Duality and Axionic Weak Gravity Stefano Andriolo KU Leuven [based - PowerPoint PPT Presentation

Duality and Axionic Weak Gravity Stefano Andriolo KU Leuven [based on: SA, Huang, Noumi, Ooguri, Shiu ’20 — 2004.13721] StringPheno Summer series 28th July 2020

THE SWAMPLAND [Vafa ’05, Ooguri,Vafa ’06] Landscape: Swampland: EFT’s with QG completion EFT’s that do not have QG completion Boundary defined by Swampland criteria

WEB OF CONJECTURES [Reviews: Brennan, Carta, Vafa 1711.00864 Palti 1903.06239] Maybe… String Lamppost Principle: all consistent QG theories are part of the string landscape

MOTIVATIONS OF OUR WORK Test swampland criteria: - self-consistency : Linking conjectures in the web - consistency with other principles Unitarity, causality, locality, analyticity, duality, BH physics, SUSY, holography, anomalies,…

MOTIVATIONS OF OUR WORK Test swampland criteria: - self-consistency : Linking conjectures in the web - consistency with other principles Unitarity, causality, locality, analyticity, duality, BH physics, SUSY, holography, anomalies,… Highlight the relevant properties/principles of QG Understand what makes string theory so special (QG unique?) “string theory so complete/rich ☑ ☑ ☑ = insurance with full options” ☑ ☑ ☑

MOTIVATIONS OF OUR WORK Test swampland criteria: - self-consistency : Linking conjectures in the web - consistency with other principles Unitarity, causality, locality, analyticity, duality, BH physics, SUSY, holography, anomalies,… Highlight the relevant properties/principles of QG Understand what makes string theory so special (QG unique?) “string theory so complete/rich ☑ ☑ ☑ = insurance with full options” ☑ ☑ ☑

THE PUNCH-LINE Analyse WGC (axionic version) vs positivity (unitarity, analyticity, locality) [Cheung,Remmen ’14, Andriolo,Junghans,Noumi,Shiu ’18, Hamada,Noumi,Shiu ’18,…] Result: - in simple systems: positivity is sufficient to imply the WGC - more often: positivity alone is not enough, but specifying some UV info is sufficient to satisfy the WGC (e.g., SL(2,R) symm) positivity [Heidenreich, Reece,Rudelius ’16, + WGC Montero,Shiu,Soler ’16, UV info Aalsma, Cole, Shiu ’19] See also Gregory’s talk on September 1st! [Loges,Noumi,Shiu ’19, ’20]

OUTLINE Review of WGC and its axionic version ( A WGC) Question addressed Illustration of setup Positivity vs AWGC Adding SL(2,R) and implications

WGC and AWGC

Standard formulation of WGC : [Arkani-Hamed, Motl, Nicolis, Vafa ’06] - “An EFT with gauge U(1)+gravity is QG-consistent if it admits at least a state with charge-to-mass ratio greater than that of an extremal black hole (EBH)” qgM P since M EBH = gM P Q EBH (here D=4) ≥ 1 m - Motivated by requiring instability and decay of EBH’s - As swampland criterium, trivial for M P → ∞ - Encapsulates “no global symm in QG”, since never satisfied for g → 0 - Generalized to multiple U(1)’s [Tower/(sub-)lattice WGC] [Heidenreich, Reece, Rudelius ’15,’16, Montero,Shiu,Soler ’16, SA, Junghans, Noumi, Shiu ’18] - Generalized to other dimensions and abelian p-forms potentials

AWGC is the generalisation to p=0 form potential (= axion ): (here D=4) WGC AWGC form field potential photon A µ axion/2-form dual θ /B µ ν charged states particles & black holes instantons & grav. instantons 1 coupling gauge coupling f=axion decay constant g f ( m, q ) relevant quantities mass, charge ( S, q ) action, charge m WGC bound Sf < 1 < O (1) qgM P Exists a state s.t. nM P regular solutions Extremal obj’s EBH’s [Eucl. wormholes] Interpretation Instability of EBH’s tunneling process via collection of smaller instantons favoured over single instanton w/ same tot q

