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We analyse the classical moduli spaces of supersymmetric vacua of 3d N=2 Chern-Simons quiver gauge theories. We show quite generally that the moduli space of the 3d theory always contains a baryonic branch of a parent 4d N=1 quiver gauge... more
We analyse the classical moduli spaces of supersymmetric vacua of 3d N=2 Chern-Simons quiver gauge theories. We show quite generally that the moduli space of the 3d theory always contains a baryonic branch of a parent 4d N=1 quiver gauge theory, where the 4d baryonic branch is determined by the vector of 3d Chern-Simons levels. In particular, starting with a 4d quiver theory dual to a 3-fold singularity, for certain general choices of Chern-Simons levels this branch of the moduli space of the corresponding 3d theory is a 4-fold singularity. Our results suggest a simple general method, using existing 4d techniques, for constructing candidate 3d N=2 superconformal Chern-Simons quivers with AdS_4 gravity duals.
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We provide a general set of rules for extracting the data defining a quiver gauge theory from a given toric Calabi–Yau singularity. Our method combines information from the geometry and topology of Sasaki–Einstein manifolds, AdS/CFT,... more
We provide a general set of rules for extracting the data defining a quiver gauge theory from a given toric Calabi–Yau singularity. Our method combines information from the geometry and topology of Sasaki–Einstein manifolds, AdS/CFT, dimers, and brane tilings. We explain how the field content, quantum numbers, and superpotential of a superconformal gauge theory on D3–branes probing a toric Calabi–Yau singularity can be deduced. The infinite family of toric singularities with known horizon Sasaki–Einstein manifolds L is used to illustrate these ideas. We construct the corresponding quiver gauge theories, which may be fully specified by giving a tiling of the plane by hexagons with certain gluing rules. As checks of this construction, we perform a-maximisation as well as Z-minimisation to compute the exact R-charges of an arbitrary such quiver. We also examine a number of examples in detail, including the infinite subfamily L, whose smallest member is the Suspended Pinch Point.
We construct supersymmetric AdS5 × Σ solutions of D = 7 gauged supergravity, where Σ is a two-dimensional orbifold known as a spindle. These uplift on S4 to solutions of D = 11 supergravity which have orbifold singularites. We argue that... more
We construct supersymmetric AdS5 × Σ solutions of D = 7 gauged supergravity, where Σ is a two-dimensional orbifold known as a spindle. These uplift on S4 to solutions of D = 11 supergravity which have orbifold singularites. We argue that the solutions are dual to d = 4, $$ \mathcal{N} $$ 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.
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We continue our study of a general class of $$ \mathcal{N} $$ N = 2 supersymmetric AdS3 x Y7 and AdS2 x Y9 solutions of type IIB and D = 11 supergravity, respectively. The geometry of the internal spaces is part of a general family of “GK... more
We continue our study of a general class of $$ \mathcal{N} $$ N = 2 supersymmetric AdS3 x Y7 and AdS2 x Y9 solutions of type IIB and D = 11 supergravity, respectively. The geometry of the internal spaces is part of a general family of “GK geometries”, Y2n+l, n ≥ 3, and here we study examples in which Y2n+l fibres over a Kahler base manifold B2k, 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 Kähler 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 Y7 or Y9 geometry. We illustrate with a number of examples, finding agreement with explicit supergravity solutions in cases where these are k...
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We consider d = 3, $$ \mathcal{N}=2 $$ N = 2 gauge theories arising on membranes sitting at the apex of an arbitrary toric Calabi-Yau 4-fold cone singularity that are then further compactified on a Riemann surface, Σ g , with a... more
We consider d = 3, $$ \mathcal{N}=2 $$ N = 2 gauge theories arising on membranes sitting at the apex of an arbitrary toric Calabi-Yau 4-fold cone singularity that are then further compactified on a Riemann surface, Σ g , with a topological twist that preserves two supersymmetries. If the theories flow to a superconformal quantum mechanics in the infrared, then they have a D = 11 supergravity dual of the form AdS2 × Y 9, with electric four-form flux and where Y 9 is topologically a fibration of a Sasakian Y 7 over Σ g . These D = 11 solutions are also expected to arise as the near horizon limit of magnetically charged black holes in AdS4 × Y 7, with a Sasaki-Einstein metric on Y 7. We show that an off-shell entropy function for the dual AdS2 solutions may be computed using the toric data and Kähler class parameters of the Calabi-Yau 4-fold, that are encoded in a master volume, as well as a set of integers that determine the fibration of Y 7 over Σ g and a Kähler class parameter for Σ...
