An important ingredient in the construction of phenomenologically viable superstring models is the uplifting of Anti-de Sitter supersymmetric critical points in the moduli sector to metastable Minkowski or de Sitter vacua with broken supersymmetry. In all cases described so far, uplifting results in a displacement of the potential minimum away from the critical point and, if the uplifting is large, can lead to the disappearance of the minimum altogether. We propose a variant of F-term uplifting which exactly preserves supersymmetric critical points and shift symmetries at tree level. In spite of a direct coupling, the moduli do not contribute to supersymmetry breaking. We analyse the stability of the critical points in a toy one-modulus sector before and after uplifting, and find a simple stability condition depending solely on the amount of uplifting and not on the details of the uplifting sector. There is a region of parameter space, corresponding to the uplifting of local AdS maxima -or, more importantly, local minima of the Kähler function-where the critical points are stable for any amount of uplifting. On the other hand, uplifting to (non-supersymmetric) Minkowski space is special in that all SUSY critical points, that is, for all possible compactifications, become stable or neutrally stable.

A bubble of nothing is a spacetime instability where a compact dimension collapses. After nucleation, it expands at the speed of light, leaving “nothing” behind. We argue that the topological and dynamical mechanisms which could protect a compactification against decay to nothing seem to be absent in string compactifications once supersymmetry is broken. The topological obstruction lies in a bordism group and, surprisingly, it can disappear even for a SUSY-compatible spin structure. As a proof of principle, we construct an explicit bubble of nothing for a T3 with completely periodic (SUSY-compatible) spin structure in an Einstein dilaton Gauss-Bonnet theory, which arises in the low-energy limit of certain heterotic and type II flux compactifications. Without the topological protection, supersymmetric compactifications are purely stabilized by a Coleman-deLuccia mechanism, which relies on a certain local energy condition. This is violated in our example by the nonsupersymmetric GB term. In the presence of fluxes this energy condition gets modified and its violation might be related to the Weak Gravity Conjecture.We expect that our techniques can be used to construct a plethora of new bubbles of nothing in any setup where the low-energy bordism group vanishes, including type II compactifications on CY3, AdS flux compactifications on 5-manifolds, and M-theory on 7-manifolds. This lends further evidence to the conjecture that any non-supersymmetric vacuum of quantum gravity is ultimately unstable.

Abstract:We consider flux compactifications of type IIB string theory and F-theory in which the respective superpotentials at large complex structure are dominated by cubic or quartic terms in the complex structure moduli. In this limit, the low-energy effective theory exhibits universal properties that are insensitive to the details of the compactification manifold or the flux configuration. Focussing on the complex structure and axio-dilaton sector, we show that there are no vacua in this region and the spectrum of the Hessian matrix is highly peaked and consists only of three distinct eigenvalues (0, 2m 2 3/2 and 8m 2 3/2 ), independently of the number of moduli. We briefly comment on how the inclusion of Kähler moduli affect these findings. Our results generalise those of Brodie & Marsh [1], in which these universal properties were found in a subspace of the large complex structure limit of type IIB compactifications.

We study in detail the stability properties of the simplest F -term uplifting mechanism consistent with the integration of heavy moduli. This way of uplifting vacua guarantees that the interaction of the uplifting sector with the moduli sector is consistent with integrating out the heavy fields in a supersymmetric way. The interactions between light and heavy fields are characterized in terms of the Kähler invariant function, G = K + log |W | 2 , which is required to be separable in the two sectors. We generalize earlier results that when the heavy fields are stabilized at a minimum of the Kähler function G before the uplifting (corresponding to stable AdS maxima of the potential), they remain in a perturbatively stable configuration for arbitrarily high values of the cosmological constant (or the Hubble parameter during inflation). By contrast, supersymmetric minima and saddle points of the scalar potential are always destabilized for sufficiently large amount of uplifting. We prove that these results remain unchanged after including gauge couplings in the model. We also show that in more general scenarios, where the Kähler function is not separable in the light and heavy sectors, the minima of the Kähler function still have better stability properties at large uplifting than other types of critical points.

We consider the conditions for integrating out heavy chiral fields and moduli in N = 1 supergravity, subject to two explicit requirements. First, the expectation values of the heavy fields should be unaffected by low energy phenomena. Second, the low energy effective action should be described by N = 1 supergravity. This leads to a working definition of decoupling in N = 1 supergravity that is different from the usual condition of gravitational strength couplings between sectors, and that is the relevant one for inflation with moduli stabilization, where some light fields (the inflaton) can have long excursions in field space. It is also important for finding de Sitter vacua in flux compactifications such as LARGE volume and KKLT scenarios, since failure of the decoupling condition invalidates the implicit assumption that the stabilization and uplifting potentials have a low energy supergravity description.We derive a sufficient condition for supersymmetric decoupling, namely, that the Kähler invariant function G = K + log |W | 2 is of the form G = L(light, H(heavy)) with H and L arbitrary functions, which includes the particular case G = L(light) + H(heavy). The consistency condition does not hold in general for the ansatz K = K(light) + K(heavy), W = W (light) + W (heavy) and we discuss under what circumstances it does hold.The viability of theories based on extra dimensions, in particular string theory, relies on being able to stabilize and integrate out the fields (moduli) that describe the shapes and sizes of those extra dimensions, for which so far there is no observational evidence. In flux compactifications [1] some moduli are stabilized at a high energy scale and decouple from the low energy theory. From that moment on we never see them in the effective low energy description.Unlike in global supersymmetry, complete decoupling is of course impossible in supergravity -even in principlebecause gravity couples to all fields; so at low energies one is usually satisfied with gravitational strength couplings between the heavy, stabilized, fields and the low energy fields. However such interaction terms are of or-, where E is the energy scale and M P ≈ 2.4 × 10 18 GeV the reduced Planck mass. Even if they are strongly suppressed at low energy and in particle accelerators, these couplings become sizeable at the energy scales relevant to the early Universe, and one must look for a more robust definition of decoupling that can be extrapolated over a wide range of energy scales. The purpose of this note is to provide such a definition, and a simple test of whether it holds in specific models.There are at least two situations in which the details of decoupling are important. One is supersymmetry breaking, which will affect the heavy fields in a way that is not accounted for in the low energy effective action. Uplifting in KKLT scenarios [2] is a prime example. The second is inflation with moduli stabilization, because the inflaton, which is a low energy field in this language, can have its expectation value vary ov...