Three-dimensional $ \mathcal{N} = 2 $ (AdS) supergravity and associated supercurrents

172

415

We consider supersymmetric field theories on compact manifolds M and obtain constraints on the parameter dependence of their partition functions Z M . Our primary focus is the dependence of Z M on the geometry of M, as well as background gauge fields that couple to continuous flavor symmetries. For N = 1 theories with a U(1) R symmetry in four dimensions, M must be a complex manifold with a Hermitian metric. We find that Z M is independent of the metric and depends holomorphically on the complex structure moduli. Background gauge fields define holomorphic vector bundles over M and Z M is a holomorphic function of the corresponding bundle moduli. We also carry out a parallel analysis for three-dimensional N = 2 theories with a U(1) R symmetry, where the necessary geometric structure on M is a transversely holomorphic foliation (THF) with a transversely Hermitian metric. Again, we find that Z M is independent of the metric and depends holomorphically on the moduli of the THF. We discuss several applications, including manifolds diffeomorphic to S 3 ×S 1 or S 2 ×S 1 , which are related to supersymmetric indices, and manifolds diffeomorphic to S 3 (squashed spheres). In examples where Z M has been calculated explicitly, our results explain many of its observed properties.

Section: Supersymmetric Backgrounds In Three Dimensionsmentioning

confidence: 99%

The geometry of supersymmetric partition functions

Closset

Dumitrescu

Festuccia

et al. 2014

172

415

“…The off-shell actions for N -extended supergravity theories in three dimensions were given in [13] for N = 1, [14,15] for N = 2, and [14] for the cases N = 3, 4. The off-shell actions for N -extended conformal supergravity were given in [5] for N = 1, [16] for N = 2, and [17] for N = 3, 4.…”

Section: Jhep03(2017)109mentioning

confidence: 99%

“…In both cases the super-Cotton tensor is constant, 15) while the constraints on the remaining torsion components differ. For the on-shell self-dual vector multiplet one finds the following consistency conditions…”

Section: Analysing the Equations Of Motionmentioning

confidence: 99%

Minimal N = 4 $$ \mathcal{N}=4 $$ topologically massive supergravity

Kuzenko¹,

Novak²,

Sachs³

2017

Self Cite

Using the superconformal framework, we construct a new off-shell model for N = 4 topologically massive supergravity which is minimal in the sense that it makes use of a single compensating vector multiplet and involves no free parameter. As such, it provides a counterexample to the common lore that two compensating multiplets are required within the conformal approach to supergravity with eight supercharges in diverse dimensions. This theory is an off-shell N = 4 supersymmetric extension of chiral gravity. All of its solutions correspond to non-conformally flat superspaces. Its maximally supersymmetric solutions include the so-called critical (4,0) anti-de Sitter superspace introduced in [25], and well as warped critical (4,0) anti-de Sitter superspaces. We also propose a dual formulation for the theory in which the vector multiplet is replaced with an off-shell hypermultiplet. Upon elimination of the auxiliary fields belonging to the hypermultiplet and imposing certain gauge conditions, the dual action reduces to the one introduced in [20].

“…The conformal N = 2 supergravity, and the two-derivative invariants were considered in [8][9][10][11]. Off-shell matter-coupled suprgravity theories were investigated in the superspace framework in [12][13][14][15]. The on-shell construction and the matter couplings of the three dimensional N = 2 supergravity were studied in [16][17][18].…”

Section: Jhep02(2015)125mentioning

confidence: 99%

“…The Poincaré supergravity and its cosmological extension has already been given in [12,13], and it is also referred to as Type II minimal supergravity. In this section, we first introduce our gauge fixing choices, and construct the Poincaré supergravity and the supersymmetric cosmological constant based on the conformal vector multiplet actions discussed in section 2.…”

Section: N = (2 0) Supergravity Modelsmentioning

confidence: 99%

Massive N $$ \mathcal{N} $$ = 2 supergravity in three dimensions

Alkaç

Basanisi

Bergshoeff

et al. 2015

There exists two distinct off-shell N = 2 supergravities in three dimensions. They are also referred to as N = (1, 1) and N = (2, 0) supergravities, and they arise from the coupling of the Weyl multiplet to a compensating scalar or vector multiplet, respectively, followed by fixing of conformal symmetries. The N = (p, q) terminology refers to the underlying anti-de Sitter superalgebras OSp(2, p)⊕OSp(2, q) with R-symmetry group SO(p) × SO(q). We construct off-shell invariants of these theories up to fourth order in derivatives. As an application of these results, we determine the special combinations of the N = (1, 1) invariants that admit anti-de Sitter vacuum solution about which there is a ghost-free massive spin-2 multiplet of propagating modes. We also show that the N = (2, 0) invariants do not allow such possibility.