Stable Ads Flux Vacua Must Endure Supersymmetric: A Conjecture

Famous physicists Hiroši Ooguri as well as Cumrun Vafa proposed a novel branch of the Swampland computer programme inwards their novel paper

Non-supersymmetric AdS as well as the Swampland

In 2005, Cumrun Vafa coined the term swampland to push clitoris would-be theories or their low-energy effective plain theory limits that facial expression consistent according to the rules of effective quantum plain theory but that are banned according to the to a greater extent than stringent rules of string theory or quantum gravity (which are ultimately equivalent concepts) i.e. that accept no realization within string/M-theory.

The swampland (TRF) is the "larger" but messier realm surrounding the stringy landscape. The swampland shouldn't hold upwards confused amongst the related but inequivalent technical notion of the role of the Internet as well as media that is critical towards string theory. It's non called a "swampland" but rather a "cesspool" as well as the technical term for the individuals inwards the cesspool is "scumbags". The largest as well as stinkiest ii scumbags are known every bit "Šmoits" but I don't desire to overwhelm this weblog postal service amongst the review of the criterion terminology.

The extra constraints imposed past times string/M-theory may hold upwards interpreted every bit "general predictions of string/M-theory". They're unremarkably qualitative. Our weak gravity conjecture is the most intensely studied illustration of such extra constraints. It says that in that place accept to be particles low-cal plenty thence that the repulsive electrical forcefulness betwixt them trumps the gravitational attraction. In this sense, gravity is the weakest forcefulness as well as it has to be.




This declaration may hold upwards justified past times diverse arguments using many viewpoints as well as it to a greater extent than oft than non seems nontrivial yet at to the lowest degree much to a greater extent than right than y'all would await if it were a random guess. However, nosotros couldn't settle – as well as the researchers silent haven't agreed – on many of the details. Do the low-cal charged particle accept to be for every type of an electrical force? Every direction inwards the accuse space? Every site inwards the lattice of charges allowed past times the Dirac quantization rules as well as thence on? Should the price inwards the inequality hold upwards modified inwards roughly way?

And isn't in that place a deeper insight or construction from which the regulation may hold upwards derived – much similar Heisenberg's dubiety relation (inequality) may hold upwards derived from the nonzero commutators?




In the novel paper, Hiroši as well as Cumrun assume a somewhat stronger version of the weak gravity conjecture. It sure enough has to apply to every sort of an electric-like force, including forces betwixt branes. If I sympathize well, they basically enjoin that the weak gravity conjecture should imply the existence of branes of depression plenty tension, non only point-like charged particles, for every sort of a \(p\)-form plain i.e. a generalization of electromagnetism amongst many indices.

Now, the existence of these charged branes has consequences for the flux vacua.

The flux vacua deport roughly nonzero values of \(\int_C F_p\), the integral of a plain strength \(p\)-form over roughly \(p\)-cycle inwards the compactification manifold. These fluxes could hold upwards used every bit only roughly sourceless, electromagnetic-style fields. However, the weak gravity conjecture says that the charged sources genuinely accept to be as well as their tension has to hold upwards depression enough. When it's true, it's beingness shown that such branes may nucleate within the anti de Sitter space, larn to the boundary inwards a finite time, as well as trim down the flux past times a unit.

The whole vacuum spontaneously changes inwards this way. So the master copy vacuum nosotros started amongst was unstable. The authors conclude that every anti de Sitter vacuum supported past times fluxes has to hold upwards either unstable or supersymmetric. Supersymmetric vacua larn an "exception" because the total attractive gravitational forcefulness precisely cancels against the repulsive generalized electromagnetic forcefulness – because of the well-known BPS relations. The BPS status is cypher else than the illustration inwards which the defining inequality of the weak gravity conjecture is saturated – gravity is every bit strong every bit the non-gravitational force. Consequently, the spontaneous nucleation of the brane cannot occur amongst a finite probability and/or the brane isn't driven to the AdS boundary at a finite time.

It's too my agreement that all stable AdS flux vacua that accept been establish are supersymmetric. Well, my preferred illustration of a non-supersymmetric AdS vacuum amongst a CFT dual would hold upwards Witten's pure AdS₃ gravity whose CFT dual carries the monster grouping symmetry (it exclusively exists for the minimum radius thence the curved shape is "Planckian" as well as y'all powerfulness enjoin that it's non a "full-fledged" illustration of a gravitational theory amongst a nearly apartment space). Either the depression spacetime dimension or the absence of the appropriate "flux" is in all probability what allows an exception for this case. I am non sure nigh the precise logic here.

You could enjoin that fifty-fifty if it is true, the derived restriction doesn't accept "practical" consequences because vacua may hold upwards unstable but real long-lived. They debate that piece the lifetime could hold upwards long for a CFT, the near-horizon dual geometry inwards the volume sees the instability every bit a much stronger one. So the restriction is harsh as well as real.

If these statements are right – as well as ideally derivable inwards a to a greater extent than rigorous agency – thence y'all powerfulness translate the outcome every bit a prediction of string theory. We accept observed the globe to hold upwards rather stable as well as non-supersymmetric – thence it cannot hold upwards AdS. We may usage the stability to predict that the cosmological constant is non-negative. It's nigh i predicted flake of data but it's a prediction nevertheless. Needless to say, the implications for our agreement of the inner construction of string/M-theory as well as its configuration infinite could hold upwards to a greater extent than far-reaching.

The weather condition facial expression conceptually different. Whether the gravitational forcefulness is stonger than roughly other i seems to hold upwards only a "boring technicality". On the other hand, this technicality may imply, similar inwards this case, that a whole degree of candidate vacua – non-supersymmetric stable AdS flux vacua – is genuinely non-existent. So fifty-fifty previously overlooked technicalities such every bit the weak gravity conjecture may accept the potential to solve the vacuum pick work as well as other seemingly insurmountable hurdles.