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## Particle physics from quantum gravity Lee Smolin

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**Particle physics fromquantum gravityLee Smolin**I Basic assumptions and results II Quantum information and quantum gravity F.Markopoulou hep-th/0604120 D. Krebs and F. Markopoulou gr-qc/0510052 III Unification of quantum geometry with matter S. Bilson-Thompson, F. Markopoulou, LS hep-th/0603022 IV Dark energy from quantum gravity F. Markopoulou, C. Prescod-Weinstein, LS V. Doubly special relativity as the low energy limit**A.Sen**A.Ashtekar L. Smolin C. Rovelli P. Renteln T. Jacobson V. Husain R Gambini J Pullin B Bruegmann R. Loll F.Markopoulou J. Samuels T. Newmann P Morao A. Perez J Iwasaki A Mikovic J Wisniewski C Beetle B Dettrich P. Sungh H, Sahlmann, Fleishhack T. Thiemann J. Lewandowski J. Morao E. Hawkins H. Sahlman O. Winkler M. Reisenberger L. Crane J. Baez J. Barrett R. de Pietro L. Freidel K. Krasnov R. Livine L. Kauffman H. Morales-Tecotl O. Dreyer C. Soo S Fairhurst M Varadarajan S Speciale A. Toporeski G. Datta Y Ling S Major D. Longais A Stradobodsov M Arnsdorf C Isham R Garcia S Alexandrapov H Kodama J. Dell R. Capovilla, J. Romano S Alexander M Shepard G Amelino-Camelia J. Magueijo J Kiwalski-Glickman L.N. Chang B Krishnan G Egan M Ansari S. Hoffman J. Brunnemann M. Okolo Loop quantum gravity community • D. Oriti • R. Williams • D.Christensen • S. Gupta • J. Ambjorn • K.Anagastopolo • K. Christensen • R. Tate • L. Mason • O. Dreyer • M. Bojowald • D. Yetter • A Corichi • J Zapata • J Malecki • M. Varadarajan • L. F. Urrutia • J. Alfaro • K. Noui • P. Roche • M Bojowald • F. Girelli • T. Konopka**Causal spin network theories**• Pick an algebra G • Def: G-spin network is a graph G with edges labeled by representations of G and vertices labeled by invariants. • Pick a differential manifold S. • {G } an embedding of G in S, up to diffeomorphisms • Define a Hilbert space H: • |{G }> Orthonormal basis element for each {G } • Define a set of local moves and give each an amplitude • A history is a sequence of moves from an in state to an out state • Each history has a causal structure**These theories realize three principles:**• 1) The Gauge principle: All forces are described by gauge fields • Gauge fields: Aa valued in an algebra G • Gravity: Aa valued in the lorentz group of SU(2) subgroup • p form gauge fields • Supergravity: Ym is a component of a connection. • 2) Duality: equivalence of gauge and loopy (stringy) descriptions • observables of gauge degrees of freedom are non-local: • described by measuring parallel transport around loops • Wilson loop T[g,A] = Tr exp ∫gAg • 3) Diffeomorphism invariance and background independence**The gravitational field can be described as a gauge theory:**• Spacetime connection = Gauge field. • Spacetime metric = Electric field • Quantum gauge fields can be described in terms of operators that • correspond to Wilson loops and electric flux. These have a natural • algebra that can be quantized: • The loop/surface algebra. • T[g,A] = Trexp ∫gA E[S]= ∫SE [ ] = h G Int ,**The fundamental theorem:**Consider a background independent gauge theory, compact Lie group G on a spatial manifold S of dim >1. No metric!! (G=SU(2) for 3+1 gravity) There is a unique cyclic representation of the loop/surface algebra in which the Hilbert space carries a unitary rep of the diffeomorphism group. Lewandowski, Okolo, Sahlmann, Thiemann+ Fleishhack(LOST theorem) This means that there is a unique diffeomorphism invariant quantum quantum theory for each G. It is the one just defined! (up to fine print) Ashtekar: GR is a diffeomorphism invariant gauge theory!! Hence this class of theories includes loop quantum gravity and spin foam models**Role of the cosmological constant:**Requires quantum deformation of SU(2) q=e2pi/k+2 k= 6p/GL To represent this the spin network graphs must be framed:**Some old and new results in LQG:**• There exist semiclassical states. • Excitations of semiclassical states include long wavelength gravitons • Sums over labels in 3+1d and 4d spin foam models are convergent. • analytically and numerically (Crane, Perez,Rovelli,Baez,Christensen..) • Graviton propagator, and Newton’s law derived in 4d (Rovelli et al 05) • 2+1 gravity with matter solved, gives an effective field theory on • k-Poincare non-commutative manifold, implying DSR. (Freidel-Livine) • Reduced models for cosmology and black hole interiors solved: • Spacelike singularities eliminated and replaced by bounce. (Bojowald …) Predictions for corrections to CMB (Hoffman-Winkler) Black hole entropy understood including corrections and radiation • (Krasnov, Baez, Ashtekar, Corichi, Dreyer, Ansari,….)