The superconformal index of the quiver gauge theory dual to type IIB string theory on the product of an arbitrary smooth Sasaki-Einstein manifold with five-dimensional AdS space is calculated both from the gauge theory and gravity viewpoints. We find complete agreement. Along the way, we find that the index on the gravity side can be expressed in terms of the Kohn-Rossi cohomology of the Sasaki-Einstein manifold and that the index of a quiver gauge theory equals the Euler characteristic of the cyclic homology of the Ginzburg dg algebra associated to the quiver.
The superconformal index of the quiver gauge theory dual to type IIB string theory on the product of an arbitrary smooth Sasaki-Einstein manifold with five-dimensional AdS space is calculated both from the gauge theory and gravity viewpoints. We find complete agreement. Along the way, we find that the index on the gravity side can be expressed in terms of the Kohn-Rossi cohomology of the Sasaki-Einstein manifold and that the index of a quiver gauge theory equals the Euler characteristic of the cyclic homology of the Ginzburg dg algebra associated to the quiver.
Abstract:We study super Yang-Mills theories on five-dimensional Sasaki-Einstein manifolds. Using localisation techniques, we find that the contribution from the vector multiplet to the perturbative partition function can be calculated by counting holomorphic functions on the associated Calabi-Yau cone. This observation allows us to use standard techniques developed in the context of quiver gauge theories to obtain explicit results for a number of examples; namely S 5 ,
Abstract:We derive the superconformal index of the world-volume theory on M2-branes probing the cone over an arbitrary Sasaki-Einstein seven-manifold. The index is expressed in terms of the cohomology groups of the cone. We match our supergravity results with known results from gauge theory. Along the way we derive the spectrum of short KaluzaKlein multiplets on generic Sasaki-Einstein seven-manifolds.
We consider N = 2 supersymmetric pure gauge theories on toric Kähler manifolds, with particular emphasis on CP 2 . By choosing a vector generating a U(1) action inside the torus of the manifold, we construct equivariantly twisted theories. Then, using localization, we compute their supersymmetric partition functions. As expected, these receive contributions from a classical, a one-loop, and an instanton term. It turns out that the oneloop term is trivial and that the instanton contributions are localized at the fixed points of the U(1). In fact the full partition function can be re-written in a factorized form with contributions from each of the fixed points. The full significance of this is yet to be understood.
Making use of generalized calibrated geometry and G-structures we put the problem of finding string-duals with smeared backreacting flavor branes in a more mathematical setting. This more formal treatment of the problem allows us to easily smear branes without good coordinate representations, establish constraints on the smearing form and identify a topological central charge in the SUSY algebra. After exhibiting our methods for a series of well known examples, we apply them to the problem of flavoring a supergravity-dual to a d = 2 + 1 dimensional N = 2 super Yang-Mills-like theory. We find new solutions to both the flavored and unflavored systems. Interpretating these turns out to be difficult. * pyjg@swansea.ac.uk † pyjs@swansea.ac.uk
We study the rigid limit of 5d conformal supergravity with minimal supersymmetry on Riemannian manifolds. The necessary and sufficient condition for the existence of a solution is the existence of a conformal Killing vector. Whenever a certain SU(2) curvature becomes abelian the backgrounds define a transversally holomorphic foliation. Subsequently we turn to the question under which circumstances these backgrounds admit a kinetic Yang-Mills term in the action of a vector multiplet. Here we find that the conformal Killing vector has to be Killing. We supplement the discussion with various appendices.
This paper is concerned with an extension of the well known Kaluza-Klein
mechanism. As the standard ansatz for Kaluza-Klein reduction implies the
existence of a gauge potential associated with the KK field strength, it
follows immediately that this field strength satisfies its Bianchi identity.
Hence, the standard KK formalism breaks down in the presence of a violated
Bianchi identity. This occurs for example in the context of D6 sources.
We will investigate and partially solve this problem in the context of the
type IIA/M-theory duality. Our discussion is motivated by the construction of
gauge/string duals with backreacting flavor branes using D6-branes, which
appear in M-theory as KK-monopoles. We are able to derive source-modified
equations of motion for the eleven-dimensional theory, and are subsequently
able to obtain the source-modified type IIA equations by direct dimensional
reduction.Comment: 25 pages plus appendices - As published in JHE
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