S WAMPLAND C ONJECTURES FOR S TRINGS AND M EMBRANES Stefano Lanza H ARVARD U NIVERSITY based on arXiv: 2006.15154 with Fernando Marchesano, Luca Martucci, Irene Valenzuela Summer Series on String Phenomenology ~ September 1, 2020
L OW C ODIMENSION O BJECTS AND B ACKREACTIONS Extended objects with low codimension strongly backreact on the geometry; in 4D Particle String Membrane Strong backreaction as the distance from the source increases, Backreaction negligible as r → ∞ with the metric breaking down at a finite distance from the object
S TRONG B ACKREACTIONS AND EFT S Does the inclusion of strings or membranes break the EFT? How can we understand the backreaction of the objects at EFT level? Backreaction of the extended objects onto the spacetime metric and the fields of the EFT RG flow of the EFT couplings [Goldberger, Wise 2001; Polchinski et al. 2014] We will show this correspondence in N=1 Supergravity EFTs.
E XTENDED O BJECTS AND S WAMPLAND C ONJECTURES Completeness hypothesis Trivial bordism group No Global Symmetries Weak Gravity Conjecture Distance Conjecture No de Sitter Repulsive Force Conjecture Conjecture Instability of non- Transplanckian AdS supersymmetric Censorship distance Conjecture AdS vacua Conjecture
E XTENDED O BJECTS AND S WAMPLAND C ONJECTURES Completeness hypothesis Trivial bordism group No Global Symmetries Weak Gravity Conjecture Distance Conjecture No de Sitter Repulsive Force Conjecture Conjecture Instability of non- Transplanckian AdS supersymmetric Censorship distance Conjecture AdS vacua Conjecture
E XTENDED O BJECTS AND S WAMPLAND C ONJECTURES Completeness hypothesis Trivial bordism group No Global Symmetries Axionic Strings Weak Gravity Conjecture Distance Conjecture No de Sitter Repulsive Force Conjecture Conjecture Instability of non- Transplanckian AdS supersymmetric Censorship distance Conjecture AdS vacua Conjecture
E XTENDED O BJECTS AND S WAMPLAND C ONJECTURES Completeness hypothesis Trivial bordism group No Global Symmetries Membranes Weak Gravity Conjecture Distance Conjecture No de Sitter Repulsive Force Conjecture Conjecture Instability of non- Transplanckian AdS supersymmetric Censorship distance Conjecture AdS vacua Conjecture
A XIONIC S TRINGS AND I NFINITE F IELD D ISTANCE
A XIONIC S TRINGS IN N=1 S UPERGRAVITY We will consider fundamental axionic strings : they are included directly within the EFT as fundamental objects, with strict codimension two; electrically coupled to gauge two-forms via: magnetically coupled to the dual axions: In order to consider strings semiclassically within an EFT with cuto ff Λ , their tension needs to satisfy In order to embed fundamental strings in Supergravity, we need a proper formulation which supersymmetrically includes gauge 2-forms.
A XIONIC S TRINGS IN N=1 S UPERGRAVITY Φ i The bosonic components of an N=1 supersymmetric action of a set of chiral multiplets is axions saxions Assume that the Kähler potential is invariant under axionic shifts: Φ i Dualize the chiral multiplets to linear multiplets . L i At the bosonic level: dual saxions saxions axions gauge (gauge 0-forms) 2-forms The dual action expressed in terms of a set of linear multiplets is and Ν =1 supersymmetry fixes the scalar metric and gauge kinetic function to be equal: [SL, Marchesano, Martucci, Sorokin, 2019]
A XIONIC S TRINGS IN N=1 S UPERGRAVITY We can now couple a fundamental string: with The string tension is fixed by supersymmetry: N = 1 N = 1 The physical string charge is defined by bulk susy worldvolume susy The string tension obeys the tautological identity Over its worldsheet, the string with preserves at most 1/2 of the bulk supersymmetry, the other half being nonlinearly realized.