**If LQG really unifies gravity and QM, shouldn’t it**automatically tell us about unifying the rest of physics? S. Bilson-Thompson, F. Markopoulou, ls, hep-th/0603022**Some questions for LQG theories:**• The geometric observables such as area and volume measure the • combinatorics of the graph. But they don’t care how the • edges are braided or knotted. What physical information • does the knotting and braiding correspond to? • What is an observable in quantum gravity? • A conserved quantity. • But what are the conserved quantities? • How do we describe the low energy limit of the theory? • How do we define local without a background? • How do we recognize states that correspond to gravitons or • other local excitations? • What keeps them from loosing coherence by mixing into the • quantum spacetime foam?**Some answers: (Markopoulou et al )**• hep-th/0604120 gr-qc/0510052 • Define local as a characteristic of excitations of the graph states. To identify them in a background independent way look for noiseless subsystems, in the language of quantum information theory. • Identify the ground state as the state in which these propagate coherently, without decoherence. 3) This can happen if there is also an emergent symmetry which protect the excitations from decoherence. Thus the ground state has symmetries because this is necessary for for excitations to persist as pure states.**Suppose we find, a set of emergent symmetries which protect**some local excitations from decoherence. Those local excitations will be emergent particle degrees of freedom.**Two results:**A large class of causal spinnet theories have noiseless subsystems that can be interpreted as local excitations.**Two results:**A large class of causal spinnet theories have noiseless subsystems that can be interpreted as local excitations. There is a class of such models for which the simplest such coherent excitations match the fermons of the standard model.**We study theories based on framed graphs in three spatial**dimensions. The edges are framed: The nodes become trinions: Basis States: Oriented, twisted ribbon graphs, embedded in S3 topology, up to topological class. Labelings: any quantum group…or none.**The evolution moves:**Exchange moves: Expansion moves: The amplitudes: arbitrary functions of the labels Questions: Are there invariants under the moves? What are the simplest states preserved by the moves?**Invariance under the exchange moves:**The topology of the embedding remain unchanged All ribbon invariants are constants of the motion.**Invariance under the exchange moves:**The topology of the embedding: All ribbon invariants For example: the link of the ribbon:**Invariance under the exchange moves:**The topology of the embedding: All ribbon invariants For example: the link of the ribbon:**Invariance under the exchange moves:**The topology of the embedding: All ribbon invariants For example: the link of the ribbon:**Invariance under the exchange moves:**The topology of the embedding: All ribbon invariants For example: the link of the ribbon: But we also want invariance under the expansion moves:**Invariance under the exchange moves:**The topology of the embedding: All ribbon invariants For example: the link of the ribbon: But we also want invariance under the expansion moves: The reduced link of the ribbon is a constant of the motion Reduced = remove all unlinked unknotted circles**Definition of a subsystem: The reduced link disconnects**from the reduced link of the whole graph. This gives conserved quantities labeling subsystems. After an expansion move:**Chirality is also an invariant:**P: • Properties of these invariants: • Distinguish over-crossings from under-crossings • Distinguish twists • Are chiral: distinguish left and right handed structures • These invariants are independent of choice of algebra G and • Evolution amplitudes. They exist for a large class of theories.**What are the simplest subsystems with non-trivial**invariants? Braids on N strands, attached at either or both the top and bottom. The braids and twists are constructed by sequences of moves. The moves form the braid group. To each braid B there is then a group element g(B) which is a product of braiding and twisting. Charge conjugation: take the inverse element. hence reverses twisting.**We can measure complexity by minimal crossings**required to draw them: The simplest conserved braids then have three ribbons and two crossings: Each of these is chiral: Other two crossing braids have unlinked circles. P:**Braids on three ribbons and preons (Bilson-Thompson)**preon ribbon Charge/3 twist P,C P,C triplet 3-strand braid Position?? Position in braid In the preon models there is a rule about mixing charges: No triplet with both positive and negative charges. This becomes: No braid with both left and right twists. In the future we should find a dynamical justification, for the moment we just assume it. The preons are not independent degrees of freedom, just elements of quantum geometry. But braided triplets of them are bound by topological conservation laws from quantum geometry.