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Flux Tube S-matrix bootstrap Non-Perturbative Methods in Quantum - - PowerPoint PPT Presentation
Flux Tube S-matrix bootstrap Non-Perturbative Methods in Quantum - - PowerPoint PPT Presentation
Flux Tube S-matrix bootstrap Non-Perturbative Methods in Quantum Field Theory ICTP 9/2019 Joan Elias Mir talk based on hep-th/1906.08098 w/ A. Guerrieri, A. Hebbar, J. Penedones, P . Vieira 1.- Flux tube effecive action 2.-
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Set up: a QFTD, gapped, with string like states. for instance:
- Yang Mills Fluxe Tubes,
- Nielsen-Abrikosov stirngs,
- Domain walls in 3D Ising.
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Bulk Poincaré is spontaneously broken, Goldstone modes
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Bulk Poincaré is spontaneously broken, Goldstone modes We build the effective action out of
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Bulk Poincaré is spontaneously broken, Goldstone modes We build the effective action out of
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S-matrix We scatter two massless vectors of O(D-2), It is convenient to use phase-shifts
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S-matrix We scatter two massless vectors of O(D-2), It is convenient to use phase-shifts Unitarity: for
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Phase-shfits, units target Lorentz implies
(rotation of non univ. ops.)
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Phase-shfits, units target Lorentz implies
(rotation of non univ. ops.)
D=3
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Phase-shfits, units target Lorentz implies
s
s+iε
4m2
Unitarity and maximum modulus principle imply In the massless limit points in the UHP are related by s
s+iε
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Unitarity and maximum modulus principle imply s
s+iε
Trick!
Again, unitarity and maximum modulus principle imply Expansion around threshold leads to , Generalisation to multiple points
Schwarz-Pick thm.
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Phase-shfits, units target Lorentz implies
(rotation of non univ. ops.)
D=3
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Phase-shfits, units target Lorentz implies
(rotation of non univ. ops.)
Numerics
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Finite volume energy levels This high order calculation is possible thanks to a trick combining also splitting of excited energy levels is sensitive to TBA +
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Flux Tube Phenomenology
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- First time optimal bounds on Wilson coefficients are derived.
- Would be nice to apply similar ideas to 4D EFTs.
Summary and outlook
- Derive the D=4 Flux tube line analytically, maybe some theorem
for vector valued holomorphic functions?
- Take into account what is known about universal inelasticity.
- Understand better the high energy regime.
- It would be nice to fully pin down the Yang-Mills flux tube EFT :-)
- …
On the branon scattering
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Backup slides
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S-matrix We scatter two massless vectors of O(D-2), Crossing symmetry
a b c d a b c d a b c d
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S-matrix We scatter two massless vectors of O(D-2), It is convenient to use phase-shifts Unitarity: for
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