arXiv subjects

James Sparks

Publications and source records attributed to James Sparks.

At least 73 records · Page 4Linked to original sources

arXiv2012

The gravity dual of supersymmetric gauge theories on a squashed three-sphere

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.

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arXiv2012

N=2 supersymmetric AdS_4 solutions of M-theory

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.

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arXiv2012

The gravity dual of supersymmetric gauge theories on a biaxially squashed three-sphere

We present the gravity dual to a class of three-dimensional N=2 supersymmetric gauge theories on a biaxially squashed three-sphere, with a non-trivial background gauge field. This is described by a 1/2 BPS Euclidean solution of four-dimensional N=2 gauged supergravity, consisting of a Taub-NUT-AdS metric with a non-trivial instanton for the graviphoton field. The holographic free energy of this solution agrees precisely with the large N limit of the free energy obtained from the localized partition function of a class of Chern-Simons quiver gauge theories. We also discuss a different supersymmetric solution, whose boundary is a biaxially squashed Lens space S^3/Z_2 with a topologically non-trivial background gauge field. This metric is of Eguchi-Hanson-AdS type, although it is not Einstein, and has a single unit of gauge field flux through the S^2 cycle.

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arXiv2012

The large N limit of M2-branes on Lens spaces

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.

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arXiv2011

The free energy of N=2 supersymmetric AdS_4 solutions of M-theory

We show that general N=2 supersymmetric AdS_4 solutions of M-theory with non-zero M2-brane charge admit a canonical contact structure. The free energy of the dual superconformal field theory on S^3 and the scaling dimensions of operators dual to supersymmetric wrapped M5-branes are expressed via AdS/CFT in terms of contact volumes. In particular, this leads to topological and localization formulae for the coefficient of N^{3/2} in the free energy of such solutions.

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arXiv2011

The large N limit of quiver matrix models and Sasaki-Einstein manifolds

We study the matrix models that result from localization of the partition functions of N=2 Chern-Simons-matter theories on the three-sphere. A large class of such theories are conjectured to be holographically dual to M-theory on Sasaki-Einstein seven-manifolds. We study the M-theory limit (large N and fixed Chern-Simons levels) of these matrix models for various examples, and show that in this limit the free energy reproduces the expected AdS/CFT result of N^{3/2}/Vol(Y)^{1/2}, where Vol(Y) is the volume of the corresponding Sasaki-Einstein metric. More generally we conjecture a relation between the large N limit of the partition function, interpreted as a function of trial R-charges, and the volumes of Sasakian metrics on links of Calabi-Yau four-fold singularities. We verify this conjecture for a family of U(N)^2 Chern-Simons quivers based on M2 branes at hypersurface singularities, and for a U(N)^3 theory based on M2 branes at a toric singularity.

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arXiv2011

Non-Kahler heterotic rotations

We study a supersymmetry-preserving solution-generating method in heterotic supergravity. In particular, we use this method to construct one-parameter non-Kahler deformations of Calabi-Yau manifolds with a U(1) isometry, in which the complex structure remains invariant. We explain how to obtain corresponding solutions to heterotic string theory, up to first order in α', by a modified form of the standard embedding. In the course of the paper we also show that Abelian heterotic supergravity embeds into type II supergravity, and note that the solution-generating method in this context is related to a dipole-type deformation when there is a field theory dual.

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arXiv2010

Generalized Geometry in AdS/CFT and Volume Minimization

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.

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arXiv2010

Sasaki-Einstein Manifolds

This article is an overview of some of the remarkable progress that has been made in Sasaki-Einstein geometry over the last decade, which includes a number of new methods of constructing Sasaki-Einstein manifolds and obstructions.

math.DG↗

arXiv2010

Baryonic symmetries and M5 branes in the AdS_4/CFT_3 correspondence

We study U(1) symmetries dual to Betti multiplets in the AdS_4/CFT_3 correspondence for M2 branes at Calabi-Yau four-fold singularities. Analysis of the boundary conditions for vector fields in AdS_4 allows for a choice where wrapped M5 brane states carrying non-zero charge under such symmetries can be considered. We begin by focusing on isolated toric singularities without vanishing six-cycles, and study in detail the cone over Q^{111}. The boundary conditions considered are dual to a CFT where the gauge group is U(1)^2 x SU(N)^4. We find agreement between the spectrum of gauge-invariant baryonic-type operators in this theory and wrapped M5 brane states. Moreover, the physics of vacua in which these symmetries are spontaneously broken precisely matches a dual gravity analysis involving resolutions of the singularity, where we are able to match condensates of the baryonic operators, Goldstone bosons and global strings. We also argue more generally that theories where the resolutions have six-cycles are expected to receive non-perturbative corrections from M5 brane instantons. We give a general formula relating the instanton action to normalizable harmonic two-forms, and compute it explicitly for the Q^{222} example. The holographic interpretation of such instantons is currently unclear.

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arXiv2010

(Un)Higgsing the M2-brane

We study various aspects of N=2 quiver-Chern-Simons theories, conjectured to be dual to M2-branes at toric Calabi-Yau four-fold singularities, under Higgsing. In particular we study in detail the orbifold C^4/Z_2^3, obtaining a number of different quiver-Chern-Simons phases for this model, and all 18 toric partial resolutions thereof. In the process we develop a general un-Higgsing algorithm that allows one to construct quiver-Chern-Simons theories by blowing up, thus obtaining a plethora of new models. In addition we explain how turning on torsion G-flux non-trivially affects the supergravity dual of Higgsing, showing that the supergravity and field theory analyses precisely match in an example based on the Sasaki-Einstein manifold Y^(1,2)(CP^2).

