sundance bilson thompson- braided topology and the emergence of matter
TRANSCRIPT
8/3/2019 Sundance Bilson Thompson- Braided Topology and the Emergence of Matter
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Introduction
Interactions
Braided Networks
Extracting the standard model
Braids and Twists
Braided topology and the emergence of matter
Sundance Bilson-Thompson
School of Chemistry and PhysicsUniversity of Adelaide
Adelaide, Australia
Sundance Bilson-Thompson Braided topology and the emergence of matter
8/3/2019 Sundance Bilson Thompson- Braided Topology and the Emergence of Matter
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Introduction
Interactions
Braided Networks
Extracting the standard model
Braids and Twists
INTRODUCTION
Ideas developed in collaboration/discussion with
Jonathan Hackett
Lou Kauffman
Lee Smolin
Fotini Markopoulou-Kalamara
Isabeau Premont-Schwarz
Yidun Wan
Sundance Bilson-Thompson Braided topology and the emergence of matter
8/3/2019 Sundance Bilson Thompson- Braided Topology and the Emergence of Matter
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Introduction
Interactions
Braided Networks
Extracting the standard model
Braids and Twists
FERMIONS FROM HELONS
Based on the Shupe-Harari models (1979).
Assume three basic components called helons: H +, H −, H 0
Combine into triplets. H + and H − together not allowed.
Possible combinations are;
H + H + H + (e+) H + H + H 0 (qu) H + H 0 H + (qu) H 0 H + H + (qu)
H 0 H 0 H 0 (ν e) H 0 H 0 H + (qd ) H 0 H + H 0 (qd ) H + H 0 H 0 (qd )
H − H − H − (e−) H − H − H 0 (qu) H − H 0 H − (qu) H 0 H − H − (qu)
H 0 H 0 H − (qd ) H 0 H − H 0 (qd ) H − H 0 H 0 (qd )
NB: No anti-neutrino
Permutations define colour.
Sundance Bilson-Thompson Braided topology and the emergence of matter
8/3/2019 Sundance Bilson Thompson- Braided Topology and the Emergence of Matter
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Introduction
Interactions
Braided Networks
Extracting the standard model
Braids and Twists
FERMIONS FROM HELONS
Based on the Shupe-Harari models (1979).
Assume three basic components called helons: H +, H −, H 0
Combine into triplets. H + and H − together not allowed.
Possible combinations are;
H + H + H + (e+) H + H + H 0 (qu) H + H 0 H + (qu) H 0 H + H + (qu)
H 0 H 0 H 0 (ν e) H 0 H 0 H + (qd ) H 0 H + H 0 (qd ) H + H 0 H 0 (qd )
H − H − H − (e−) H − H − H 0 (qu) H − H 0 H − (qu) H 0 H − H − (qu)
H 0 H 0 H − (qd ) H 0 H − H 0 (qd ) H − H 0 H 0 (qd )
NB: No anti-neutrino
Permutations define colour.
Sundance Bilson-Thompson Braided topology and the emergence of matter
8/3/2019 Sundance Bilson Thompson- Braided Topology and the Emergence of Matter
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Introduction
Interactions
Braided Networks
Extracting the standard model
Braids and Twists
FERMIONS FROM HELONS
Based on the Shupe-Harari models (1979).
Assume three basic components called helons: H +, H −, H 0
Combine into triplets. H + and H − together not allowed.
Possible combinations are;
H + H + H + (e+) H + H + H 0 (qu) H + H 0 H + (qu) H 0 H + H + (qu)
H 0 H 0 H 0 (ν e) H 0 H 0 H + (qd ) H 0 H + H 0 (qd ) H + H 0 H 0 (qd )
H − H − H − (e−) H − H − H 0 (qu) H − H 0 H − (qu) H 0 H − H − (qu)
H 0 H 0 H − (qd ) H 0 H − H 0 (qd ) H − H 0 H 0 (qd )
NB: No anti-neutrino
Permutations define colour.
Sundance Bilson-Thompson Braided topology and the emergence of matter
B id d N k
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Introduction
Interactions
Braided Networks
Extracting the standard model
Braids and Twists
RELEVANCE TO LQG
Represent spacetime structure by networks (framed).
