String Theory An Introduction Paramita Barai Physics 8610

String Theory: An Introduction Paramita Barai Physics 8610 Course Project Presentation P. Barai

Contents n n Why Strings ? String Theory – Basics, New Ideas & Concepts String Interactions & Particles Successful Predictions of String Theory n n n 2 In Cosmology As the Theory of Everything (Grand Unification) Experimental tests People & Groups Conclusions 3/9/2021 P. Barai

Why String Theory ? n n Several discrepancies in existing theories to explain the nature completely Particle Physics n n 3 No connection between fermions & bosons by any existing theory Calculations lead to infinite quantities (Singular behavior) in several cases: at very short distances (Planck Scale). n Cosmology n n Big Bang & Black Hole Singularity unexplained All theories break down (can’t be applied meaningfully) n n 3/9/2021 Relativity, Quantum Field Theory Infinite answers Grand Unification n Can’t unify Relativity with Quantum Mechanics: no massless, spin– 2 particle (graviton) in Quantum Mechanics P. Barai

String Theory: Basics n n Everything in the universe – oscillations of tiny, vibrating STRINGS Characteristic size / Minimum observable length for Quantum String Theory, LString ~ Planck length, LPlanck (Lowest distance probed ~ 10– 16 cm) n n n String tension, TString Open String Standard particles Closed String Gravitons n 4 From different Boundary Conditions 3/9/2021 P. Barai

Revolutionary ideas n Requires 10 dimensions n n Extra dimensions n n Small compact space (of size Lst) attached to each point in ordinary 4 D space-time: Compactification Large – Brane-world hypothesis - We are trapped on the surface of a higher dimensional brane Branes: Membrane–like objects You can think of a brane as being a slice through the higher dimensional world that string theory says exists n 5 10 = 3 (Space: x, y, z) + 1 (Time: t) + 6 (Where are they ? ) Particles that we're made out of and the forces that hold us together might actually be living on one of these branes 3/9/2021 P. Barai

Brief timeline n n 1921: Kaluza–Klein theory: (4 D space) 1970: Birth of String Theory – by Yoichiro Nambu, Leonard Susskind, Holger Nielsen – (To describe the strong force) n n n 6 1971: Supersymmetry (SUSY) 1974: String Theory predicts Gravitons: Unification 1980: Superstrings: Supersymmetry + Strings (Michael Green & John Schwarz) 1984: First Revolution: Quantum anomalies cancel 1991 -95: Second Revolution, Duality, M Theory (Edward Witten & Townsend) 1996: Black Hole entropy accounted for (Andy Strominger & Cumrun Vafa) 3/9/2021 P. Barai

Strings Particles n n n String vibrates – Sweeps out a 2–dimensional surface in spacetime: ‘world sheet’ (compared to 1 D ‘world line’ of a particle) Quantum modes of vibration of strings Particles in Spacetime String vibrational modes characterized by various quantum numbers: mass, spin, etc. n n n The quantized string oscillator modes wind up giving representations of the Poincaré group, through which quantum states of mass and spin are classified in a relativistic quantum field theory. Characteristics of particles: n n 7 Each mode carries a set of quantum numbers that correspond to a distinct type of fundamental particle. Distance – momentum relation Mass – Spin relation 3/9/2021 P. Barai

Strings interact in ways that correspond to the observed interactions of particles. n Particle physics interactions n n String interactions n n n Not at a point; but spread out. More sensible quantum behavior. Feynman diagram in Standard Model 2–D smooth surface in String Theory n 8 At a point Zero distance in Feynman diagram Loop Integrals – Infinite Loop Integrals – Finite 3/9/2021 P. Barai

Successful Predictions n The right types of particles and the right types of interactions among them. n n 9 At low energies the interactions are precisely of the type appearing in the Standard Model. Explains gravitation (via massless spin– 2 particle -graviton -- the quantum of gravitation), approximated at low energies by general relativity. (No other quantum theory has this) Supersymmetry (SUSY) at low energies (the electroweak scale): Fermions Bosons Successful predictions in Cosmology & Grand Unification 3/9/2021 P. Barai

Cosmology: the present universe n Constituents of the Universe n Matter: n n n n Radiation Vacuum ( ? ) History of Universe from Big Bang till today. . Universe is Flat & Isotropic in large scale n 10 Galaxies Other structures Dark matter Inflation 3/9/2021 P. Barai

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Stringy Solution to Big Bang n String Theory changes the nature of the Big Bang. n n n Stringy minimum distance phenomenon turns the initial infinite behavior into something that's finite By String Theory : n n n 12 Universe starts in less singular way Everything crunched down to a very small size, but not infinitely small. Temperature very large, but not infinitely big. Big bounce: before Big Bang, there was an universe that was bigger contraction quantum mechanical intermediate stage Big Bang & our present Universe Big Bang by Collisions of branes Branes in String Theory helps to explain Inflation 3/9/2021 P. Barai

The Grand Unified Theory: The Holy Grail of Physics n n n Should unify all forces Complete description of quantum dynamics All other physical constants like = 1/137; Mproton/Melectron; e … are pure numbers and they should be calculable in this theory. Contain very less number of input parameters Should provide initial conditions, (to explain why we are in the particular universe we do) Only serious candidate – String Theory. n 13 Unified Quantum Mechanics with Gravity 3/9/2021 P. Barai

Advantages of Strings in Unification n Superstring theory overcomes the problem of singularity at short distances n n n Superstring theory: n n n 14 Point–like particles one-dimensional extended strings Introduces fuzziness, which captures the reality Modifies General Relativity. Difficult to integrate Relativity to Quantum Field Theory by perturbation Recent discoveries non-perturbative solns. 3/9/2021 P. Barai

Can String theory be the probable Grand Unified Theory ? n n Unifies in a single 4 – dimensional quantum theory all known forces and elementary particles Reduces the number of parameters (that need to be determined by experiments) n 15 3/9/2021 20 & 30 (assuming massive neutrinos) 1 (String Tension) + Planck's constant + velocity of light P. Barai

Possible experimental tests n Detect extra dimension. n Energy can leak from our known 4 dimensions to the extra compactified dimensions in appropriate conditions Missing Energy in accelerators n Detect s partner of some particle (prediction of SUSY) n n n 16 3/9/2021 s particles much more massive So cant be generated by present accelerators Big string produced at exotic conditions of Big Bang – Observe by telescopes. P. Barai

People and Groups n n n 17 Princeton (Witten, David Gross) Caltech (Schwarz) Columbia University (Brian Green) Cambridge Cornell UCSB n CERN n n Fermilab n 3/9/2021 Accelerator LHC – will begin operating in Geneva, Switzerland ~ 2007; its energy will be about 8000 Ge. V per beam Search for missing energy P. Barai

Conclusions n n 18 ‘String Theory is the science of 21 st century accidentally discovered in 20 th century’ … THANK YOU ALL Wait for what future gives … 3/9/2021 P. Barai