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Moduli spaces of ChernSimons quiver gauge theories
"... We analyse the classical moduli spaces of supersymmetric vacua of 3d N = 2 ChernSimons 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 ..."
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Cited by 85 (4 self)
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We analyse the classical moduli spaces of supersymmetric vacua of 3d N = 2 ChernSimons 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 ChernSimons levels. In particular, starting with a 4d quiver theory dual to a 3fold singularity, for certain general choices of ChernSimons levels this branch of the moduli space of the corresponding 3d theory is a 4fold singularity. Our results lead to a simple general method, using existing 4d techniques, for constructing candidate 3d N = 2 superconformal ChernSimons quivers with AdS4 gravity duals. As simple, but nontrivial, examples, we identify a family of ChernSimons quiver gauge theories which are candidate AdS4/CFT3 duals to an infinite class of toric SasakiEinstein sevenmanifolds with explicit metrics.
Baryonic branches and resolutions of Ricciflat Kähler cones
, 2007
"... We study deformations of N = 1 superconformal field theories that are AdS/CFT dual to Type IIB string theory on SasakiEinstein manifolds, characterised by nonzero vacuum expectation values for certain baryonic operators. Generally, such baryonic branches are constructed from (partially) resolved, ..."
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Cited by 22 (7 self)
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We study deformations of N = 1 superconformal field theories that are AdS/CFT dual to Type IIB string theory on SasakiEinstein manifolds, characterised by nonzero vacuum expectation values for certain baryonic operators. Generally, such baryonic branches are constructed from (partially) resolved, asymptotically conical Ricciflat Kähler manifolds, together with a choice of point where the stack of D3branes is placed. The complete solution then describes a renormalisation group flow between two AdS fixed points. We also discuss the use of probe Euclidean D3branes 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.
Seiberg duality for ChernSimons quivers and Dbrane mutations
 JHEP 1203 (2012) 056 [arXiv:1201.2432 [hepth
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Holographic flows in nonAbelian Tdual geometries.
 Journal of High Energy Physics,
, 2015
"... Abstract: We use nonAbelian Tduality to construct new N = 1 solutions of type IIA supergravity (and their Mtheory lifts) that interpolate between AdS 5 geometries. We initiate a study of the holographic interpretation of these backgrounds as RG flows between conformal fixed points. Along the way ..."
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Cited by 3 (3 self)
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Abstract: We use nonAbelian Tduality to construct new N = 1 solutions of type IIA supergravity (and their Mtheory lifts) that interpolate between AdS 5 geometries. We initiate a study of the holographic interpretation of these backgrounds as RG flows between conformal fixed points. Along the way we give an elegant formulation of nonAbelian Tduality when acting on a wide class of backgrounds, including those corresponding to such flows, in terms of their SU(2) structure.
Brane Tilings and NonCommutative Geometry
 JHEP
, 2011
"... We derive the quiver gauge theory on the worldvolume of D3branes transverse to an La,b,c singularity by computing the endomorphism algebra of a tilting object first constructed by Van den Bergh. The quiver gauge theory can be concisely specified by an embedding of a graph into a facecentered cu ..."
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Cited by 3 (1 self)
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We derive the quiver gauge theory on the worldvolume of D3branes transverse to an La,b,c singularity by computing the endomorphism algebra of a tilting object first constructed by Van den Bergh. The quiver gauge theory can be concisely specified by an embedding of a graph into a facecentered cubic lattice. In this description, planar Seiberg dualities of the gauge theory act by changing the graph embedding. We use this description of Seiberg duality to show these quiver gauge theories possess periodic Seiberg dualities whose existence were expected from the AdS/CFT correspondence.
RICCIFLAT KÄHLER METRICS ON CREPANT RESOLUTIONS OF Kähler Cones
, 2008
"... We prove that a crepant resolution π: Y → X of a Ricciflat Kähler cone X admits a complete Ricciflat Kähler metric asymptotic to the cone metric in every Kähler class in H2 c (Y, R). A Kähler cone (X, ¯g) is a metric cone over a Sasaki manifold (S, g), i.e. X = C(S): = S × R>0 with ¯g = dr2 +r ..."
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We prove that a crepant resolution π: Y → X of a Ricciflat Kähler cone X admits a complete Ricciflat Kähler metric asymptotic to the cone metric in every Kähler class in H2 c (Y, R). A Kähler cone (X, ¯g) is a metric cone over a Sasaki manifold (S, g), i.e. X = C(S): = S × R>0 with ¯g = dr2 +r2g, and (X, ¯g) is Ricciflat precisely when (S, g) Einstein of positive scalar curvature. This result contains as a subset the existence of ALE Ricciflat Kähler metrics on crepant resolutions π: Y → X = Cn /Γ, with Γ ⊂ SL(n, C), due to P. Kronheimer (n = 2) and D. Joyce (n> 2). We then consider the case when X = C(S) is toric. It is a result of A. Futaki, H. Ono, and G. Wang that any Gorenstein toric Kähler cone admits a Ricciflat Kähler cone metric. It follows that if a toric Kähler cone X = C(S) admits a crepant resolution π: Y → X, then Y admits a T ninvariant Ricciflat Kähler metric asymptotic to the cone metric (X, ¯g) in every Kähler class in H2 c(Y, R). A crepant resolution, in this context, is a simplicial fan refining the convex polyhedral cone defining X. We then list some examples which are easy to construct using toric geometry.
Invariants of Toric Seiberg Duality
 Int. J. Mod. Phys. A
"... Threebranes at a given toric Calabi–Yau singularity lead to different phases of the conformal field theory related by toric (Seiberg) duality. Using the dimer model/brane tiling description in terms of bipartite graphs on a torus, we find a new invariant under Seiberg duality, namely the Klein ji ..."
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Threebranes at a given toric Calabi–Yau singularity lead to different phases of the conformal field theory related by toric (Seiberg) duality. Using the dimer model/brane tiling description in terms of bipartite graphs on a torus, we find a new invariant under Seiberg duality, namely the Klein jinvariant of the complex structure parameter in the distinguished isoradial embedding of the dimer, determined by the physical Rcharges. Additional number theoretic invariants are described in terms of the algebraic number field of the Rcharges. We also give a new compact description of the amaximization procedure by introducing a generalized incidence matrix.
Un)Higgsing the M2brane
 JHEP
, 2010
"... All intext references underlined in blue are linked to publications on ResearchGate, letting you access and read them immediately. ..."
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Cited by 1 (0 self)
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All intext references underlined in blue are linked to publications on ResearchGate, letting you access and read them immediately.