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arXiv2010

AdS_5 Solutions of Type IIB Supergravity and Generalized Complex Geometry

We use the formalism of generalized geometry to study the generic supersymmetric AdS_5 solutions of type IIB supergravity that are dual to N=1 superconformal field theories (SCFTs) in d=4. Such solutions have an associated six-dimensional generalized complex cone geometry that is an extension of Calabi-Yau cone geometry. We identify generalized vector fields dual to the dilatation and R-symmetry of the dual SCFT and show that they are generalized holomorphic on the cone. We carry out a generalized reduction of the cone to a transverse four-dimensional space and show that this is also a generalized complex geometry, which is an extension of Kahler-Einstein geometry. Remarkably, provided the five-form flux is non-vanishing, the cone is symplectic. The symplectic structure can be used to obtain Duistermaat-Heckman type integrals for the central charge of the dual SCFT and the conformal dimensions of operators dual to BPS wrapped D3-branes. We illustrate these results using the Pilch-Warner solution.

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arXiv2009

AdS_4/CFT_3 duals from M2-branes at hypersurface singularities and their deformations

We construct three-dimensional N=2 Chern-Simons-quiver theories which are holographically dual to the M-theory Freund-Rubin solutions AdS_4 x V_{5,2}/Z_k (with or without torsion G-flux), where V_{5,2} is a homogeneous Sasaki-Einstein seven-manifold. The global symmetry group of these theories is generically SU(2) x U(1) x U(1)_R, and they are hence non-toric. The field theories may be thought of as the n=2 member of a family of models, labelled by a positive integer n, arising on multiple M2-branes at certain hypersurface singularities. We describe how these models can be engineered via generalized Hanany-Witten brane constructions. The AdS_4 x V_{5,2}/Z_k solutions may be deformed to a warped geometry R^{1,2} x T^* S^4/Z_k, with self-dual G-flux through the four-sphere. We show that this solution is dual to a supersymmetric mass deformation, which precisely modifies the classical moduli space of the field theory to the deformed geometry.

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arXiv2009

The central charge of supersymmetric AdS_5 solutions of type IIB supergravity

We show that generic supersymmetric AdS_5 solutions of type IIB supergravity admit a canonical contact structure. This structure determines the central charge of the dual field theory and the conformal dimension of operators dual to supersymmetric wrapped D3-branes. Hence both quantities can be calculated using incomplete information about the solutions, allowing us to prove that they are rational numbers for solutions with a U(1) R-symmetry, in agreement with field theory expectations. We also discuss related Duistermaat-Heckman integrals and localization formulae.

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arXiv2009

AdS_3 x S^3 x S^3 x S^1 Solutions of Type IIB String Theory

We analyse a recently constructed class of local solutions of type IIB supergravity that consist of a warped product of AdS_3 with a seven-dimensional internal space. In one duality frame the only other non-vanishing fields are the NS three-form and the dilaton. We analyse in detail how these local solutions can be extended to globally well-defined solutions of type IIB string theory, with the internal space having topology S^3 x S^3 x S^1 and with properly quantised three-form flux.

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arXiv2008

Symmetry-breaking vacua and baryon condensates in AdS/CFT

We study the gravity duals of symmetry-breaking deformations of superconformal field theories, AdS/CFT dual to Type IIB string theory on AdS_5 x 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 manifolds, and match this to the gauge theory vacuum moduli space. We discuss certain linearised fluctuations of the moduli, identifying the Goldstone bosons associated with spontaneous breaking of non-anomalous baryonic symmetries. The remaining moduli fields are related to spontaneous breaking of anomalous baryonic symmetries. We also elaborate on the proposal that computing condensates of baryon operators is equivalent to computing the partition function of a non-compact Euclidean D3-brane in the background supergravity solution, with fixed boundary conditions at infinity.

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arXiv2008

New Results in Sasaki-Einstein Geometry

This article is a summary of some of the author's work on Sasaki-Einstein geometry. A rather general conjecture in string theory known as the AdS/CFT correspondence relates Sasaki-Einstein geometry, in low dimensions, to superconformal field theory; properties of the latter are therefore reflected in the former, and vice versa. Despite this physical motivation, many recent results are of independent geometrical interest, and are described here in purely mathematical terms: explicit constructions of infinite families of both quasi-regular and irregular Sasaki-Einstein metrics; toric Sasakian geometry; an extremal problem that determines the Reeb vector field for, and hence also the volume of, a Sasaki-Einstein manifold; and finally, obstructions to the existence of Sasaki-Einstein metrics. Some of these results also provide new insights into Kahler geometry, and in particular new obstructions to the existence of Kahler-Einstein metrics on Fano orbifolds.

math.DG↗

arXiv2008

Moduli spaces of Chern-Simons quiver gauge theories and AdS_4/CFT_3

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 lead to a simple general method, using existing 4d techniques, for constructing candidate 3d N=2 superconformal Chern-Simons quivers with AdS_4 gravity duals. As simple, but non-trivial, examples, we identify a family of Chern-Simons quiver gauge theories which are candidate AdS_4/CFT_3 duals to an infinite class of toric Sasaki-Einstein seven-manifolds with explicit metrics.

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