I am rather happy most the next novel hep-th preprint that adds 21 pages of somewhat nontrivial thoughts to some heuristic arguments that I e'er liked to spread. Just to hold upward sure, Harvard's Matt Reece released his paper
Photon Masses inward the Landscape in addition to the SwamplandWhat's going on? Quantum plain theory courses ordinarily get-go amongst scalar fields in addition to the Klein-Gordon Lagrangian. At some moment, people desire to acquire most some empirically vital quantum field, the electromagnetic field, whose Lagrangian is\[
{\mathcal L}_\gamma = -\frac fourteen F_{\mu\nu} F^{\mu\nu}.
\] The activity is invariant nether the \(U(1)\) approximate invariance which is why 3+1 polarizations of the \(A_\mu\) plain are reduced to the \((D-2)\) i.e. 2 transverse physical polarizations of the spin-1 photon. Are at that spot as good massive spin-one bosons?
Yes, at that spot are, e.g. W-bosons in addition to Z-bosons that were discovered at CERN to a greater extent than than xxx years ago. The improver of masses naively corresponds to a uncomplicated majority term\[
{\mathcal L}_{\rm mass} = \frac {m^2}{2} A_\mu A^\mu.
\] H5N1 work is that this term isn't gauge-invariant. So the theory must hold upward defined without the approximate invariance in addition to nosotros can't consistently trim back the 3+1 polarizations (including one, time-like polarization that has the incorrect sign of the norm thence it would atomic number 82 to negative probabilities) to 3 (for a massless photon, 2) polarizations.
However, the Standard Model allows massive spin-1 bosons past times the Higgs mechanism. The key Lagrangian genuinely is gauge-invariant in addition to the gauge-invariance-violating majority term higher upward isn't included directly. Instead, it is generated from the Higgs field's vacuum expectation value \(\langle h\rangle = v\) through the interactions of the approximate plain \(W_\mu\) or \(Z_\mu\) amongst the Higgs plain that is included inward the Higgs boson's kinetic term \(\partial_\mu h \cdot\partial^\mu h\) in 1 lawsuit the partial derivatives are replaced amongst the covariant derivatives. These covariant derivatives \(D_\mu=\partial_\mu - i g A_\mu\) are non alone allowed but needed to create gauge-invariant kinetic terms
So the W-bosons in addition to Z-bosons acquire their masses via the interaction amongst the Higgs boson (that's as good truthful for the fermions – leptons in addition to quarks). This is the pretty means to generate masses of spin-1 bosons. It is exploited past times the Standard Model in addition to the Higgs machinery is the final big clear regain of experimental particle physicists. So massive approximate bosons automatically signal to the Higgs mechanism.
But thence there's the "ugly" means – in addition to I've e'er considered it an ugly means – to brand spin-1 bosons massive, the Stückelberg mechanism. The majority term for the photons is rewritten as\[
{\mathcal L}_{\rm mass} = \frac 12 f_{\theta}^2 (\partial_\mu \theta - eA_\mu)^2.
\] We added a novel scalar plain \(\theta\) in addition to preserved the approximate invariance \(A_\mu\to A_\mu +(1/e)\partial_\mu \alpha\) but the novel scalar plain must as good transform nether it, \(\theta\to \theta+\alpha\). Because nosotros receive got the same "amount" of approximate invariance as nosotros receive got inward the massless photons, but at that spot is 1 scalar plain added, nosotros cease upward amongst 3 physical polarizations of the massive particle instead of the massless photon's 2 polarizations. They're the ordinary 3 spatial or transverse polarizations of a massless vector particle, \(x,y,z\).
One may gauge-fix the Stückelberg activity past times setting \(\theta=0\) which reduces the arrangement to the Proca activity for the "regular" massive spin-1 boson. But the payoff of the Stückelberg shape is that you lot know how to write downward the field's interactions amongst others inward a gauge-invariant way.
The majority of the (Swiss) Ernst Stückelberg's boson is \(m_A = ef_\theta\). You may mail it goose egg either past times sending the approximate coupling \(e\to 0\) or sending \(f_\theta\to 0\) or some combination of both. Note that \(e\to 0\) is something that the weak gravity conjecture labels unsafe and, nether for certain assumptions, forbidden. OK, this form of a description of a massive spin-1 boson doesn't seem to hold upward exploited past times the Standard Model. It's ugly because the scalar plain transforms inward a suicidal means in addition to the theory doesn't signal to whatsoever non-Abelian approximate symmetry in addition to other pretty things.
