- voorstellen - interrumpeer vooral - preliminary, ‘dust hasn’t settled yet’ so mainly focus on ideas, rather then hardcore calculations
SUPERSYMMETRY NONCOMMUTATIVE& GEOMETRY
Thijs van den Broek Workshop Bayrischzell Radboud Univ. Nijmegen / NIKHEF May 22nd, 2011 INTRODUCTIONIntro The project Approach Applica on Preliminary results Outlook
The research project
Joint work with Walter van Suijlekom and Wim Beenakker
Try to extend the Standard Model from NCG with supersymmetry
Title may be a bit (Everywhere: N=1 supersymmetry , i.e. MSSM) misleading
Merits come from spectral action
Thijs van den Broek (RU Nijmegen) Noncommuta ve geometry & supersymmetry The project Approach Applica on Preliminary results Outlook
The research project
Joint work with Walter van Suijlekom and Wim Beenakker
Try to extend the Standard Model from NCG with supersymmetry
Title may be a bit (Everywhere: N=1 supersymmetry , i.e. MSSM) misleading
How supersymmetric is the resul ng ac on?
Merits come from spectral (So: no superfields or anything...) action
Thijs van den Broek (RU Nijmegen) Noncommuta ve geometry & supersymmetry The project Approach Applica on Preliminary results Outlook
The research project
Joint work with Walter van Suijlekom and Wim Beenakker
Try to extend the Standard Model from NCG with supersymmetry
Title may be a bit (Everywhere: N=1 supersymmetry , i.e. MSSM) misleading
How supersymmetric is the resul ng ac on?
Merits come from spectral (So: no superfields or anything...) action
Does it share the merits of ‘ordinary’ supersymmetry? (E.g. hierarchy problem)
Thijs van den Broek (RU Nijmegen) Noncommuta ve geometry & supersymmetry The project Approach Applica on Preliminary results Outlook
The research project
Joint work with Walter van Suijlekom and Wim Beenakker
Try to extend the Standard Model from NCG with supersymmetry
Title may be a bit (Everywhere: N=1 supersymmetry , i.e. MSSM) misleading
How supersymmetric is the resul ng ac on?
Merits come from spectral (So: no superfields or anything...) action
Does it share the merits of ‘ordinary’ supersymmetry? (E.g. hierarchy problem)
Can we predict anything from this? (E.g. scalar masses, c.f Higgs mass)
Thijs van den Broek (RU Nijmegen) Noncommuta ve geometry & supersymmetry The project Approach Applica on Preliminary results Outlook
The research project
Joint work with Walter van Suijlekom and Wim Beenakker
Try to extend the Standard Model from NCG with supersymmetry
Title may be a bit (Everywhere: N=1 supersymmetry , i.e. MSSM) misleading
How supersymmetric is the resul ng ac on?
Merits come from spectral (So: no superfields or anything...) action
Does it share the merits of ‘ordinary’ supersymmetry? (E.g. hierarchy problem)
Can we predict anything from this? (E.g. scalar masses, c.f Higgs mass) Why want this?
Thijs van den Broek (RU Nijmegen) Noncommuta ve geometry & supersymmetry The project Approach Applica on Preliminary results Outlook
The research project
Joint work with Walter van Suijlekom and Wim Beenakker
Try to extend the Standard Model from NCG with supersymmetry (Everywhere: N=1 supersymmetry , i.e. MSSM)
Why want this?
Thijs van den Broek (RU Nijmegen) Noncommuta ve geometry & supersymmetry The project Approach Applica on Preliminary results Outlook
The research project
Joint work with Walter van Suijlekom and Wim Beenakker
Try to extend the Standard Model from NCG with supersymmetry (Everywhere: N=1 supersymmetry , i.e. MSSM)
Why want this?
Promising BSM candidate.
