Aspects of holographic axion dynamics Yuta Hamada (Harvard) - - PowerPoint PPT Presentation
Aspects of holographic axion dynamics Yuta Hamada (Harvard) 1905.03663, 2001.05510 and 2007.13535, with Elias Kiritsis (APC&Crete), Francesco Nitti (APC), and Lukas T. Witkowski (IAP) 1 2020/11/18 Strings and Fields 2020 2 Axion
Yuta Hamada (Harvard)
1905.03663, 2001.05510 and 2007.13535, with Elias Kiritsis (APC&Crete), Francesco Nitti (APC), and Lukas T. Witkowski (IAP)
2020/11/18 Strings and Fields 2020
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Ubiquitous in field theory and string theory. In the context of particle physics, roles of axion are
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Ubiquitous in field theory and string theory. In the context of particle physics, roles of axion are
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String theory setup (flux, brane) for axion monodromy inflation.
[(McAllister-)Silverstein-Westphal ’08, Kaloper-Sorbo ‘08]
Field theory [Witten ’80], Holography [Witten ’98]
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There are many branches parametrized by integer .
In the context of axion monodromy inflation, large field excursion is typically needed. Is there effect of axion backreacion? Result: We find that there exists a significant backreaction when the field excursion is order of the Planck scale.
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Ubiquitous in field theory and string theory.
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In the context of particle physics, roles of axion are
Ubiquitous in field theory and string theory.
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In the context of particle physics, roles of axion are
ℒ ∼ − FμνFμν + θ Fμν ˜ Fμν
Experimental constraint is .
θ ≲ 10−9
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An explanation is given by QCD axion , whose Lagrangian is
a ℒ ∼ (∂μa)2 − FμνFμν + a fa Fμν ˜ Fμν
EOM for axion requires .
δaZ ∼ ⟨Fμν ˜ Fμν⟩ = 0 θ = 0
QCD Lagrangian is
Dynamical solution to Strong CP? It is possible that term receives finite renormalization. A speculation: -angle flows to zero in the IR, and strong CP- problem is alleviated.
θ θ
[Knizhnik-Morozov ’84, Levine-Libbt ’85, Latorre-Luken ’97, Nakamura-Schierholz, ’19]
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Similar observation is obtained in holography. Bulk axion becomes zero in the IR. → The -angle flows to zero.
θ
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Since the IR theta angle itself is not observable, the physical meaning is not clear. We compute CP-violating interaction among glueballs, and see if these couplings are
Result: We do not see the suppression, which implies strong CP problem remains.
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Ansatz
Sbulk = M3
5 ∫ d5x
−g [R − 1 2 gab∂aφ∂bφ − 1 2Y(φ)gab∂aa∂ba − V(φ)] + SGHY
Axion kinetic term
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Boundary term 5d Ricci scalar 5d Planck mass
We use a bottom up holography model. 5d Axion-Dilaton-Einstein theory, ( and RG coordinate ).
ds2 = e2A(r) (dr2 + ημνdxμdxν), φ = φ(r), a = a(r)
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IR: , , is either finite or infinity. IR is singular, but is expected to be resolved, e.g. by adding KK modes. (Good singularity)
UV: Asymptotically , , .
: 4d energy scale
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dilaton
φ
axion
a
metric
gμν
energy momentum tensor
Tμν
, is field strength
Tr[FμνFμν] Fμν
: instanton density
Tr[Fμν ˜ Fμν]
dual 4d operator Bulk field
Near-boundary ( ) solution: ,
r → 0 a(r) = aUV + Q r4 + . . . aUV = θ + 2πk Nc Q ∼ ⟨Fμν ˜ Fμν⟩
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In the IR, we put .
Support: The axion is a form field component along an internal cycle, which shrinks to zero-size in the IR. Single-valuedness then demands that the axion field vanishes at such points.
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Sbulk = M3
5 ∫ d5x
−g [R − 1 2 gab∂aφ∂bφ − 1 2Y(φ)gab∂aa∂ba − V(φ)] + SGHY
Choose and (next slide).
Compute RG flow solutions with given ansatz and IR b.c, scanning over for all possible values for axion source .
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Take model such that in the IR:
φ → ∞, V(φ) ≃ − V∞ebφφP, Y(φ) ≃ Y∞e
6φ
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Two classes of potentials: 1: Steep
,
2: Soft
, . . Glueball spectra
b > 2/3, arbitrary P b = 2/3 1 < P rIR m2
n ∼ n2
b = 2/3 0 < P < 1 rIR = + ∞ m2
n ∼ n2P
In the probe approximation, any value of is possible. Backreaction → range of becomes bounded.
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UV IR UV IR
There are no regular RG flow solutions satisfying the boundary conditions with .
|aUV| > amax
UV
This can be understood analytically: Using the EOMs, one can show that . is the function which appears in axion kinetic term.
|aUV| ≤ ∫
IR UV
dφ Y Y
String-inspired choice is , which leads
Y = e
6φ
|aUV| ≤ 2/ 6 ∼ 𝒫(1)
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Constraints on large field excursion. This is reminiscent of swampland distance conjecture [Ooguri-Vafa ’06].
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Swampland distance conjecture When field excursion is large, the tower of particle becomes light. Original EFT breaks down. We may need to go another EFT.
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Similar story for axion? In this case, charged object is instanton rather than particle. Axion version of WGC? [work in progress] [Horowitz-Santos ’19] observes similar bound on large gauge field source in Maxwell theory. However, they found if there exists scalar field which satisfies (charge) > (mass), then the singularity disappears by condensation. This is nothing but Weak Gravity Conjecture (WGC).
[ArkaniHamed-Motl-Nicolis-Vafa ‘06]
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What does this mean in physics?
θ
UV IR UV IR
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We compute wavefunctions and spectra of glueballs. Masses are decreasing functions of . Qualitatively consistent with lattice result. [Del-Debbio et. al. ’10]
θ
(glueball) = Normalizable linearized fluctuations. Roughly speaking, (Dilaton fluctuation) = glueball, (Axion fluctuation) = glueball, (Metric fluctuation) = glueball. Solutions of eigenvalue problem give spectra.
0++ 0−+ 2++
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Glueball cubic couplings are obtained by looking terms third order in gauge- invariant fluctuations. Expand the fluctuation by using wavefucntion of glueball. Cubic interactions among glueballs are
CP conserving: (even)-(even)-(even) interaction, … CP violating: (even)-(even)-(odd), (odd)-(odd)-(odd) interaction
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CP-violating couplings are not suppressed. Blue: (odd-odd-odd)/(even-even-even) Red: (odd-even-even)/(even-even-even)
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We investigated the dynamics of axion by using bottom up holography model. We find
Planckian field excursion.
the suppression of CP-violating effect is not seen in physical observable.