In principle, people would e'er say that the photon that nosotros know in addition to love (and peculiarly see) tin inward regulation hold upward massive, thank you lot to a Stückelberg mechanism. Well, I e'er protested when soul presented it as a existent possibility. If a photon were massive, nosotros withal know that the majority must hold upward much smaller than the inverse radius of the public – because nosotros know that the magnetic fields some the public bear as those inward the proper massless electromagnetism, non inward some Proca-Yukawa way. And if the photon were massive but this light, it would at to the lowest degree amount to a new, unsubstantiated fine-tuning. It's to a greater extent than probable in addition to nosotros are encouraged to assume that the photon is precisely massless.
Reece places this "negative sentiment" of mine into a potentially axiomatic if non provable framework. He argues that the boundary of the really low-cal photon is "very far inward the configuration space" in addition to inward consistent theories of quantum gravity, the swampland reasoning implies the being of some low-cal plenty particles (well, a whole tower of them) and/or other reasons why the effective plain theory has to intermission at relatively depression let on energy scales. Quantitatively, Reece claims that the effective plain theory has to intermission above\[
\Lambda_{UV} = \sqrt{ \frac{m_\gamma M_{\rm Planck}}{e} }.
\] Well, the theory would receive got to intermission downward earlier, at the scale \(e^{1/3} M_{\rm Planck}\), if the latter scale were fifty-fifty lower. At whatsoever rate, using the scale inward the displayed equation above, nosotros know that the photon majority is rather tiny (recall my comments most the geomagnetic plain etc.) in addition to the geometric average amongst the Planck majority sends us to an atomic physics scale where QED withal seems OK, in addition to that's how the massive photon hypothesis could hold upward strictly refuted.
We're non quite for certain most whatsoever of these swampland-based principles but I tend to intend that many of them, when properly formulated, are right in addition to powerful. I abide by this film intriguing. Lots of the constructions inward effective plain theory, similar the Stückelberg masses, looked ugly in addition to heuristically "less consistent" to the people who had as practiced a gustation as your humble correspondent. Finally, nosotros may hold upward becoming able to clearly articulate the arguments showing that this "feeling of reduced consistency" is non just some emotion. When coupled to quantum gravity, these ugly scenarios could indeed hold upward strictly forbidden.
Quantum gravity and/or string theory could alone let the solutions that seemed "more pretty" than their ugly competitors. And you lot could halt issuing politically right disclaimers such as "we are assuming that the photon majority is precisely zero; if it had a nonzero mass, nosotros would receive got to revise the whole analysis".
Reece newspaper has no withdraw human relationship to the de Sitter vacua in addition to the cosmological controversies. But if it's right or at to the lowest degree accepted, it clearly strengthens the Vafa Team inward that dispute. There are genuinely unlike sketches of the full general spirit of the stringy enquiry inward the future. In Team Stanford's plan, we're satisfied amongst some Rube Goldberg-style construction, nosotros don't know which 1 (or which class) is the right one, nosotros acquire used to it, in addition to nosotros develop ourselves to hold upward happy that nosotros won't acquire anything new.
On the other hand, inward Team Vafa's conception for the future, string theory enquiry continues to hit actual progress, trying to respond well-defined questions most the public some us that weren't previously answered, such as "Can some massive bosons nosotros volition hit receive got Stückelberg masses? Is our photon allowed past times string theory to hold upward massive?" Truly curious physicists just desire novel answers similar that to hold upward found. It may hold upward impossible to respond some of these questions, peculiarly if our vacuum is a relatively random 1 inward a laid of vacua that receive got unlike properties. But this possibility is non a proven fact in addition to fifty-fifty if it is truthful for some properties, it is non truthful for all questions.
We can't ever receive got the belief that all questions that haven't been answered so far volition rest unanswered forever! That would hold upward a clear religious mental attitude that stops progress inward scientific discipline – in addition to that could receive got stopped it at every instant inward the past. Harvard's Reece sketched some arguments that may prohibit Stückelberg masses inward quantum gravity in addition to you lot – I am primarily talking most you, honey reader inward Palo Alto – should meliorate intend most it in addition to create upward one's heed whether he's right or not.
In some technical questions inside the de Sitter controversy, I am uncertain, in addition to thence are others. But I am for certain most for certain principles of the scientific method. The existent pleasance of scientific discipline is to abide by ways to respond questions – to discriminate betwixt possible answers. Many people inward Northern California (which includes Palo Alto) may receive got adopted a non-discrimination approach to gild in addition to scientific discipline (all people in addition to answers in addition to vacua are as good) – but without discrimination, at that spot is no science.