Spontaneous $$ \mathcal{N} $$ = 2 → $$ \mathcal{N} $$ = 1 supersymmetry breaking in supergravity and type II string theory

Abstract

Using the embedding tensor formalism we give the general conditions for the existence of N = 1 vacua in spontaneously broken N = 2 supergravities. Our results confirm the necessity of having both electrically and magnetically charged multiplets in the spectrum, but also show that no further constraints on the special Kähler geometry of the vector multiplets arise. The quaternionic field space of the hypermultiplets must have two commuting isometries, and as an example we discuss the special quaternionic-Kähler geometries which appear in the low-energy limit of type II string theories. For these cases we find the general solution for stable Minkowski and AdS N = 1 vacua, and determine the charges in terms of the holomorphic prepotentials. We find that the string theory realisation of the N = 1 Minkowski vacua requires the presence of non-geometric fluxes, whereas they are not needed for the AdS vacua. We also argue that our results should hold in the presence of spacetime and worldsheet instanton corrections.

Holographic RG flows for four-dimensional $$ \mathcal{N}=2 $$ SCFTs

“…This "bottom-up" approach to studying general properties of SCFTs with holographic duals by employing gauged supergravity has recently received some attention in the context of understanding the space of exactly marginal couplings of SCFTs in various dimensions, see [3][4][5][6][7][8][9][10][11][12] and references thereof. While these results present interesting holographic predictions for strongly interacting SCFTs it should be noted that some of the supergravity results can also be shown more generally, without a reference to holography, using purely algebraic techniques [13].…”

“…Here we provide their complete characterization (when ξ M = 0), which to the best of our knowledge has not appeared in the literature before. 4 Starting from the gravitino shift matrix P defined in (2.15), we introduce the superpotential W = 2 P mn P mn . (3.27)…”

Observations on BI from N = 2 $$ \mathcal{N}=2 $$ supergravity and the general Ward identity

“…It was indeed shown in [15] that partial supersymmetry breaking can be achieved in any symplectic frame (and in particular in one in which the prepotential does exist) using an embedding tensor [16][17][18] with both electric and magnetic components. Consistency of such gaugings requires the introduction of antisymmetric tensor fields dual to scalars [10][11][12][13][14].…”

“…In the latter case, the gauging should involve abelian generators in the universal Heisenberg algebra of isometries of these manifolds [15,[49][50][51].…”

Enhanced supersymmetry from vanishing Euler number

“…16 For an N = 4 Minkowski vacuum, we need both K and the J a to be closed, and we find that the manifold is K3 × T 2 . If we want to have at least an N = 2 supersymmetric vacuum, the discussion is rather similar to N = 2 → N = 1 supersymmetry breaking as discussed in [31]. A requirement for an N = 2 Minkowski vacuum therefore is that A ij 1 , given in (B.16), should be of rank one.…”