigma_g\times \Sigma$, respectively. These are holographically dual to $d=2$, $(0,2)$ SCFTs, and we show that the central charge and superconformal R-symmetry of the gravity solutions agree with dual field theory calculations., Comment: 25 pages

We construct supersymmetric $AdS_3\times \Sigma$ solutions of minimal gauged supergravity in $D=5$, where $\Sigma$ is a two-dimensional orbifold known as a spindle. Remarkably, these uplift on $S^5$, or more generally on any regular Sasaki-Einstein manifold, to smooth solutions of type IIB supergravity. The solutions are dual to $d=2$, $\mathcal{N}=(0,2)$ SCFTs and we show that the central charge for the gravity solution agrees with a field theory calculation associated with D3-branes wrapped on $\Sigma$. Unlike for smooth $\Sigma$ the superconformal R-symmetry mixes with the $U(1)$ isometry of the spindle., Comment: 6 pages. Minor changes. Matches published version

We study the holographic dual to $c$-extremization for 2d $(0,2)$ superconformal field theories (SCFTs) that have an AdS$_3$ dual realized in Type IIB with varying axio-dilaton, i.e. F-theory. M/F-duality implies that such AdS$_3$ solutions can be mapped to AdS$_2$ solutions in M-theory, which are holographically dual to superconformal quantum mechanics (SCQM), obtained by dimensional reduction of the 2d SCFTs. We analyze the corresponding map between holographic $c$-extremization in F-theory and $\mathcal{I}$-extremization in M-theory, where in general the latter receives corrections relative to the F-theory result., Comment: 45 pages, v2: references added

SARS-CoV-2 infection causes diverse outcomes ranging from asymptomatic infection to respiratory distress and death. A major unresolved question is whether prior immunity to endemic, human common cold coronaviruses (hCCCoV) impacts susceptibility to SARS-CoV-2 infection or immunity following infection and vaccination. Therefore, we analyzed samples from the same individuals before and after SARS-CoV-2 infection or vaccination. We found hCCCoV antibody levels increase after SARS-CoV-2 exposure, demonstrating cross-reactivity. However, a case-control study indicates baseline hCCCoV antibody levels are not associated with protection against SARS-CoV-2 infection. Rather, higher magnitudes of pre-existing betacoronavirus antibodies correlate with more SARS-CoV-2 antibodies following infection, an indicator of greater disease severity. Additionally, immunization with hCCCoV spike proteins before SARS-CoV-2 immunization impedes generation of SARS-CoV-2 neutralizing antibodies in mice. Together, these data suggest pre-existing hCCCoV antibodies hinder SARS-CoV-2 antibody-based immunity following infection and provide insight on how pre-existing coronavirus immunity impacts SARS-CoV-2 infection, which is critical considering emerging variants., Graphical Abstract, A major unresolved question is whether prior immunity to endemic, human common cold coronaviruses (hCCCoV) impacts susceptibility to SARS-CoV-2 infection. Lin et al. analyze hCCCoV antibodies in the same individuals before and after SARS-CoV-2 infection, finding pre-existing betacoronavirus antibodies may hinder SARS-CoV-2 effective immunity following infection.

We continue our study of a general class of $\mathcal{N}=2$ supersymmetric $AdS_3\times Y_7$ and $AdS_2\times Y_9$ solutions of type IIB and $D=11$ supergravity, respectively. The geometry of the internal spaces is part of a general family of "GK geometries", $Y_{2n+1}$, $n\ge 3$, and here we study examples in which $Y_{2n+1}$ fibres over a K\"ahler base manifold $B_{2k}$, with toric fibres. We show that the flux quantization conditions, and an action function that determines the supersymmetric $R$-symmetry Killing vector of a geometry, may all be written in terms of the "master volume" of the fibre, together with certain global data associated with the K\"ahler base. In particular, this allows one to compute the central charge and entropy of the holographically dual $(0,2)$ SCFT and dual superconformal quantum mechanics, respectively, without knowing the explicit form of the $Y_7$ or $Y_9$ geometry. We illustrate with a number of examples, finding agreement with explicit supergravity solutions in cases where these are known, and we also obtain new results. In addition we present, en passant, new formulae for calculating the volumes of Sasaki-Einstein manifolds., Comment: 49 pages