Nodes dual to volumes, connections dual to areas.
Twisting and braiding allowed, but these DoFs don’t affectarea and volume operators.
View helons as extended ribbon-like structures
Electric charge of helons is twist of ribbons
Interpret topology of connections between nodes using
helon model
Sundance Bilson-Thompson Braided topology and the emergence of matter
B id d N t k
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Introduction
Interactions
Braided Networks
Extracting the standard model
Braids and Twists
RELEVANCE TO LQG
Represent spacetime structure by networks (framed).
Nodes dual to volumes, connections dual to areas.
Twisting and braiding allowed, but these DoFs don’t affectarea and volume operators.
View helons as extended ribbon-like structures
Electric charge of helons is twist of ribbons
Interpret topology of connections between nodes using
helon model
Sundance Bilson-Thompson Braided topology and the emergence of matter
Braided Networks
8/3/2019 Sundance Bilson Thompson- Braided Topology and the Emergence of Matter
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Introduction
Interactions
Braided Networks
Extracting the standard model
Braids and Twists
RELEVANCE TO LQG
Sundance Bilson-Thompson Braided topology and the emergence of matter
Braided Networks
8/3/2019 Sundance Bilson Thompson- Braided Topology and the Emergence of Matter
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Introduction
Interactions
Braided Networks
Extracting the standard model
Braids and Twists
FIRST GENERATION FERMIONS
Construct half the 1st generation fermions from +ve andnull twists on a braid
Sundance Bilson-Thompson Braided topology and the emergence of matter
Braided Networks
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Introduction
Interactions
Braided Networks
Extracting the standard model
Braids and Twists
FIRST GENERATION FERMIONS
Construct half the 1st generation fermions from +ve andnull twists on a braid
Construct the anti-particles as mirror images
Sundance Bilson-Thompson Braided topology and the emergence of matter
Braided Networks
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Introduction
Interactions
Braided Networks
Extracting the standard model
Braids and Twists
FIRST GENERATION FERMIONS
Construct half the 1st generation fermions from +ve andnull twists on a braid
Construct the anti-particles as mirror images
Sundance Bilson-Thompson Braided topology and the emergence of matter
I t d tiBraided Networks
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Introduction
Interactions
Braided Networks
Extracting the standard model
Braids and Twists
BRAID/TWIST EQUIVALENCE
Fermions are defined by braiding (crossings) and twists.
We can flip a node over to exchange twist ←→ crossing.
This induces one specific triple of twists; [+, +,−]
Sundance Bilson-Thompson Braided topology and the emergence of matter
I t d tiBraided Networks
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Introduction
InteractionsExtracting the standard model
Braids and Twists
BRAID/TWIST EQUIVALENCE
We can imagine the node at the "top", and the legs bent"downwards"
Let σ i be the crossing of leg i over leg i+1
Let σ −1
i be the crossing of leg i under leg i+1;
[+, +,−]↔ σ 1 [−,−, +]↔ σ −
11 (1)
[−, +, +]↔ σ 2 [+,−,−]↔ σ −1
2(2)
σ 1, . . . ,σ N −1 are generators of the braid group on N strands.
Sundance Bilson-Thompson Braided topology and the emergence of matter
IntroductionBraided Networks
8/3/2019 Sundance Bilson Thompson- Braided Topology and the Emergence of Matter
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Introduction
InteractionsExtracting the standard model
Braids and Twists
BRAID/TWIST EQUIVALENCE
We can imagine the node at the "top", and the legs bent"downwards"
Let σ i be the crossing of leg i over leg i+1
Let σ −1
i be the crossing of leg i under leg i+1;
[+, +,−]↔ σ 1 [−,−, +]↔ σ −
11 (1)
[−, +, +]↔ σ 2 [+,−,−]↔ σ −1
2(2)
σ 1, . . . ,σ N −1 are generators of the braid group on N strands.
