9 research outputs found
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Topological AdS/CFT and the Ω deformation
In this note, we define a holographic dual to four-dimensional superconformal
field theories formulated on arbitrary Riemannian manifolds equipped with a
Killing vector. Moreover, assuming smoothness of the bulk solution, we study
the variation of the holographically renormalized supergravity action in the
class of metrics on the boundary four-manifold with a prescribed isometry
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Localization of the action in AdS/CFT
We derive a simple formula for the action of any supersymmetric solution to
minimal gauged supergravity in the AdS/CFT correspondence. Such
solutions are equipped with a supersymmetric Killing vector, and we show that
the holographically renormalized action may be expressed entirely in terms of
the weights of this vector field at its fixed points, together with certain
topological data. In this sense, the classical gravitational partition function
localizes in the bulk. We illustrate our general formula with a number of
explicit examples, in which exact dual field theory computations are also
available, which include supersymmetric Taub-NUT and Taub-bolt type spacetimes,
as well as black hole solutions. Our simple topological formula also allows us
to write down the action of any solution, provided it exists
Instantons, symmetries and anomalies in five dimensions
All five-dimensional non-abelian gauge theories have a global
symmetry associated with instantonic particles. We describe an obstruction to
coupling to a classical background gauge field that occurs whenever
the theory has a one-form center symmetry. This is a finite-order mixed 't
Hooft anomaly between the two symmetries. We also show that a similar
obstruction takes place in gauge theories with fundamental matter by studying
twisted bundles for the ordinary flavor symmetry. We explore some general
dynamical properties of the candidate phases implied by the anomaly. Finally,
we apply our results to supersymmetric gauge theories in five dimensions and
analyze the symmetry enhancement patterns occurring at their conjectured RG
fixed points
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Boundary conditions in topological AdS<inf>4</inf>/CFT<inf>3</inf>
We revisit the construction in four-dimensional gauged supergravity
of the holographic duals to topologically twisted three-dimensional
field theories. Our focus in this paper is to highlight some
subtleties related to preserving supersymmetry in AdS/CFT, namely the inclusion
of finite counterterms and the necessity of a Legendre transformation to find
the dual to the field theory generating functional. Studying the geometry of
these supergravity solutions, we conclude that the gravitational free energy is
indeed independent from the metric of the boundary, and it vanishes for any
smooth solution
Evidence for a non-supersymmetric 5d CFT from deformations of 5d SU(2) SYM
We study supersymmetry breaking deformations of the 5d fixed
point known as , the UV completion of super-Yang-Mills. The phases
of the non-supersymmetric theory can be characterized by Chern-Simons terms
involving background gauge fields, allowing us to identify a phase
transition at strong coupling. We propose that this may signify the emergence
of a non-trivial, non-supersymmetric CFT in dimensions
Topological AdS/CFT
We define a holographic dual to the Donaldson-Witten topological twist of N = 2 gauge theories on a Riemannian four-manifold. This is described by a class of asymptotically locally hyperbolic solutions to N = 4 gauged supergravity in five dimensions, with the four-manifold as conformal boundary. Under AdS/CFT, minus the logarithm of the partition function of the gauge theory is identified with the holographically renormalized supergravity action. We show that the latter is independent of the metric on the boundary four-manifold, as required for a topological theory. Supersymmetric solutions in the bulk satisfy first order differential equations for a twisted Sp(1) structure, which extends the quaternionic Kahler structure that exists on any Riemannian four-manifold boundary. We comment on applications and extensions, including generalizations to other topological twists
Refined 3d-3d correspondence
We explore aspects of the correspondence between Seifert 3-manifolds and 3d supersymmetric theories with a distinguished abelian flavour symmetry. We give a prescription for computing the squashed three-sphere partition functions of such 3d theories constructed from boundary conditions and interfaces in a 4d theory, mirroring the construction of Seifert manifold invariants via Dehn surgery. This is extended to include links in the Seifert manifold by the insertion of supersymmetric Wilson-'t Hooft loops in the 4d theory. In the presence of a mass parameter for the distinguished flavour symmetry, we recover aspects of refined Chern-Simons theory with complex gauge group, and in particular construct an analytic continuation of the -matrix of refined Chern-Simons theory
Refined 3d-3d correspondence
We explore aspects of the correspondence between Seifert 3-manifolds and 3d
supersymmetric theories with a distinguished abelian flavour
symmetry. We give a prescription for computing the squashed three-sphere
partition functions of such 3d theories constructed from
boundary conditions and interfaces in a 4d theory, mirroring
the construction of Seifert manifold invariants via Dehn surgery. This is
extended to include links in the Seifert manifold by the insertion of
supersymmetric Wilson-'t Hooft loops in the 4d theory. In the
presence of a mass parameter for the distinguished flavour symmetry, we recover
aspects of refined Chern-Simons theory with complex gauge group, and in
particular construct an analytic continuation of the -matrix of refined
Chern-Simons theory