**Two crossing left handed invariant braids:**No twists:**Two crossing left handed invariant braids:**No twists: 3 + twists**Two crossing left handed invariant braids:**No twists: 3 + twists 1+ twist**Two crossing left handed invariant braids:**No twists: 3 + twists 1+ twist 2+ twists**Two crossing left handed + twist braids:**No twists: 3 + twists Charge= twist/3 nL eL+ 1+ twist dLr dLb dLg 2+ twists uLr uLb uLg**Two crossing left handed + twist braids:**No twists: 3 + twists Charge= twist/3 nL Including the negative twists (charge) these area exactly the 15 left handed states of the first generation of the standard model. Straightforward to prove them distinct. eL+ 1+ twist dLr dLb dLg 2+ twists uLr uLb uLg**The right handed states come from parity inversion:**No twists: 3 - twists nR eR- 1- twist dRr dRb dRg 2- twists uRr uRb uRg**nR**nL eR- eL+ dLr dLb dLg dRr dRb dRg uLr uRr uRb uLb uLg uRg Left Positive twist plus Right negative twist states:**So the emergent symmetries include:**• SU(2)L + SU(2)R + U(1) acts on twistings, keeps place fixed • SU(3) exchanges place in braid, in cases where they are distinct. • P: parity, left to right exchange • C: invert braid vertically (top vrs bottom) • Only 2 neutrino states P: nL = C: nL = nR • 4 of each charged state eL,R+ eL,R- • Fractionally charged states also have color.**Higher generations come from braids with more crossings**generation= crossings -1 Second generation from three crossing braids: From all allowed twists we get a copy of the 1st generation. These give additional states which are SU(3) + SU(2) singlets but come in left and right versions. Could these be the right handed neutrinos?**What we don’t know yet:**• That these excitations are fermions • They are chiral but could be spinors or chiral vectors. • How to best incorporate interactions. • That there are candidate ground states in which these carry • conserved energy and momentum. • What the mass matrix is. • Where P and CP breaking comes from • But work is underway addressed to these and other questions.**CONCLUSIONS:**A large class of causal spin network theories have coherent (noisefree) subsystems which are emergent particle like excitations. SO THESE ARE ALREADY UNIFIED THEORIES! In a large subclass the simplest excitations correspond to the standard model fermions.**CONCLUSIONS:**A large class of causal spin network theories have coherent (noisefree) subsystems which are emergent particle like excitations. SO THESE ARE ALREADY UNIFIED THEORIES! In a large subclass the simplest excitations correspond to the standard model fermions. “The most important lesson I’ve learned in my career is to trust coincidences.” -John Schwarz.**So the standard model fermions naturally occur as coherent**• conserved excitations in a large class of quantum gravity models. • Many open questions…. • Mass matrix: must be a graph invariant. Kauffman bracket?? • Gauge invariance (symmetries are local)?? • Cabibbo and other mixing? • CP violation? Natural source is Imirzi parameter, Soo, Alexander • Emergent effective dynamics?? • But the minimal conclusion is that LQG is an already • unified theory.**Cosmology and disordered locality**F. Markopoulou, C. Prescod Weinstein, LS**The problem of non-locality (F. Markopoulou,**hep-th/0604120 ) Two kinds of locality: Microlocality: connectivity of a single spin net graph causal structure of a single spin foam history. Macrolocality: nearby in the classical metric that emerges Issues: Semiclassical states may involve superpositions of large numbers of graphs. In addition being semiclassical is a coarse grained, low energy property. Could there not be mismatches between micro and macrolocality? What if these are rare, but characterized by the cosmological rather than the Planck scale?**The inverse problem for discrete spacetimes:**Its easy to approximate smooth fields with discrete structures.**The inverse problem for discrete spacetimes:**Its easy to approximate smooth fields with combinatoric structures. But generic graphs do not embed in manifolds of low dimension, preserving even approximate distances. ? Those that do satisfy constraints unnatural in the discrete context,**If locality is an emergent property of graphs, it is**unstable: G: a graph with N nodes that has only links local in an embedding (or whose dual is a good manifold triangulation) in d dimensions.**If locality is an emergent property of graphs, it is**unstable: G: a graph with N nodes that has only links local in an embedding (or whose dual is a good manifold triangulation) in d dimensions. Lets add one more link randomly. Does it conflict with the locality of the embedding?