Sundance Bilson-Thompson Braided topology and the emergence of matter
IntroductionBraided Networks
8/3/2019 Sundance Bilson Thompson- Braided Topology and the Emergence of Matter
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Introduction
InteractionsExtracting the standard model
Braids and Twists
PURE TWIST NUMBERS
We can unravel a braid to obtain its "pure twist form"
The twists define a triplet of numbers [a, b, c]
Braids with the same twist numbers are topologicallyequivalent
Yields the linking numbers for an equivalent link/knot
Only works in 3-valent case
Sundance Bilson-Thompson Braided topology and the emergence of matter
IntroductionBraided Networks
8/3/2019 Sundance Bilson Thompson- Braided Topology and the Emergence of Matter
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Introduction
InteractionsExtracting the standard model
Braids and Twists
KEEPING IT SIMPLE
Can construct arbitrary braids, in general
This “node flipping” trick combines them into equivalenceclasses
(Hopefully) limits the number and type of fermions
If more complex crossings give higher generations, does
this limit the number of generations?
Sundance Bilson-Thompson Braided topology and the emergence of matter
IntroductionBraided Networks
E i h d d d l
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Introduction
InteractionsExtracting the standard model
Braids and Twists
KEEPING IT SIMPLE
Can construct arbitrary braids, in general
This “node flipping” trick combines them into equivalenceclasses
(Hopefully) limits the number and type of fermions
If more complex crossings give higher generations, does
this limit the number of generations?
Sundance Bilson-Thompson Braided topology and the emergence of matter
IntroductionBraided Networks
E t ti th t d d d l
8/3/2019 Sundance Bilson Thompson- Braided Topology and the Emergence of Matter
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InteractionsExtracting the standard model
Braids and Twists
KEEPING IT SIMPLE
Can construct arbitrary braids, in general
This “node flipping” trick combines them into equivalenceclasses
(Hopefully) limits the number and type of fermions
If more complex crossings give higher generations, does
this limit the number of generations?
Sundance Bilson-Thompson Braided topology and the emergence of matter
IntroductionBraided Networks
Extracting the standard model
8/3/2019 Sundance Bilson Thompson- Braided Topology and the Emergence of Matter
http://slidepdf.com/reader/full/sundance-bilson-thompson-braided-topology-and-the-emergence-of-matter 19/31
InteractionsExtracting the standard model
Braids and Twists
KEEPING IT SIMPLE
Can construct arbitrary braids, in general
This “node flipping” trick combines them into equivalence
classes
(Hopefully) limits the number and type of fermions
If more complex crossings give higher generations, does
this limit the number of generations?
Sundance Bilson-Thompson Braided topology and the emergence of matter
Introduction Weak Interactions
8/3/2019 Sundance Bilson Thompson- Braided Topology and the Emergence of Matter
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Interactions Bosons
WEAK INTERACTIONS
Braid product links braids top-to-bottom(σ i . . .σ j)∗ (σ k . . .σ l) = σ i . . .σ jσ k . . .σ l
Twists can spread up and down the strands
Hence charges can be exchanged, turning up quarks into
down quarks, electrons into neutrinos, and so on
Sundance Bilson-Thompson Braided topology and the emergence of matter
Introduction Weak Interactions
8/3/2019 Sundance Bilson Thompson- Braided Topology and the Emergence of Matter
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Interactions Bosons
WEAK INTERACTIONS
Braid product links braids top-to-bottom(σ i . . .σ j)∗ (σ k . . .σ l) = σ i . . .σ jσ k . . .σ l
Twists can spread up and down the strands
Hence charges can be exchanged, turning up quarks into
down quarks, electrons into neutrinos, and so on
Sundance Bilson-Thompson Braided topology and the emergence of matter
Introduction Weak Interactions
8/3/2019 Sundance Bilson Thompson- Braided Topology and the Emergence of Matter
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Interactions Bosons
BOSONS
Weak interactions suggest bosons are braids which inducetrivial permutations
Simplest case;
Other braids which induce trivial permutations are
possible, in principle
Sundance Bilson-Thompson Braided topology and the emergence of matter
Introduction
I i
Weak Interactions
B
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Interactions Bosons
INTERACTIONS IN NETWORKS
Interactions are quite constrained - must not undo all
network structure. Need to create twists in opposing pairs
Braid product requires that braids join ”base to base”
Nodes act like (composite) 4-valent nodesNeed a move that allows opposing twists to form over
4-valent nodes
Sundance Bilson-Thompson Braided topology and the emergence of matter
Introduction
I t ti
Weak Interactions
B
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Interactions Bosons
INTERACTIONS IN NETWORKS
Interactions are quite constrained - must not undo all
network structure. Need to create twists in opposing pairs
Braid product requires that braids join ”base to base”
Nodes act like (composite) 4-valent nodesNeed a move that allows opposing twists to form over
4-valent nodes
Sundance Bilson-Thompson Braided topology and the emergence of matter
Introduction
Interactions
Weak Interactions
Bosons
8/3/2019 Sundance Bilson Thompson- Braided Topology and the Emergence of Matter
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Interactions Bosons
3-VALENT OR 4-VALENT?