We explore how various anomaly-cancelling terms in M-theory and string theory transform non-trivially into each other under duality. Specifically, we study the phenomenon in which bulk terms in M-theory get mapped to brane worldvolume terms in string theory. The key mathematical ingredient is G-index theory., Comment: 15 pages, no figures; minor changes, reference added

We present the gravity dual to a class of three-dimensional N=2 supersymmetric gauge theories on a U(1) x U(1)-invariant squashed three-sphere, with a non-trivial background gauge field. This is described by a supersymmetric solution of four-dimensional N=2 gauged supergravity with a non-trivial instanton for the graviphoton field. The particular gauge theory in turn determines the lift to a solution of eleven-dimensional supergravity. We compute the partition function for a class of Chern-Simons quiver gauge theories on both sides of the duality, in the large N limit, finding precise agreement for the functional dependence on the squashing parameter. This constitutes an exact check of the gauge/gravity correspondence in a non-conformally invariant setting., Comment: 37 pages. v2: typos fixed, references added, new section 2.5 added discussing the solution in standard global coordinates; v3: more typos fixed, version published on Nucl. Phys. B

Holographic renormalization is a systematic procedure for regulating divergences in observables in asymptotically locally AdS spacetimes. For dual boundary field theories which are supersymmetric it is natural to ask whether this defines a supersymmetric renormalization scheme. Recent results in localization have brought this question into sharp focus: rigid supersymmetry on a curved boundary requires specific geometric structures, and general arguments imply that BPS observables, such as the partition function, are invariant under certain deformations of these structures. One can then ask if the dual holographic observables are similarly invariant. We study this question in minimal N = 2 gauged supergravity in four and five dimensions. In four dimensions we show that holographic renormalization precisely reproduces the expected field theory results. In five dimensions we find that no choice of standard holographic counterterms is compatible with supersymmetry, which leads us to introduce novel finite boundary terms. For a class of solutions satisfying certain topological assumptions we provide some independent tests of these new boundary terms, in particular showing that they reproduce the expected VEVs of conserved charges., 70 pages; corrected typos

We consider a general class of asymptotically locally AdS_5 solutions of minimal gauged supergravity, that are dual to superconformal field theories on curved backgrounds S^1 x M_3 preserving two supercharges. We demonstrate that standard holographic renormalization corresponds to a scheme that breaks supersymmetry. We propose new boundary terms that restore supersymmetry, and show that for smooth solutions with topology S^1 x R^4 the improved on-shell action reproduces both the supersymmetric Casimir energy and the field theory BPS relation between charges., 4 pages; v2: minor changes

We analyse the most general N = 2 supersymmetric solutions of D = 11 supergravity consisting of a warped product of four-dimensional anti-de-Sitter space with a seven-dimensional Riemannian manifold Y7. We show that the necessary and sufficient conditions for supersymmetry can be phrased interms of a local SU(2)-structure on Y7. Solutions with non-zero M2-brane charge also admit a canonical contact structure, in terms of which many physical quantities can be expressed, including the free energy and the scaling dimensions of operators dual to supersymmetric wrapped M5-branes. We show that a special class of solutions is singled out by imposing an additional symmetry, for which the problem reduces to solving a second order non-linear ODE. As well as recovering a known class of solutions, that includes the IR fixed point of a mass deformation of the ABJM theory, we also find new solutions which are dual to cubic deformations. In particular, we find a new supersymmetric warped AdS4 × S 7 solution with non-trivial four-form flux.

