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 Ubiquitous in field theory and string theory. In the context of particle physics, roles of axion are 
 - Inflaton candidate 
 - Solution of strong CP problem. - Dark Matter candidate

2 Axion Ubiquitous in field theory and string theory. In the context of particle physics, roles of axion are 
 - Inflaton candidate 
 - Solution of strong CP problem. - Dark Matter candidate

Axion Monodromy 3 Field theory [Witten ’80] , Holography [Witten ’98] There are many branches 
 parametrized by integer . k String theory setup (flux, brane) for axion monodromy inflation. [(McAllister-)Silverstein-Westphal ’08, Kaloper-Sorbo ‘08]

Axion Backreaction 4 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.

Axion 5 Ubiquitous in field theory and string theory. In the context of particle physics, roles of axion are 
 - Inflaton candidate 
 - Solution of strong CP problem. - Dark Matter candidate

Axion 5 Ubiquitous in field theory and string theory. In the context of particle physics, roles of axion are 
 - Inflaton candidate 
 - Solution of strong CP problem. - Dark Matter candidate

Strong CP problem 6 QCD Lagrangian is ℒ ∼ − F μν F μν + θ F μν ˜ F μν θ ≲ 10 − 9 Experimental constraint is . An explanation is given by QCD axion , a whose Lagrangian is ℒ ∼ ( ∂ μ a ) 2 − F μν F μν + a F μν ˜ F μν f a EOM for axion requires δ a Z ∼ ⟨ F μν ˜ F μν ⟩ = 0 . θ = 0

Strong CP problem? 7 Dynamical solution to Strong CP? It is possible that term receives θ finite renormalization. A speculation: -angle flows to θ zero in the IR, and strong CP- problem is alleviated. [Knizhnik-Morozov ’84, Levine-Libbt ’85, Latorre-Luken ’97, Nakamura-Schierholz, ’19]

Holography 8 Similar observation is obtained in holography. Bulk axion becomes zero in the IR. → The -angle flows to zero. θ 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 suppressed. 
 Result: We do not see the suppression, which implies strong CP problem remains.

Talk Plan 9 1. Introduction and results 2. Setup: Axion-Dilaton-Einstein theory 3. Axion backreaction 4. Strong CP-violation

Talk Plan 10 1. Introduction and results 2. Setup: Axion-Dilaton-Einstein theory 3. Axion backreaction 4. Strong CP-violation

11 Setup We use a bottom up holography model. 5d Axion-Dilaton-Einstein theory, 
 x μ ( and RG coordinate ). r − g [ R − 1 5 ∫ d 5 x 2 Y ( φ ) g ab ∂ a a ∂ b a − V ( φ ) ] + S GHY 2 g ab ∂ a φ ∂ b φ − 1 S bulk = M 3 Axion kinetic term 5d Planck mass 5d Ricci scalar Boundary term Ansatz ds 2 = e 2 A ( r ) ( dr 2 + η μν dx μ dx ν ) , φ = φ ( r ), a = a ( r )

UV and IR 12 UV: Asymptotically AdS 5 e A → ∞ , , . φ → 0 r → 0 IR: e A → 0 , , φ → ∞ r → r IR is either finite or infinity. r IR IR is singular, but is expected to be resolved, e.g. by adding KK modes. (Good singularity) e A ( r ) : 4d energy scale

Correspondence 
 13 Bulk field 4d operator dual metric energy momentum tensor g μν T μν Tr [ F μν F μν ] F μν , is field strength dilaton φ Tr [ F μν ˜ F μν ] axion : instanton density a Near-boundary ( ) solution: r → 0 a ( r ) = a UV + Q r 4 + . . . a UV = θ + 2 π k Q ∼ ⟨ F μν ˜ F μν ⟩ , N c

IR axion boundary 14 In the IR, we put . a IR = 0 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.

Talk Plan 15 1. Introduction and results 2. Setup: Axion-Dilaton-Einstein theory 3. Axion backreaction 4. Strong CP-violation

Numerical Analysis 16 − g [ R − 1 5 ∫ d 5 x 2 Y ( φ ) g ab ∂ a a ∂ b a − V ( φ ) ] + S GHY 2 g ab ∂ a φ ∂ b φ − 1 S bulk = M 3 Choose and (next slide). V ( φ ) Y ( φ ) Compute RG flow solutions with given ansatz and IR b.c, scanning over for all possible values for axion source . a UV

Parametrizing IR 17 
 Take model such that in the IR: φ → ∞ , V ( φ ) ≃ − V ∞ e b φ φ P , Y ( φ ) ≃ Y ∞ e 6 φ Two classes of potentials: 1: Steep 
 or , b > 2/3, arbitrary P b = 2/3 1 < P m 2 n ∼ n 2 finite. Glueball spectra r IR 2: Soft , . b = 2/3 0 < P < 1 m 2 n ∼ n 2 P . Glueball spectra r IR = + ∞

18 is bounded a UV In the probe approximation, any value of is possible. a UV Backreaction → range of becomes bounded. a UV UV IR UV IR

Analytical Results 19 There are no regular RG flow solutions satisfying | a UV | > a max the boundary conditions with . UV This can be understood analytically: 
 Using the EOMs, one can show that | a UV | ≤ ∫ IR d φ . Y UV is the function which appears in axion kinetic term. Y 6 φ String-inspired choice is , which leads 
 Y = e | a UV | ≤ 2/ 6 ∼ 𝒫 (1)

Implication 20

Implication 20

Implication 20

Implication 20 Constraints on large field excursion. This is reminiscent of swampland distance conjecture [Ooguri-Vafa ’06] .

Implication 20

Implication 20 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.

Connection to WGC? 21 [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] Similar story for axion? In this case, charged object is instanton rather than particle. 
 Axion version of WGC? [work in progress]

Talk Plan 22 1. Introduction and results 2. Setup: Axion-Dilaton-Einstein theory 3. Axion backreaction 4. Strong CP-violation

Flow of -angle 23 θ UV IR UV IR -angle becomes zero in the IR, as we required. 
 θ What does this mean in physics?

Glueballs spectra 24 (glueball) = Normalizable linearized fluctuations. 
 Roughly speaking, 
 0 ++ (Dilaton fluctuation) = glueball, 0 − + (Axion fluctuation) = glueball, 2 ++ (Metric fluctuation) = glueball. 
 Solutions of eigenvalue problem give spectra. We compute wavefunctions and spectra of glueballs. Masses are decreasing functions of . θ Qualitatively consistent with lattice result. [Del-Debbio et. al. ’10]

Glueballs interaction 25 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 obtained by overlap integration. CP conserving: (even)-(even)-(even) interaction, … CP violating: (even)-(even)-(odd), (odd)-(odd)-(odd) interaction

CP-violating interaction 26 Blue: (odd-odd-odd)/(even-even-even) Red: (odd-even-even)/(even-even-even) CP-violating couplings are not suppressed.

Summary 27 We investigated the dynamics of axion 
 by using bottom up holography model. We find 
 - significant backreaction for trans- Planckian field excursion. 
 - although -angle flows to 0 in IR, θ the suppression of CP-violating effect is not seen in physical observable.