Thijs van den Broek (RU Nijmegen) Noncommuta ve geometry & supersymmetry The project Approach Applica on Preliminary results Outlook
The research project
Joint work with Walter van Suijlekom and Wim Beenakker
Try to extend the Standard Model from NCG with supersymmetry (Everywhere: N=1 supersymmetry , i.e. MSSM)
Why want this?
Promising BSM candidate.
To see what NCG might have in store for us.
Thijs van den Broek (RU Nijmegen) Noncommuta ve geometry & supersymmetry The project Approach Applica on Preliminary results Outlook
The research project
Joint work with Walter van Suijlekom and Wim Beenakker
Try to extend the Standard Model from NCG with supersymmetry (Everywhere: N=1 supersymmetry , i.e. MSSM)
Why want this?
Promising BSM candidate.
To see what NCG might have in store for us.
Unifica on of coupling constants:
vs
Thijs van den Broek (RU Nijmegen) Noncommuta ve geometry & supersymmetry The project Approach Applica on Preliminary results Outlook
Mo va ng example: super-QCD [1] (1/2) Opmerken dat canoniek spectraal tripel voor de rest van het praatje geimpliceerd is.
Take: - 3, 3^o: Breakdown vanaf SM - Dus je voegt M_3(C) toe aan de eindige Hilbert ruimte. tensored with
where
parametrizing a 3-tuple and its conjugate.
1TvdB, W. D. van Suijlekom, Physics Letters B 699 (2011), 119–122
Thijs van den Broek (RU Nijmegen) Noncommuta ve geometry & supersymmetry The project Approach Applica on Preliminary results Outlook
Mo va ng example: super-QCD [1] (1/2) Opmerken dat canoniek spectraal tripel voor de rest van het praatje geimpliceerd is.
Take: - 3, 3^o: Breakdown vanaf SM - Dus je voegt M_3(C) toe aan de eindige Hilbert ruimte. tensored with
where
parametrizing a 3-tuple and its conjugate.
1TvdB, W. D. van Suijlekom, Physics Letters B 699 (2011), 119–122
Thijs van den Broek (RU Nijmegen) Noncommuta ve geometry & supersymmetry The project Approach Applica on Preliminary results Outlook
Mo va ng example: super-QCD [1] (2/2)
Inner fluctua ons
parametrize (an )squark
Extra termen = tov ‘qcd’
Inner product goed?
1TvdB, W. D. van Suijlekom, Physics Letters B 699 (2011), 119–122
Thijs van den Broek (RU Nijmegen) Noncommuta ve geometry & supersymmetry The project Approach Applica on Preliminary results Outlook
Mo va ng example: super-QCD [1] (2/2)
Inner fluctua ons
parametrize (an )squark
Gauge group : superpartners
Extra termen = tov ‘qcd’
Inner product goed?
1TvdB, W. D. van Suijlekom, Physics Letters B 699 (2011), 119–122
Thijs van den Broek (RU Nijmegen) Noncommuta ve geometry & supersymmetry The project Approach Applica on Preliminary results Outlook
Mo va ng example: super-QCD [1] (2/2)
Inner fluctua ons
parametrize (an )squark
Gauge group : superpartners
Spectral ac on , extra terms:
Extra termen = tov ‘qcd’
Inner product: Inner product goed?
1TvdB, W. D. van Suijlekom, Physics Letters B 699 (2011), 119–122
Thijs van den Broek (RU Nijmegen) Noncommuta ve geometry & supersymmetry The project Approach Applica on Preliminary results Outlook
Mo va ng example: super-QCD [1] (2/2)
Inner fluctua ons
parametrize (an )squark
Gauge group : superpartners
Spectral ac on , extra terms:
Extra termen = tov ‘qcd’
Inner product: Inner product goed?
SUSY automa cally broken: (minus) mass terms for squarks.