We study gravity duals to a broad class of N=2 supersymmetric gauge theories defined on a general class of three-manifold geometries. The gravity backgrounds are based on Euclidean self-dual solutions to four-dimensional gauged supergravity. As well as constructing new examples, we prove in general that for solutions defined on the four-ball the gravitational free energy depends only on the supersymmetric Killing vector, finding a simple closed formula when the solution has U(1) x U(1) symmetry. Our result agrees with the large N limit of the free energy of the dual gauge theory, computed using localization. This constitutes an exact check of the gauge/gravity correspondence for a very broad class of gauge theories with a large N limit, defined on a general class of background three-manifold geometries., 74 pages, 2 figures; v2: minor changes

We consider deformations of N=1 superconformal field theories that are AdS/CFT dual to Type IIB string theory on Sasaki-Einstein manifolds, characterised by non-zero vacuum expectation values for certain baryonic operators. Such baryonic branches are constructed from (partially) resolved, asymptotically conical Ricci-flat Kahler manifolds, together with a choice of point where the stack of D3-branes is placed. The complete solution then describes a renormalisation group flow between two AdS fixed points. We discuss the use of probe Euclidean D3-branes in these backgrounds as a means to compute expectation values of baryonic operators. The Y^{p,q} theories are used as illustrative examples throughout the paper. In particular, we present supergravity solutions describing flows from the Y^{p,q} theories to various different orbifold field theories in the infra-red, and successfully match this to an explicit field theory analysis., 51 pages, v2: reference added and minor changes; v3: minor changes, published version

We study Euclidean Romans supergravity in six dimensions with a non-trivial Abelian R-symmetry gauge field. We show that supersymmetric solutions are in one-to-one correspondence with solutions to a set of differential constraints on an SU(2) structure. As an application of our results we (i) show that this structure reduces at a conformal boundary to the five-dimensional rigid supersymmetric geometry previously studied by the authors, (ii) find a general expression for the holographic dual of the VEV of a BPS Wilson loop, matching an exact field theory computation, (iii) construct holographic duals to squashed Sasaki-Einstein backgrounds, again matching to a field theory computation, and (iv) find new analytic solutions., Comment: 31 pages; v2: published version (with reference added)

We study a system of N D2-branes probing a generic Calabi-Yau three-fold singularity in the presence of a non-zero quantized Romans mass n. We argue that the low-energy effective N = 2 Chern-Simons quiver gauge theory flows to a superconformal fixed point in the IR, and construct the dual AdS_4 solution in massive IIA supergravity. We compute the free energy F of the gauge theory on S^3 using localization. In the large N limit we find F = c(nN)^{1/3}a^{2/3}, where c is a universal constant and a is the a-function of the "parent" four-dimensional N = 1 theory on N D3-branes probing the same Calabi-Yau singularity. It follows that maximizing F over the space of admissible R-symmetries is equivalent to maximizing a for this class of theories. Moreover, we show that the gauge theory result precisely matches the holographic free energy of the supergravity solution, and provide a similar matching of the VEV of a BPS Wilson loop operator., Comment: 19 pages; v2: minor corrections

We study a variational problem whose critical point determines the Reeb vector field for a Sasaki-Einstein manifold. This extends our previous work on Sasakian geometry by lifting the condition that the manifolds are toric. We show that the Einstein-Hilbert action, restricted to a space of Sasakian metrics on a link L in a Calabi-Yau cone X, is the volume functional, which in fact is a function on the space of Reeb vector fields. We relate this function both to the Duistermaat-Heckman formula and also to a limit of a certain equivariant index on X that counts holomorphic functions. Both formulae may be evaluated by localisation. This leads to a general formula for the volume function in terms of topological fixed point data. As a result we prove that the volume of a Sasaki-Einstein manifold, relative to that of the round sphere, is always an algebraic number. In complex dimension n=3 these results provide, via AdS/CFT, the geometric counterpart of a-maximisation in four dimensional superconformal field theories. We also show that our variational problem dynamically sets to zero the Futaki invariant of the transverse space, the latter being an obstruction to the existence of a Kahler-Einstein metric., 82 pages, 9 figures; homogeneity of the (n,0)-form now derived from the Einstein-Hilbert action of the link, example of an orbifold resolution added, various clarifications and references added; minor changes; published version

