Off-shell supergravity-matter couplings in three dimensions

Abstract:The off-shell version of the c-map is presented, based on a systematic offshell reduction from four to three space-time dimensions for supergravity theories with eight supercharges. In the reduction, the R-symmetry group is enhanced to local [SU(2) × SU(2)]/Z 2 ∼ = SO(4) and the c-map is effected by a parity transformation in the internal space that interchanges the two SU(2) factors. Vector and tensor supermultiplets are each others conjugate under the c-map and both can be dualized in three dimensions to (on-shell) hypermultiplets.As shown in this paper the off-shell formulation indeed leads to a clarification of many of the intricate issues that play a role in the c-map. The results for off-shell Lagrangians quadratic in space-time derivatives are analyzed in detail and compared to the literature. The underlying reasons are identified why not all of the four-dimensional tensor multiplet Lagrangians can be in the image of the c-map. The advantage of the off-shell approach is, that it also enables a systematic analysis of theories with higher-derivative couplings. This is demonstrated for a particular subclass of such theories, which, under certain conditions, are consistent under the c-map. In principle, explicit results for realistic four-dimensional type-II string compactifications can be explored in this way.

Section: N = 4 Conformal Supergravity In Three Dimensionssupporting

confidence: 83%

Section: Jhep01(2016)156mentioning

confidence: 99%

Section: Jhep01(2016)156mentioning

confidence: 99%

See 1 more Smart Citation

The off-shell c-map

Banerjee

Wit

Katmadas

2016

“…The corresponding supergravity theory was recently studied in superspace [19][20][21], as well as in components [3,4,16]. The supergravity background fields that couple to the operators in (1.15) are given by 16 16) 14 Under these conditions the flat-space theory does not admit a Ferrara-Zumino (FZ) supercurrent multiplet [6,18].…”

Section: Supersymmetric Backgrounds In Three Dimensionsmentioning

confidence: 99%

The geometry of supersymmetric partition functions

Closset

Dumitrescu

Festuccia

et al. 2014

167

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.

“…Note that Φ 0 ,Φ 0 obtained from the left tropical multiplet by this way belong to the right multiplet [11,10]. The construction of the action is the same in the N = 3 case.…”

Section: N = 4 In Three Dimensionsmentioning

confidence: 99%

Non-Abelian gauge groups and hypermultiplets in projective superspaces

Arai

Sasaki

2013

We construct off-shell superconformal actions of hypermultiplets coupled with nonAbelian gauge multiplets in three-dimensional N = 3 and N = 4 projective superspaces. We establish the explicit embeddings of the N = 2 vector and adjoint chiral superfields, that constitute the N = 4 gauge multiplets, into the tropical multiplets. We also construct the action in the four-dimensional N = 2 projective superspace.