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Published byMelody Demers Modified about 1 year ago

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String Theory A picture book

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Closed strings and SUGRA Closed string theory in background X Infinite tower of vibrational modes M 2 ~ n/ℓ s String interaction through 3-vertex g s String length At low energies (E « ℓ s ): massless closed str. modes behave like gravitons 10D SUGRA String coupling 2

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Closed strings and SUGRA Closed string theory in background X Infinite tower of vibrational modes M 2 ~ n/ℓ s String interaction through 3-vertex g s String length At low energies (E « ℓ s ): massless closed str. modes behave like gravitons 10D SUGRA String coupling 2

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Solitonic & Dirichlet p-branes D-branes are objects on which open strings can end [Polchinski] 10-dim SUGRA has solutions describing massive & charged objects localized on p+1 - dim. surfaces. [black branes] Branes in string theory ?

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Open strings & gauge theory At low energies (E«ℓ s ): massless modes of the open string behave like gauge bosons + matter on the world-volume of D-branes. p+1- dimensional gauge theory a.. b N A ab

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Gauge-String theory dualities Closed string in curved 10-dimensional space Gauge theory loop classical string theory ! Holography ← Δy → Depending on Δy one side simpler Δy << ℓ s : gauge th ↔ closed string th High redshift ↔ soft strings ↔ meson resonances

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Example: AdS 5 / CFT 4 duality N=4 4D S Yang-MillsStrings in AdS 5 x S 5 U(N c ) gauge field A; 6 scalars Φ Gauge theory on stack Strings in their near of N c D3 - branes horizon geometry par.: λ=g 2 YM N c ; N c par.: λ=g 2 YM N c ; N c R 4 / ℓ s 4 =λ ; g s =λ/N c Gauge inv. operators Gauge inv. operators Closed string states Anomalous dimensions Anomalous dimensions Mass of string mode …...

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pert. Gauge Theory pert. String Theory NcNc λ l s /R gsgs Lattice Gauge Theory [‘t Hooft] [Polyakov, Maldacena] Map of Physics Quantum Gravity

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