We compute the supersymmetric Renyi entropy across an entangling three-sphere for five-dimensional superconformal field theories using localization. For a class of USp(2N) gauge theories we construct a holographic dual 1/2 BPS black hole solution of Euclidean Romans F(4) supergravity. The large N limit of the gauge theory results agree perfectly with the supergravity computations., Comment: 19 pages

We construct rigid supersymmetric gauge theories on Riemannian five-manifolds. We follow a holographic approach, realizing the manifold as the conformal boundary of a six-dimensional bulk supergravity solution. This leads to a systematic classification of five-dimensional supersymmetric backgrounds with gravity duals. We show that the background metric is furnished with a conformal Killing vector, which generates a transversely holomorphic foliation with a transverse Hermitian structure. Moreover, we prove that any such metric defines a supersymmetric background. Finally, we construct supersymmetric Lagrangians for gauge theories coupled to arbitrary matter on such backgrounds., Comment: 35 pages: v2: minor corrections and references added. Published version

We study the supersymmetric Casimir energy $E_\mathrm{susy}$ of $\mathcal{N}=1$ field theories with an R-symmetry, defined on rigid supersymmetric backgrounds $S^1\times M_3$, using a Hamiltonian formalism. These backgrounds admit an ambi-Hermitian geometry, and we show that the net contributions to $E_\mathrm{susy}$ arise from certain twisted holomorphic modes on $\mathbb{R}\times M_3$, with respect to both complex structures. The supersymmetric Casimir energy may then be identified as a limit of an index-character that counts these modes. In particular this explains a recent observation relating $E_\mathrm{susy}$ on $S^1\times S^3$ to the anomaly polynomial. As further applications we compute $E_\mathrm{susy}$ for certain secondary Hopf surfaces, and discuss how the index-character may also be used to compute generalized supersymmetric indices., Comment: 47 pages; v2: footnote 6 added, formula (5.29) changed, Section 6 moved to Appendix A

We compute the large N limit of Wilson loop expectation values for a broad class of N=2 supersymmetric gauge theories defined on a general class of background three-manifolds M_3, diffeomorphic to S^3. We find a simple closed formula which depends on the background geometry only through a certain supersymmetric Killing vector field. The supergravity dual of such a Wilson loop is an M2-brane wrapping the M-theory circle, together with a complex curve in a self-dual Einstein manifold M_4, whose conformal boundary is M_3. We show that the regularized action of this M2-brane also depends only on the supersymmetric Killing vector, precisely reproducing the large N field theory computation., Comment: 24 pages; v2: references and discussion of torus knots added

We present a countably infinite number of new explicit co-homogeneity one Sasaki-Einstein metrics on $S^2\times S^3$ of both quasi-regular and irregular type. These give rise to new solutions of type IIB supergravity which are expected to be dual to $\mathcal{N}=1$ superconformal field theories in four dimensions with compact or non-compact $R$-symmetry and rational or irrational central charges, respectively.

We present the gravity dual of large N supersymmetric gauge theories on a squashed five-sphere. The one-parameter family of solutions is constructed in Euclidean Romans F(4) gauged supergravity in six dimensions, and uplifts to massive type IIA supergravity. By renormalizing the theory with appropriate counterterms we evaluate the renormalized on-shell action for the solutions. We also evaluate the large N limit of the gauge theory partition function, and find precise agreement., Comment: 4 pages; v2: minor corrections