OBSERVATION… Higher order (string) corrections modify the classical BH extremality bound in a way that the same EBH’s (Q,M) can be the WGC states M M classically = 1 gQM P gQM P 1 Q 0 Q ∗ macroscopic obj’s M � M P (semi-classical reasonings)

OBSERVATION… Higher order (string) corrections modify the classical BH extremality bound in a way that the same EBH’s (Q,M) can be the WGC states M M classically = 1 gQM P gQM P 1 HO corrections ∆ M < 0 � ∆ M M � < 1 = 1 + � gQM P gQM P � Q HO 0 Q ∗ macroscopic obj’s [Kats, Motl, Padi ’06] M � M P (semi-classical reasonings)

…QUESTION Can the same happen for Euclidean wormholes? Sf � = 1 + ∆ Sf Sf � nM P < 1 ? � nM P nM P � HO 1 n 0 Under which circumstances ? ∆ S < 0

SETUP

β = 0 Classical Axio-dilaton-gravity (ADG) Axion-gravity (AG) 2( ∂ µ φ ) 2 − f 2  R � 2 − 1 Z d 4 x √− g 2 e βφ ( ∂ µ θ ) 2 S = 4 Euclidean wormhole solutions (non-singular class of solutions for ) β < √ 6 [reviews: Hebecker,Mangat,Theisen,Witkowski ’16, Hebecker-Mikhail-Soler ’18, Van Riet ’20] can be regarded as instanton—anti-instanton pair dr 2 ds 2 = + r 2 d Ω 2 r = r 0 3 1 − r 4 0 r 4 0 = n 2 f 2 24 π 4 cos 2 h √ i r 4 6 4 β · π 2 semiwormhole S = 2 | n | M P √ 4 π · | n | M P 6 h √ i (instanton) β = 0 6 4 β · π sin 2 β f f action

β = 0 Classical Axio-dilaton-gravity (ADG) Axion-gravity (AG) 2( ∂ µ φ ) 2 − f 2  R � 2 − 1 Z d 4 x √− g 2 e βφ ( ∂ µ θ ) 2 S = 4 Euclidean wormhole solutions (non-singular class of solutions for ) β < √ 6 + HO (4-derivative) corrections , generic Z h a 1 ( φ )( ∂ µ φ∂ µ φ ) 2 + a 2 ( φ ) f 4 ( ∂ µ θ∂ µ θ ) 2 d 4 x √− g ∆ S = + a 3 ( φ ) f 2 ( ∂ µ φ∂ µ φ )( ∂ µ θ∂ µ θ ) + a 4 ( φ ) f 2 ( ∂ µ φ∂ µ θ ) 2 + a 5 ( φ ) W 2 + a 6 θ W ˜ i W Evaluation of gives… ∆ S

- AG system : ∆ S = − 24 π 2 a 2 β = 0 - ADG system π  Z tan 4 h √ e − 2 βφ ( t ) sec 4 h √ 2 i i dt cos 3 t ∆ S = 36 π 2 6 6 � � � � φ ( t ) φ ( t ) − a 1 4 β · t − a 2 4 β · t 0 i � e − βφ ( t ) tan 2 h √ sec 2 h √ ⇣ �⌘ i 6 6 � � � + φ ( t ) + a 4 φ ( t ) a 3 4 β · t 4 β · t

- AG system : ∆ S = − 24 π 2 a 2 β = 0 - ADG system π  Z tan 4 h √ e − 2 βφ ( t ) sec 4 h √ 2 i i dt cos 3 t ∆ S = 36 π 2 6 6 � � � � φ ( t ) φ ( t ) − a 1 4 β · t − a 2 4 β · t 0 i � e − βφ ( t ) tan 2 h √ sec 2 h √ ⇣ �⌘ i 6 6 � � � + φ ( t ) + a 4 φ ( t ) a 3 4 β · t 4 β · t we can use positivity conditions to determine (for any bg ) φ = φ ∗ − a 4 − 2 √ a 1 a 2 ≤ a 3 ≤ 2 √ a 1 a 2 a 1 ≥ 0 , a 2 ≥ 0 , a 4 ≥ 0 ,

