Heidelberg, June 2008 Volker Schomerus - DESY Hamburg - Of Mesons and Metals Bethe & the 5th Dimension Introduction: Mesons Even perturbative physics difficult flux tubes ~ strings Can meson physics be modeled by strings ? Non-perturbative QCD physics remains to be understood confinement, sQG plasma... But: String amplitudes are too soft ( extended nature) experiment! QCD description of perturbative regime through gauge theory (GT). Similar issues for SM of many body systems Loops & legs The 5 th Dimension The 5 th Dimension Large N c exp. of GTString theory [t Hooft] Flux tube extension 5 th dim. ? [Polyakov] Maldacena 97: Many strongly coupled 4D GT s possess a weakly coupled description through strings in a curved 5D geometry. compare high-T low-T dualities Geometrization of Quantum Physics String theoretic descriptions for non-relativistic 3D systems are being investigated crit cold atoms strange metals Particle Theory String Theory = L L Laplacian H = L i L i+1 1D Spin Chain Bethe, Metals and Strings non-linear model continuum limit Solution method: (thermodynamic) Bethe Ansatz e.g. spherically sym- metric problem in ED Spectrum from solutions of non-linear integral equations Plan: Part I Part II Part III Strings & Gauge Theory Closed strings and SUGRA Closed string theory in background X Infinite tower of vibrational modes M 2 ~ n/ s String interaction through 3-vertex g s String length At low energies (E s ): massless closed str. modes behave like gravitons 10D SUGRA String coupling 2 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 ? Open strings & gauge theory At low energies (E 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 Gauge-String theory dualities Closed string in curved 10-dimensional space Gauge theory loop classical string theory ! Holography y Depending on y one side simpler y 5 gluons Kinematic data..but surface very hard to find Reformulation through TBA Thermodynamik Bubble Ansatz [Alday,Gaiotto,Maldacena] ~ calculation of vacuum energy in 1D quantum systems m,.. - parameters Y - density of part./holes A - energy Kinematic data kernel fct K known Area from nonlinear integral equations (NLIE): Amplitudes 2012 Organizers: R. Boels, G. Heinrich, J. Henn, P. Mastrolia J. Plefka, V. Schomerus Hamburg, Mar If you want to see more come to Summary Strings in 5D for mesons Strings from magnets Gluon scattering from TBA