We construct the gravity duals of large N supersymmetric gauge theories defined on squashed five-spheres with SU(3) x U(1) symmetry. These five-sphere backgrounds are continuously connected to the round sphere, and we find a one-parameter family of 3/4 BPS deformations and a two-parameter family of (generically) 1/4 BPS deformations. The gravity duals are constructed in Euclidean Romans F(4) gauged supergravity in six dimensions, and uplift to massive type IIA supergravity. We holographically renormalize the Romans theory, and use our general result to compute the renormalized on-shell actions for the solutions. The results agree perfectly with the large N limit of the dual gauge theory partition function, which we compute using large N matrix model techniques. In addition we compute BPS Wilson loops in these backgrounds, both in supergravity and in the large N matrix model, again finding precise agreement. Finally, we conjecture a general formula for the partition function on any five-sphere background, which for fixed gauge theory depends only on a certain supersymmetric Killing vector., Comment: 63 pages, no figures; v2: minor corrections and reference added

We consider supersymmetric gauge theories on Riemannian three-manifolds with the topology of a three-sphere. The three-manifold is always equipped with an almost contact structure and an associated Reeb vector field. We show that the partition function depends only on this vector field, giving an explicit expression in terms of the double sine function. In the large N limit our formula agrees with a recently discovered two-parameter family of dual supergravity solutions. We also explain how our results may be applied to prove vortex-antivortex factorization. Finally, we comment on the extension of our results to three-manifolds with non-trivial fundamental group., 34 pages; v2: discussion of vortex factorization added; v3: minor corrections

We study the matrix model for N M2-branes wrapping a Lens space L(p,1) = S^3/Z_p. This arises from localization of the partition function of the ABJM theory, and has some novel features compared with the case of a three-sphere, including a sum over flat connections and a potential that depends non-trivially on p. We study the matrix model both numerically and analytically in the large N limit, finding that a certain family of p flat connections give an equal dominant contribution. At large N we find the same eigenvalue distribution for all p, and show that the free energy is simply 1/p times the free energy on a three-sphere, in agreement with gravity dual expectations., 28 pages, 4 figures

We study the general structure of the AdS_5/CFT_4 correspondence in type IIB string theory from the perspective of generalized geometry. We begin by defining a notion of "generalized Sasakian geometry," which consists of a contact structure together with a differential system for three symplectic forms on the four-dimensional transverse space to the Reeb vector field. A generalized Sasakian manifold which satisfies an additional "Einstein" condition provides a general supersymmetric AdS_5 solution of type IIB supergravity with fluxes. We then show that the supergravity action restricted to a space of generalized Sasakian structures is simply the contact volume, and that its minimization determines the Reeb vector field for such a solution. We conjecture that this contact volume is equal to the inverse of the trial central charge whose maximization determines the R-symmetry of any four-dimensional N=1 superconformal field theory. This variational procedure allows us to compute the contact volumes for a predicted infinite family of solutions, and we find perfect agreement with the central charges and R-charges of BPS operators in the dual mass-deformed generalized conifold theories., 70 pages, 4 figures

We analyse the most general N=2 supersymmetric solutions of D=11 supergravity consisting of a warped product of four-dimensional anti-de-Sitter space with a seven-dimensional Riemannian manifold Y_7. We show that the necessary and sufficient conditions for supersymmetry can be phrased in terms of a local SU(2)-structure on Y_7. Solutions with non-zero M2-brane charge also admit a canonical contact structure, in terms of which many physical quantities can be expressed, including the free energy and the scaling dimensions of operators dual to supersymmetric wrapped M5-branes. We show that a special class of solutions is singled out by imposing an additional symmetry, for which the problem reduces to solving a second order non-linear ODE. As well as recovering a known class of solutions, that includes the IR fixed point of a mass deformation of the ABJM theory, we also find new solutions which are dual to cubic deformations. In particular, we find a new supersymmetric warped AdS_4 x S^7 solution with non-trivial four-form flux., 50 pages, 2 figures; v2: typos fixed, some intermediate formulas added to improve clarity, references added

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 B