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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 Σ g , with an arbitrary partial topological twist for the global U(1) symmetries. This... more
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 Σ 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 AdS3 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 Σ g . We furthermore conjecture that the trial central charge "Image missing", which we define in gravity, matches t...
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We consider supersymmetric AdS3 × Y 7 and AdS2 × Y 9 solutions of type IIB and D = 11 supergravity, respectively, that are holographically dual to SCFTs with (0, 2) supersymmetry in two dimensions and $$ \mathcal{N} $$ N = 2 supersymmetry... more
We consider supersymmetric AdS3 × Y 7 and AdS2 × Y 9 solutions of type IIB and D = 11 supergravity, respectively, that are holographically dual to SCFTs with (0, 2) supersymmetry in two dimensions and $$ \mathcal{N} $$ N = 2 supersymmetry in one dimension. The geometry of Y 2n+1, which can be defined for n ≥ 3, shares many similarities with Sasaki-Einstein geometry, including the existence of a canonical R-symmetry Killing vector, but there are also some crucial differences. We show that the R-symmetry Killing vector may be determined by extremizing a function that depends only on certain global, topological data. In particular, assuming it exists, for n = 3 one can compute the central charge of an AdS3 × Y 7 solution without knowing its explicit form. We interpret this as a geometric dual of c-extremization in (0, 2) SCFTs. For the case of AdS2 × Y 9 solutions we show that the extremal problem can be used to obtain properties of the dual quantum mechanics, including obtaining the e...
Research Interests: Mathematics, Physics, Metrics, High Energy Physics, Supersymmetry, and 9 moreSupergravity, Mathematical Sciences, AdS/CFT Correspondence, Physical sciences, Science Technology, Supersymmetric Gauge Theory, Theoretical and Computational High Energy & Nuclear Physics, Quiver, and Black Holes in String Theory
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Research Interests: Mathematics, Mathematical Physics, Field Theory, Physics, Quantum Physics, and 10 moreString Theory, High Energy Physics, Differential Geometry, Supergravity, Dilaton, First-Order Logic, Pure Mathematics(Differential Geometry), Theoretical and Mathematical Physics, Complex Structure, and heterotic string theory
We derive a gravitational block formula for the supersymmetric action for a general class of supersymmetric AdS solutions, described by GK geometry. Extremal points of this action describe supersymmetric AdS$$_3$$ 3 solutions of type IIB... more
We derive a gravitational block formula for the supersymmetric action for a general class of supersymmetric AdS solutions, described by GK geometry. Extremal points of this action describe supersymmetric AdS$$_3$$ 3 solutions of type IIB supergravity, sourced by D3-branes, and supersymmetric AdS$$_2$$ 2 solutions of $$D=11$$ D = 11 supergravity, sourced by M2-branes. In both cases, the branes are also wrapped over a two-dimensional orbifold known as a spindle, or a two-sphere. We develop various geometric methods for computing the gravitational block contributions, allowing us to recover previously known results for various explicit supergravity solutions, and to significantly generalize these results to other compactifications. For the AdS$$_3$$ 3 solutions we give a general proof that our off-shell supersymmetric action agrees with an appropriate off-shell c-function in the dual field theory, establishing a very general exact result in holography. For the AdS$$_2$$ 2 solutions our...
