Some remarks on the dS conjecture, fluxes and K-theory in IIB toroidal compactifications

Abstract

In this note we present a description on the implications on the refined dS Swampland conjecture by considering non-BPS states in type IIB toroidal compactifications . We concentrate on a model T-dual to type I theory for which the total K-theory charge of the non-BPS states vanishes on the six-dimensional torus modded out by an orientifold threeplane. Particularly we consider the presence of non-BPS five branes wrapping internal twocycles. We comment on the instability of this state by the presence of tachyon modes and the apparent violation of the refined dS conjecture at the minimum of the tachyon potential. The conjecture seems to be valid once we take into account that discrete K-theory charge vanishes. We also describe some issues related to the presence of NS-NS fluxes required to stabilize some moduli since they trigger the appearance of Freed-Witten anomalies. Cancellation of these anomalies implies a topological transformation between non-BPS states and fluxes with the same discrete K-theory charge. After the transition we observe that the dS vacuum constructed from the presence of non-BPS states is also unstable.

Open-closed correspondence of K-theory and cobordism

“…for the number of NS5-branes on the heterotic side. 13 The apparent controversy of this example demonstrates that starting with incomplete cobordism structures has its limitations, but still has the potential to uncover new aspects of string theory. (5.24)…”

“…12 Actually, for n odd, Fn is not Spin and one has an additional non-trivial line bundle on the Spin cmanifold. 13 Coming back to the discussion around eq. (5.22), for B = dP9 we obtain nT = 9 which is indeed the result for the Ωσ orientifold of [36].…”

“…An interesting question in this context is whether the K-theory charge need to vanish on a compact space. 2 In [11], a brane probe argument was given that suggested it, while in [12] the non-cancellation of the K-theory charge was related to a violation of the de Sitter swampland conjecture (see also [13]). 3 If the K-theory charge is a global charge, it should better vanish in QG.…”

Metastable vacua from torsion and machine learning

“…According to the Swampland conjectures, such an AdS vacuum must be at most metastable. In our case, the source for instabilities could come from two places: first, from our assumption of not considering torsional components of 3-form fluxes, which usually drives some topological transitions as pointed out in [11]. Second, since the contribution from F 5 is based on the existence of torsional cycles, it is possible that the total discrete charge must vanish following the recent proposal about having zero global charges in Quantum Gravity and its relation to Ktheory by cobordisms as proposed in [13].…”

“…Even more restrictive, the AdS conjecture establishes that the scale of the lightest moduli is not parametrically separated from the AdS scale, and thus any attempt to uplift an AdS to a dS vacuum shall result in their destabilization. 1 Recently it has been argued that the use of non-BPS states, classified by K-theory, shall be an interesting corner to evade these restrictions [10,11], unless the total K-theory charge must cancel as pointed out in [12] and related to the cobordism conjecture in [13]. 2 The minimal ingredients necessary to construct a dS vacua have been studied extensively in the last years [14,15,35].…”