THE S TRING B ACKREACTION Consider a single string located at radial coordinate and whose worldvolume is r = 0 described by the coordinates . t , x r Metric ansatz with , coordinates transverse to the string z z ¯ and . r = | z | Consider a single saxion , entering the Kähler potential as s Solving the equations of motions gives the backreacted solution: for the saxion and axion s a The solution breaks down at a finite distance for the warp factor
THE S TRING B ACKREACTION AS RG F LOW The flow of the tension is which breaks down at a distance In the limit : r → 0 Define the energy scale Consider the string tension as EFT coupling We regard the profile of the tension as RG-flow of the tension and the EFT breaks at the strong coupling scale On the other hand, the limit corresponds to weak coupling. r → 0
RFC FOR A XIONIC S TRINGS [Palti, 2017; Heidenreich, Reece, Rudelius, 2019] Two identical strings interact with the following forces No gravitational forces Scalar forces Electric forces The Repulsive Force Conjecture requires the existence of self-repulsive elementary axionic strings satisfying: which has to hold scale-wise along the RG-flow. Supersymmetric strings trivially satisfy the no-force condition
WGC FOR A XIONIC S TRINGS Weak Gravity Conjecture for strings: a super-extremal string satisfying ∃ [Arkani-Hamed et al. 2006; Heidenreich, Reece, Rudelius, 2015; with being the extremality factor. γ Reece, 2018; Craig et al. 2018, …] How to determine the extremality factor? Recall that a BPS-string satisfies the no-force condition For single scalar field, with Kähler potential the extremality factor is specified by the no-scale factor For multiple scalar fields, asymptotically in field space, we can use the sl(2) orbit theorem to approximate using which it can be shown with
A XIONIC S TRINGS AND I NFINITE F IELD D ISTANCES The limit , with r → 0 corresponds to infinite field distance , s i → ∞ d → ∞ or: string WGC 1. As d max → ∞ , the EFT cuto ff exponentially decreases: 2. Close to the string, infinite oscillatory modes become massless, with fall o ff of the masses The string extremality factor fixes the rate at which the masses become massless ⇒ [see also Gendler, Valenzuela, ’20]
THE D ISTANT A XIONIC S TRING C ONJECTURE Distant Axionic String Conjecture (DASC): All infinite distance limits of a 4d EFT can be realised as an RG flow endpoint of a fundamental axionic string. Changing Λ =RG flow For finite cuto ff Λ , the moduli space is Infinite field distances are ideally explorable only partially explorable. when Λ , corresponding to the → 0 endpoint of the string RG flow.
THE D ISTANT A XIONIC S TRING C ONJECTURE Distant Axionic String Conjecture (DASC): All infinite distance limits of a 4d EFT can be realised as an RG flow endpoint of a fundamental axionic string. Infinite tower of states become massless KK modes, D0 branes, … → 0 with r ≥ 1 Infinite field distances are ideally explorable [SL, Marchesano, Martucci, Valenzuela, to appear ] when Λ , corresponding to the → 0 endpoint of the string RG flow.
M EMBRANES AND S CALAR P OTENTIAL
M EMBRANES IN N=1 S UPERGRAVITY We will consider fundamental membranes: objects with strict codimension one; electrically coupled to a set of gauge three-forms: In order for the membranes to be treated semiclassically within an EFT with cuto ff Λ , their tension needs to satisfy Embedding membranes in Supergravity requires a formulation that supersymmetrically includes gauge three-forms.
M EMBRANES IN N=1 S UPERGRAVITY First step: including gauge three-forms in N=1 supergravity Introduce the modified chiral multiplets with and construct the N=1 supersymmetric action where is the inverse of T ab : holomorphic periods Integrating out the gauge three-forms via Gauge three-forms dual of fluxes one gets with the scalar potential and
M EMBRANES IN N=1 S UPERGRAVITY Second step: including supersymmetric membranes Fundamental membranes can be included as with The membrane modifies the 3-form eoms. The potential ‘jumps’ as the membrane is crossed
M EMBRANES IN N=1 S UPERGRAVITY Second step: including supersymmetric membranes Fundamental membranes can be included as with The membrane tension is fixed by supersymmetry The physical charge is defined as
G ENERATING M EMBRANES BPS membranes tautologically satisfy with Compare with the scalar potential ‘Generating membrane’ They coincide for generating membranes. They interpolate between a fluxless region and one with a nontrivial flux: which implies
T HE M EMBRANE B ACKREACTION Asymptotically in field space, we can use the sl(2) orbit theorem to approximate with discrete data that specify the asymptotic limit and assume we can single out a monomial with the maximal growth so that with [Grimm, Li, Palti, Valenzuela, … ’18-‘20] ‘Generating membrane’ For a supersymmetric domain wall with metric ansatz the warp factor and the membrane tension backreactions are
T HE M EMBRANE B ACKREACTION AS RG-F LOW The backreaction onto the tension is which breaks at the distance from the membrane. It is regular in the limit y → 0 Define the energy scale Consider the membrane tension as EFT coupling We regard the profile of the tension as RG-flow of the tension and the EFT breaks at the strong coupling scale The membrane tension increases as . Λ → Λ strong
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