Yidun Wan developed ideas of braids on 4-valent
networks, using dual Pachner moves (1-4 and 2-3)
Sundance Bilson-Thompson Braided topology and the emergence of matter
Introduction
Interactions
Weak Interactions
Bosons
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Interactions Bosons
3-VALENT OR 4-VALENT?
Braids can be made to interact
Wan’s braids seemed to naturally fall into two categories(fermions and bosons?)
“Node flipping” only reduces braids to pure twist form in the
3-valent case
Sundance Bilson-Thompson Braided topology and the emergence of matter
Introduction
Interactions
Weak Interactions
Bosons
8/3/2019 Sundance Bilson Thompson- Braided Topology and the Emergence of Matter
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Interactions Bosons
3-VALENT OR 4-VALENT?
Braids can be made to interact
Wan’s braids seemed to naturally fall into two categories(fermions and bosons?)
“Node flipping” only reduces braids to pure twist form in the
3-valent case
Sundance Bilson-Thompson Braided topology and the emergence of matter
Introduction
Interactions
Weak Interactions
Bosons
8/3/2019 Sundance Bilson Thompson- Braided Topology and the Emergence of Matter
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Interactions Bosons
COMBINING THE BEST BITS
Can convert twist to crossings and vice-versa
Take four 3-valent nodes in helon model, to make two
4-valent nodes
Twist in one strand becomes crossing in others before we
shrink them down
Obtain a restricted version of Wan’s braids (one strand is
twist-free)
Sundance Bilson-Thompson Braided topology and the emergence of matter
Introduction
Interactions
Weak Interactions
Bosons
8/3/2019 Sundance Bilson Thompson- Braided Topology and the Emergence of Matter
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te act o s oso s
PROBLEMS THAT KEEP ME AWAKE AT NIGHT
Do we have exotic particle species, or processes?
How do we make interactions occur?
Can we describe Cabbibo mixing, neutrino oscillations?
Origin of inertial mass?
Is there a limit to the number of generations?
Why is the weak interaction so weird?
Sundance Bilson-Thompson Braided topology and the emergence of matter
Introduction
Interactions
Weak Interactions
Bosons
8/3/2019 Sundance Bilson Thompson- Braided Topology and the Emergence of Matter
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PROBLEMS THAT KEEP ME AWAKE AT NIGHT
Do we have exotic particle species, or processes?
How do we make interactions occur?
Can we describe Cabbibo mixing, neutrino oscillations?
Origin of inertial mass?
Is there a limit to the number of generations?
Why is the weak interaction so weird?
Sundance Bilson-Thompson Braided topology and the emergence of matter
Introduction
Interactions
Weak Interactions
Bosons
8/3/2019 Sundance Bilson Thompson- Braided Topology and the Emergence of Matter
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REFERENCES AND FURTHER READING
Related papers
hep-ph/0503213 A topological model of composite preons
(S. Bilson-Thompson)
hep-th/0603022 QG and the standard model (S.
Bilson-Thompson, F. Markopolou, L. Smolin)arXiv:0804.0037 Particle identifications from symmetries of
braided ribbon network invariants (S. Bilson-Thompson, J.
Hackett, L. Kauffman, L. Smolin)
arXiv:0903.1376 Particle topology, braids, and braided belts (S. Bilson-Thompson, J. Hackett, L. Kauffman)
arXiv:0710.1548 Propogation and interaction of chiral
states in Quantum Gravity (Y. Wan, L. Smolin)
Sundance Bilson-Thompson Braided topology and the emergence of matter