Triality, periodicity and stability of SO(8) gauged supergravity

Abstract

While electromagnetic duality is a symmetry of many supergravity theories, this is not the case for the N = 8 gauged theory. It was recently shown that this rotation leads to a one-parameter family of SO(8) supergravities. It is an open question what the period of this parameter is. This issue is investigated in the SO(4) invariant sectors of the theory. We classify such critical points and find a novel branch of non-supersymmetric and unstable solutions, whose embedding is related via triality to the two known ones. Secondly, we show that the three branches of solutions lead to a π/4 periodicity of the vacuum structure. The general interrelations between triality and periodicity are discussed. Finally, we comment on the connection to other gauge groups as well as the possibility to achieve (non-)perturbative stability around AdS/Mkw/dS transitions.

On the moduli space of spontaneously broken N = 8 supergravity

“…Moreover, we can see that 47) hence also this model already appeared in Table 3. As shown in [29], [23], these models have 3 de Sitter vacua in the range c ∈ [0, √ 2 − 1[, one already known for c = 0 and two genuinely new. When we reach c = √ 2 − 1 the new vacua disappear, but defining an appropriate limit for c → √ 2 − 1 they become Minkowski vacua of a contracted model.…”

“…This produces inequivalent gaugings in a definite range, to be determined for each gauge group 4 (for SO(8) c models c ∈ [0, √ 2−1], for SO(6,2) c models we expect c ∈ [0, 1]). As noted in [6], [20][21][22][23], [29], [18], varying c also varies the structure of the scalar potential and the number of critical points. For the SO(6,2) c models, the analysis of [26] shows that there is a Minkowski vacuum at c = 1, which disappears for c = 1 (which explains why it was not found in the c = 0 model discussed in [40], [42]).…”

“…This is especially striking in the case of the SO(8) model of [7], which had been thoroughly examined in the past [8][9][10][11][12][13] and whose higherdimensional origin is well understood in terms of a consistent truncation of 11-dimensional supergravity on the seven-sphere [14][15][16][17][18][19]. One of the most intriguing aspects of the new SO (8) c theories is that they exhibit a vacuum structure [6], [20][21][22][23] different from the one of the original SO(8) model. Hence they allow for new ways of breaking supersymmetry.…”

“…The result is a powerful technique, used both in N = 4 [25] as well as in N = 8 supergravity [24], [26]. Not only many new vacua could be easily produced [26], [6], [20][21][22][23], but also simpler mass formulae have been derived, so that the problem of computing the classical spectrum can often be translated into a group-theoretical one [26], [21], [28]. Furthermore, this same technique allowed to produce the first instance of a de Sitter vacuum of maximal supergravity for which slow-roll conditions are satisfied [29].…”

$$ \mathcal{N} $$ = 2 supersymmetric S-folds

“…Unlike for the SO(8) theory, much more is by now known about the dyonically-gauged ISO (7) supergravity that arises from the reduction of massive IIA supergravity on a sixsphere S 6 [15]. In this case the electromagnetic deformation parameter is a discrete (on/off) deformation, namely, it can be set to c = 0 or 1 without loss of generality [16].…”