- AG system : ∆ S = − 24 π 2 a 2 < 0 β = 0 - ADG system π  Z tan 4 h √ e − 2 βφ ( t ) sec 4 h √ 2 i i dt cos 3 t ∆ S = 36 π 2 6 6 � � � � φ ( t ) φ ( t ) − a 1 4 β · t − a 2 4 β · t 0 i � e − βφ ( t ) tan 2 h √ sec 2 h √ ⇣ �⌘ i 6 6 � � � + φ ( t ) + a 4 φ ( t ) a 3 4 β · t 4 β · t we can use positivity conditions to determine (for any bg ) φ = φ ∗ − a 4 − 2 √ a 1 a 2 ≤ a 3 ≤ 2 √ a 1 a 2 a 1 ≥ 0 , a 2 ≥ 0 , a 4 ≥ 0 ,

- AG system : ∆ S = − 24 π 2 a 2 β = 0 - ADG system π  Z tan 4 h √ e − 2 βφ ( t ) sec 4 h √ 2 i i dt cos 3 t ∆ S = 36 π 2 6 6 � � � � φ ( t ) φ ( t ) − a 1 4 β · t − a 2 4 β · t 0 i � ? Q 0 e − βφ ( t ) tan 2 h √ sec 2 h √ ⇣ �⌘ i 6 6 � � � + φ ( t ) + a 4 φ ( t ) a 3 4 β · t 4 β · t we can use positivity conditions to determine (for any bg ) φ = φ ∗ − a 4 − 2 √ a 1 a 2 ≤ a 3 ≤ 2 √ a 1 a 2 a 1 ≥ 0 , a 2 ≥ 0 , a 4 ≥ 0 , a 4 Simplified illustration (in the plane) a 2 = a 1 ∆ S > 0 Prohibited by positivity ∆ S < 0 Satisfy positivity, but WGC violated a 3 Satisfy positivity and WGC − 2 a 1 0 2 a 1 model-dep

POSITIVITY INTERMEZZO (presto) ℒ = − 1 2( ∂ μ a ) 2 + α ( ∂ μ a ∂ μ a ) 2 + ⋯ Axion-gravity EFT where, for instance, arises after integrating out massive scalar α ϕ a a a a α = g 2 ϕ ϕ ( ∂ μ a ) 2 g g 2 m 2 ≥ 0 1 m 2 + p 2 a a a a and the sing of is related to the sign of propagator (unitarity) α generically, follows from unitarity, analyticity, locality α > 0 of UV scattering amplitudes [Adams, Arkani-Hamed, Dubovsky, Nicolis, Rattazzi ’06] - Caveat, assumption: gravitational Regge states are sub-dominant | α | > 1/ ( M 2 s M 2 Pl ) [Hamada-Noumi-Shiu ’18]

Back to the ADG system: Can we assume some additional property and show that ∆ S < 0 ?

“duality” SL(2,R) SYMMETRY [=SL(2,Z)+axion shift symm] τ = β 2 f θ + ie − β 2 φ Symmetry of the 2-derivative action τ → a τ + b ( a, b, c, d ∈ R , ad − bc = 1) c τ + d Extended to the HO 4-derivative action terms : only two SL(2,R) invariant operators τ ) 2 ( ∂ µ τ∂ µ ¯ ( ∂ µ τ∂ µ τ )( ∂ µ ¯ τ∂ µ ¯ τ ) + λ 2 λ 1 λ 1 , 2 = const ⌘ 4 ⌘ 4 ⇣ ⇣ β β (Im τ ) 4 (Im τ ) 4 2 2 4d parameter space 2d parameter space ( a 1 , a 2 , a 3 , a 4 ) ( λ 1 , λ 2 ) We are adding structure to EFT

Evaluation of gives… ∆ S ∆ S = − 24 π 2 ( λ 1 + λ 2 ) Positivity means λ 1 + λ 2 ≥ 0 λ 2 ≥ 0

Evaluation of gives… ∆ S ∆ S = − 24 π 2 ( λ 1 + λ 2 ) < 0 Positivity means λ 1 + λ 2 ≥ 0 λ 2 ≥ 0