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We study the gravity duals of symmetry-breaking deformations of superconfor- mal field theories, AdS/CFT dual to Type IIB string theory on AdS5 ×Y where Y is a Sasaki-Einstein manifold. In these vacua both conformal invariance and... more
We study the gravity duals of symmetry-breaking deformations of superconfor- mal field theories, AdS/CFT dual to Type IIB string theory on AdS5 ×Y where Y is a Sasaki-Einstein manifold. In these vacua both conformal invariance and baryonic symmetries are spontaneously broken. We present a detailed discussion of the supergravity moduli space, which involves flat form fields on asymptotically conical Calabi-Yau
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We show that by taking a certain scaling limit of a Euclideanised form of the Plebanski-Demianski metrics one obtains a family of local toric Kahler-Einstein metrics. These can be used to construct local Sasaki-Einstein metrics in five... more
We show that by taking a certain scaling limit of a Euclideanised form of the Plebanski-Demianski metrics one obtains a family of local toric Kahler-Einstein metrics. These can be used to construct local Sasaki-Einstein metrics in five di- mensions which are generalisations of the Y p,q manifolds. In fact, we find that these metrics are diffeomorphic to those recently found
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We first present a short review of general supersymmetric compactifications in string and M-theory using the language of G-structures and intrinsic torsion. We then summarize recent work on the generic conditions for supersymmetric AdS_5... more
We first present a short review of general supersymmetric compactifications in string and M-theory using the language of G-structures and intrinsic torsion. We then summarize recent work on the generic conditions for supersymmetric AdS_5 backgrounds in M-theory and the construction of classes of new solutions. Turning to AdS_5 compactifications in type IIB, we summarize the construction of an infinite class
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We study the most general supersymmetric warped M-theory backgrounds with a non-trivial G flux of the type R1,2×M8 and AdS3×M8. We give a set of necessary and sufficient conditions for preservation of supersymmetry which are phrased in... more
We study the most general supersymmetric warped M-theory backgrounds with a non-trivial G flux of the type R1,2×M8 and AdS3×M8. We give a set of necessary and sufficient conditions for preservation of supersymmetry which are phrased in terms of G structures and their intrinsic torsion. These equations may be interpreted as calibration conditions for a static ``dyonic'' M-brane, that is,
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We present a countably infinite number of new explicit co-homogeneity one Sasaki-Einstein metrics on S^2 x S^3, in both the quasi-regular and irregular classes. These give rise to new solutions of type IIB supergravity which are expected... more
We present a countably infinite number of new explicit co-homogeneity one Sasaki-Einstein metrics on S^2 x S^3, in both the quasi-regular and irregular classes. These give rise to new solutions of type IIB supergravity which are expected to be dual to N=1 superconformal field theories in four-dimensions with compact or non-compact R-symmetry and rational or irrational central charges, respectively.
We show that the Reeb vector, and hence in particular the volume, of a Sasaki-Einstein metric on the base of a toric Calabi-Yau cone of complex dimension n may be computed by minimising a function Z on R^n which depends only on the toric... more
We show that the Reeb vector, and hence in particular the volume, of a Sasaki-Einstein metric on the base of a toric Calabi-Yau cone of complex dimension n may be computed by minimising a function Z on R^n which depends only on the toric data that defines the singularity. In this way one can extract certain geometric information for a
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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... more
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.
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We study the geometry and topology of two infinite families Yp,k of Sasaki-Einstein seven-manifolds, that are expected to be AdS4/CFT3 dual to families of = 2 superconformal field theories in three dimensions. These manifolds, labelled by... more
We study the geometry and topology of two infinite families Yp,k of Sasaki-Einstein seven-manifolds, that are expected to be AdS4/CFT3 dual to families of = 2 superconformal field theories in three dimensions. These manifolds, labelled by two positive integers p and k, are Lens space bundles S3/p over P2 and P1 × P1, respectively. The corresponding Calabi-Yau cones are toric. We present their toric diagrams and gauged linear sigma model charges in terms of p and k, and find that the Yp,k manifolds interpolate between certain orbifolds of the homogeneous spaces S7,M3,2 and Q1,1,1.
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We conjecture a topology-changing transition in M-theory on a non-compact asymptotically conical Spin(7) manifold, where a 5-sphere collapses and a Bbb CP2 bolt grows. We argue that the transition may be understood as the condensation of... more
We conjecture a topology-changing transition in M-theory on a non-compact asymptotically conical Spin(7) manifold, where a 5-sphere collapses and a Bbb CP2 bolt grows. We argue that the transition may be understood as the condensation of M5-branes wrapping S5. Upon reduction to ten dimensions, it has a physical interpretation as a transition of D6-branes lying on calibrated submanifolds of flat
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We present a countably infinite number of new explicit co-homo- geneity one Sasaki-Einstein metrics on S2 × S3 of both quasi-regular and irregular type. These give rise to new solutions of type IIB super- gravity which are expected to be... more
We present a countably infinite number of new explicit co-homo- geneity one Sasaki-Einstein metrics on S2 × S3 of both quasi-regular and irregular type. These give rise to new solutions of type IIB super- gravity which are expected to be dual to N = 1 superconformal field theories in four dimensions with compact or non-compact R-symmetry and rational or irrational central charges, respectively.