1TvdB, W. D. van Suijlekom, Physics Letters B 699 (2011), 119–122
Thijs van den Broek (RU Nijmegen) Noncommuta ve geometry & supersymmetry APPROACHAPPR The project Approach Applica on Preliminary results Outlook
The approach
Problem: More realis c situa ons: calcula ons get out of hand
More systema cal approach needed (cf. superfields)
Spectral triple is the basic object: want susy at that level
Thijs van den Broek (RU Nijmegen) Noncommuta ve geometry & supersymmetry The project Approach Applica on Preliminary results Outlook
The approach
Problem: More realis c situa ons: calcula ons get out of hand
More systema cal approach needed (cf. superfields)
Plan: 1) Define ‘supersymmetric spectral triple‘
Spectral triple is the basic object: want susy at that level
2) Prove ‘susy spectral triple’ supersymmetric ac on
spectral ac on
3) MSSM as a special case
Thijs van den Broek (RU Nijmegen) Noncommuta ve geometry & supersymmetry The project Approach Applica on Preliminary results Outlook
Intermezzo: Krajewski diagrams
Finite spectral triple: Waarom deze slide: dingen wat concreter maken. Alle eigenschappen ve eindig spectraal tripel af te lezen aan K diagram
Krajewski diagram:
Thijs van den Broek (RU Nijmegen) Noncommuta ve geometry & supersymmetry The project Approach Applica on Preliminary results Outlook
Intermezzo: Krajewski diagrams
Finite spectral triple: Waarom deze slide: dingen wat concreter maken. Alle eigenschappen ve eindig spectraal tripel af te lezen aan K diagram
Krajewski diagram:
Thijs van den Broek (RU Nijmegen) Noncommuta ve geometry & supersymmetry The project Approach Applica on Preliminary results Outlook
Intermezzo: Krajewski diagrams
Finite spectral triple: Waarom deze slide: dingen wat concreter maken. Alle eigenschappen ve eindig spectraal tripel af te lezen aan K diagram
Krajewski diagram: ......
Thijs van den Broek (RU Nijmegen) Noncommuta ve geometry & supersymmetry The project Approach Applica on Preliminary results Outlook
Intermezzo: Krajewski diagrams
Finite spectral triple: Waarom deze slide: dingen wat concreter maken. Alle eigenschappen ve eindig spectraal tripel af te lezen aan K diagram
Krajewski diagram: ......
Thijs van den Broek (RU Nijmegen) Noncommuta ve geometry & supersymmetry The project Approach Applica on Preliminary results Outlook
Intermezzo: Krajewski diagrams
Finite spectral triple: Waarom deze slide: dingen wat concreter maken. Alle eigenschappen ve eindig spectraal tripel af te lezen aan K diagram
Krajewski diagram: ......
Thijs van den Broek (RU Nijmegen) Noncommuta ve geometry & supersymmetry The project Approach Applica on Preliminary results Outlook
Intermezzo: Krajewski diagrams
Finite spectral triple: Waarom deze slide: dingen wat concreter maken. Alle eigenschappen ve eindig spectraal tripel af te lezen aan K diagram
Grading
Krajewski diagram: ......
Thijs van den Broek (RU Nijmegen) Noncommuta ve geometry & supersymmetry The project Approach Applica on Preliminary results Outlook
Intermezzo: Krajewski diagrams
Finite spectral triple: Waarom deze slide: dingen wat concreter maken. Alle eigenschappen ve eindig spectraal tripel af te lezen aan K diagram
Grading
Krajewski diagram: ......
Thijs van den Broek (RU Nijmegen) Noncommuta ve geometry & supersymmetry The project Approach Applica on Preliminary results Outlook
Intermezzo: Krajewski diagrams
Finite spectral triple: Waarom deze slide: dingen wat concreter maken. Alle eigenschappen ve eindig spectraal tripel af te lezen aan K diagram
Grading
Dirac operator
Krajewski diagram: ......
Thijs van den Broek (RU Nijmegen) Noncommuta ve geometry & supersymmetry The project Approach Applica on Preliminary results Outlook
Intermezzo: Krajewski diagrams
Finite spectral triple: Waarom deze slide: dingen wat concreter maken. Alle eigenschappen ve eindig spectraal tripel af te lezen aan K diagram
Grading
Dirac operator
Krajewski diagram: ......
