Axions in supergravity and superstring models ( 송희성교수님을 추모하며 ) Kiwoon Choi Song Memorial Symposium, Apr. 12-13, SNU The IBS Center for Theoretical Physics of the Universe
My paper with Prof. H.S. Song, which was written at the last moment of my graduate study:
My first experience with Prof. H.S. Song was to take his QM course at 1979 when I was a 3 rd year undergraduate student. Unfortunately I was not enthusiastic about his QM course, so skipped the class quite often. He was the chair of the department around that year, and I heard some stories about Prof. Song from some of my classmates, which made me feel that Prof. Song is a cold and stubborn professor. Later he showed his warm concern on me when I was the 1 st year graduate student, while mentioning that he hopes good students continue to study at SNU graduate school for PhD, rather than studying abroad. His concern made me feel happy, and was one of the reasons why I decided to continue my study at SNU. Since then, Prof. Song was always a person of generous and warm character to me. Indeed I always felt easy and relaxed when I share a time or talk with him, although he and I have multi-decades gap in age.
Prof. Song at my wedding ceremony, Feb. 1 st , 1986
Strong CP Problem (C=changing particles to antiparticles, P=space inversion) Strong nuclear force Weak nuclear force | δ KM | ~ 1 | θ QCD | < 10 -10 Why | θ QCD | << | δ KM | ?
Axion solution to the strong CP problem Introduce a spontaneously broken global U(1) symmetry, which is explicitly broken mostly by the QCD anomaly (Peccei-Quinn symmetry) θ QCD becomes a dynamical field “axion” being the Nambu-Goldstone boson of non-linear U(1) PQ : “a” “a” +constant f a = axion scale = mass scale of the spontaneous breaking of U(1) PQ Low energy QCD dynamics develops an axion potential minimized at <a >= 0: QCD becomes CP conserving after the axion is settled down at its VEV. θ QCD = a/f a
Most of axion physics is determined by the axion scale f a * axion mass: * axion-photon couplings : * axion-nucleon couplings : Star cooling by axion emission: f a > 4 x10 8 GeV τ a ≫ 10 17 sec, so once axions were produced in the early universe, they constitute the dark matter in the present universe.
QCD axion not only solves the strong CP problem, but offers a compelling candidate for dark matter. Two possible origins of axion dark matter: Misalignment Axionic strings/walls θ QCD =a/f a
Two theoretical questions which should be addressed to complete the axion solution to the strong CP problem: 1) What is the UV origin of the global PQ symmetry, whose explicit breaking other than the QCD anomaly is highly suppressed, so that Δ V(a) < 10 -10 V QCD (a) θ QCD = a/f a 2) What is the physical mechanism to determine the axion scale f a ? Any connection to other mass scales such as the Planck scale, or SUSY-breaking scale, or the weak scale …? In fact, my work with Prof. Song was motivated by these two questions for non-linear PQ symmetry realized in 4D supergravity.
Later we learned that the best theoretical framework to address these questions is string theory. Extended objects in string theory predict antisymmetric tensor gauge fields, with higher-dim gauge symmetry acting on those tensor gauge fields: t x Upon compactification, antisymmetric tensor field along the compactified directions behaves like 4-dimensional axions: 6D internal space
* Origin of a good PQ symmetry explicitly broken mostly by the QCD anomaly: Non-linear global U(1) PQ : a a + constant ω mn is locally a curl of vector field, but not globally in extra dimension. PQ symmetry: a a + constant corresponds to locally a gauge symmetry , but not globally. PQ breakings other than the gauge anomalies are exponentially suppressed as Δ V(a) ∝ e -Vol(extra-dim) .
* Origin of the axion scale 1) Compactification Compactification with radius R (1/R = compactification scale) f a = O(1/R) More careful analysis: KC, Kim ’85; Svrcek, Witten ’06
Stringy axion DM with determined by compactification dynamics is severely constrained by the axion isocurvature perturbation : with Stringy inflation scenario Burgess, Cicoli, Quevedo ‘13 r = tensor to scalar ratio in CMB = 0.16 (H/10 14 GeV) 2 KC, Jeong, Seo ‘14 r < few x 10 -11 which is difficult to be compatible with most of the known stringy inflation scenario
2) SUSY breaking Compactification Stuckelberg mechanism with anomalous U(1) A gauge symmetry The stringy axion “a B “ from higher-dim antisymmetric tensor gauge field is eaten by the U(1) A gauge boson through the Stuckelberg mechanism, while leaving another PQ symmetry = global part of U(1) A in the absence of a B . In the unbroken SUSY limit, , so the axion scale in this case is generated by SUSY breaking effect: , ( Yet the origin of good PQ symmetry is the shift symmetry of a B , which is locally a gauge symmetry, but not globally in extra dimension.)
Isocurvature constraint on axion scale determined by SUSY breaking , stringy inflation scenario KC, Jeong, Seo ‘14 This scenario can be consistent with most of the known string inflation model.
Conclusion 1) Among the 3 naturalness problems of the SM+GR, the strong CP problem is the only problem which can not find its solution in multiverse, so it is likely that there is a physical mechanism to make θ QCD small. 2) The QCD axion is the most appealing such mechanism, and so should be regarded as one of the most compelling candidate for DM. But where is axion? The window looks so wide. Axion dark matter Astrophysical bound I I I I I I I I I I I f a 10 9 10 10 10 11 10 12 10 13 10 15 10 16 10 17 10 18 (GeV)
3) We need a further guideline, which may come from the top down approach such as string theory. String theory suggests two distinct possibilities: a) axion scale determined by compactification dynamics: Isocurvature perturbation constraint requires r < few x 10 -11 which would not be compatible with most of the known stringy inflation models b) axion scale determined by SUSY breaking dynamics: Isocurvature perturbation constraint allows r even as large as 10 -3 – 10 -5
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