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25
Supersymmetry on curved spaces and superconformal anomalies, JHEP 1310
, 2013
"... We study the consequences of unbroken rigid supersymmetry of fourdimensional field theories placed on curved manifolds. We show that in Lorentzian signature the background vector field coupling to the Rcurrent is determined by the Weyl tensor of the background metric. In Euclidean signature, the ..."
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We study the consequences of unbroken rigid supersymmetry of fourdimensional field theories placed on curved manifolds. We show that in Lorentzian signature the background vector field coupling to the Rcurrent is determined by the Weyl tensor of the background metric. In Euclidean signature, the same holds if two supercharges of opposite Rcharge are preserved, otherwise the (anti)selfdual part of the vector fieldstrength is fixed by the Weyl tensor. As a result of this relation, the trace and Rcurrent anomalies of superconformal field theories simplify, with the trace anomaly becoming purely topological. In particular, in Lorentzian signature, or in the presence of two Euclidean supercharges of opposite Rcharge, supersymmetry of the background implies that the term proportional to the central charge c vanishes, both in the trace and Rcurrent anomalies. This is equivalent to the vanishing of a superspace Weyl invariant. We comment on the implications of our results for holography. ar
Nonlinear sigma models with AdS supersymmetry in three dimensions
, 2012
"... In threedimensional antide Sitter (AdS) space, there exist several realizations of Nextended supersymmetry, which are traditionally labelled by two nonnegative integers p ≥ q such that p + q = N. Different choices of p and q, with N fixed, prove to lead to different restrictions on the target sp ..."
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Cited by 8 (6 self)
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In threedimensional antide Sitter (AdS) space, there exist several realizations of Nextended supersymmetry, which are traditionally labelled by two nonnegative integers p ≥ q such that p + q = N. Different choices of p and q, with N fixed, prove to lead to different restrictions on the target space geometry of supersymmetric nonlinear σmodels. We classify all possible types of hyperkähler target spaces for the cases N = 3 and N = 4 by making use of two different realizations for the most general (p, q) supersymmetric σmodels: (i) offshell formulations in terms of N = 3 and N = 4 projective supermultiplets; and (ii) onshell formulations in terms of covariantly chiral scalar superfields in (2,0) AdS superspace. Depending on the type of N = 3, 4 AdS supersymmetry, nonlinear σmodels can support one of the following target space geometries: (i) hyperkähler cones; (ii) noncompact hyperkähler manifolds with a U(1) isometry group which acts nontrivially on the twosphere of complex structures; (iii) arbitrary hyperkähler manifolds including compact ones. The option (iii) is realized only in the case of critical (4,0) AdS supersymmetry. As an application of the (4,0) AdS techniques developed, we also construct the most general nonlinear σmodel in Minkowski space with a noncentrally extended N = 4 Poincare ́ supersymmetry. Its target space is a hyperkähler cone (which is characteristic of N = 4 superconformal σmodels), but the σmodel is massive. The Lagrangian includes a positive potential constructed in terms of the homothetic conformal Killing vector the target space is endowed with. This mechanism of mass generation differs from the standard one which corresponds to a σmodel with the ordinary N = 4 Poincare ́ supersymmetry and which makes use of a triholomorphic Killing vector. ar
Rigid supersymmetric backgrounds of minimal offshell supergravity
 JHEP
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Symmetries of curved superspace
 JHEP
, 2013
"... The formalism to determine (conformal) isometries of a given curved superspace was elaborated almost two decades ago in the context of the old minimal formulation for N = 1 supergravity in four dimensions (4D). This formalism is universal, for it may readily be generalized to supersymmetric backgro ..."
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The formalism to determine (conformal) isometries of a given curved superspace was elaborated almost two decades ago in the context of the old minimal formulation for N = 1 supergravity in four dimensions (4D). This formalism is universal, for it may readily be generalized to supersymmetric backgrounds associated with any supergravity theory formulated in superspace. In particular, it has already been used to construct rigid supersymmetric field theories in 5D N = 1, 4D N = 2 and 3D (p, q) antide Sitter superspaces. In the last two years, there have appeared a number of publications devoted to the construction of supersymmetric backgrounds in offshell 4D N = 1 supergravity theories using component field considerations. Here we demonstrate how to read off the key results of these recent publications from the more general superspace approach developed in the 1990s. We also present a universal superspace setting to construct supersymmetric backgrounds, which is applicable to any of the known offshell formulations for N = 1 supergravity. This approach is based on the realizations of the new minimal and nonminimal supergravity theories as superWeyl invariant couplings of the old minimal supergravity to certain conformal compensators. ar
Rigid supersymmetry on 5dimensional riemannian manifolds and contact geometry
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Holomorphic Blocks in Three Dimensions
, 2013
"... We decompose sphere partition functions and indices of threedimensional N = 2 gauge theories into a sum of products involving a universal set of “holomorphic blocks”. The blocks count BPS states and are in onetoone correspondence with the theory’s massive vacua. We also propose a new, effective t ..."
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Cited by 1 (0 self)
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We decompose sphere partition functions and indices of threedimensional N = 2 gauge theories into a sum of products involving a universal set of “holomorphic blocks”. The blocks count BPS states and are in onetoone correspondence with the theory’s massive vacua. We also propose a new, effective technique for calculating the holomorphic blocks, inspired by a reduction to supersymmetric quantum mechanics. The blocks turn out to possess a wealth of surprising properties, such as a Stokes phenomenon that integrates nicely with actions of threedimensional mirror symmetry. The blocks also have interesting dual interpretations. For theories arising from the compactification of the sixdimensional (2, 0) theory on a threemanifold M, the blocks belong to a basis of wavefunctions in analytically continued ChernSimons theory on M. For theories engineered on branes in CalabiYau geometries, the blocks offer a nonperturbative perspective on open topological string partition functions.
de Sitter supersymmetry revisited
, 2014
"... Abstract: We present the basic N = 1 superconformal field theories in fourdimensional de Sitter spacetime, namely the nonabelian super YangMills theory and the chiral multiplet theory with gauge interactions or cubic superpotential. These theories have eight supercharges and are invariant unde ..."
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Abstract: We present the basic N = 1 superconformal field theories in fourdimensional de Sitter spacetime, namely the nonabelian super YangMills theory and the chiral multiplet theory with gauge interactions or cubic superpotential. These theories have eight supercharges and are invariant under the full SO(4, 2) group of conformal symmetries, which includes the de Sitter isometry group SO(4, 1) as a subgroup. The theories are ghostfree and the anticommutator α{Qα, Qα†} is positive. SUSY Ward identities uniquely select the BunchDavies vacuum state. This vacuum state is invariant under superconformal transformations, despite the fact that de Sitter space has nonzero Hawking temperature. TheN = 1 theories are classically invariant under the SU(2, 21) superconformal group, but this symmetry is broken by radiative corrections. However, no such difficulty is expected in the N = 4 theory, which is presented in appendix B.