Thijs van den Broek (RU Nijmegen) Noncommuta ve geometry & supersymmetry The project Approach Applica on Preliminary results Outlook
Intermezzo: Krajewski diagrams
Finite spectral triple: Waarom deze slide: dingen wat concreter maken. Alle eigenschappen ve eindig spectraal tripel af te lezen aan K diagram
Grading
Dirac operator
Krajewski diagram: ......
Thijs van den Broek (RU Nijmegen) Noncommuta ve geometry & supersymmetry The project Approach Applica on Preliminary results Outlook
Intermezzo: Krajewski diagrams
Finite spectral triple: Waarom deze slide: dingen wat concreter maken. Alle eigenschappen ve eindig spectraal tripel af te lezen aan K diagram
Grading
Dirac operator
Krajewski diagram: ......
Thijs van den Broek (RU Nijmegen) Noncommuta ve geometry & supersymmetry The project Approach Applica on Preliminary results Outlook
Intermezzo: Krajewski diagrams
Finite spectral triple: Waarom deze slide: dingen wat concreter maken. Alle eigenschappen ve eindig spectraal tripel af te lezen aan K diagram
Grading
Dirac operator ‘KO-dimension’
Krajewski diagram: ......
Thijs van den Broek (RU Nijmegen) Noncommuta ve geometry & supersymmetry The project Approach Applica on Preliminary results Outlook
Superpartners (1/2)
General scheme as in super-QCD:
Par cle Superpartner
fermions: sfermions: Hilbert space finite Dirac operator
gauge bosons: gauginos: Dirac operator on Hilbert space (adjoint reps.)
Higgs: Higgsinos: finite Dirac operator Hilbert space
Thijs van den Broek (RU Nijmegen) Noncommuta ve geometry & supersymmetry The project Approach Applica on Preliminary results Outlook
Superpartners (2/2)
Gauge group:
:
Par cle Superpartner
fermions: sfermions: case of super QCD fits in Hilbert space finite Dirac operator
gauge bosons: gauginos: Dirac operator on Hilbert space (adjoint reps.)
Thijs van den Broek (RU Nijmegen) Noncommuta ve geometry & supersymmetry The project Approach Applica on Preliminary results Outlook
Superpartners (2/2)
Gauge group:
:
Par cle Superpartner
fermions: sfermions: case of super QCD fits in Hilbert space finite Dirac operator
gauge bosons: gauginos: Dirac operator on Hilbert space (adjoint reps.)
Thijs van den Broek (RU Nijmegen) Noncommuta ve geometry & supersymmetry The project Approach Applica on Preliminary results Outlook
Superpartners (2/2)
Gauge group:
:
Par cle Superpartner
fermions: sfermions: case of super QCD fits in Hilbert space finite Dirac operator
gauge bosons: gauginos: Dirac operator on Hilbert space (adjoint reps.)
Thijs van den Broek (RU Nijmegen) Noncommuta ve geometry & supersymmetry The project Approach Applica on Preliminary results Outlook
Superpartners (2/2)
Gauge group:
:
Par cle Superpartner
fermions: sfermions: case of super QCD fits in Hilbert space finite Dirac operator
gauge bosons: gauginos: Dirac operator on Hilbert space (adjoint reps.)
Thijs van den Broek (RU Nijmegen) Noncommuta ve geometry & supersymmetry The project Approach Applica on Preliminary results Outlook
Superpartners (2/2)
Gauge group:
:
Par cle Superpartner
fermions: sfermions: case of super QCD fits in Hilbert space finite Dirac operator
gauge bosons: gauginos: Dirac operator on Hilbert space (adjoint reps.)
Thijs van den Broek (RU Nijmegen) Noncommuta ve geometry & supersymmetry The project Approach Applica on Preliminary results Outlook
R-parity & KO-dimension (1/2)
Problem the gaugino-sector (adjoint elements of ) incompa ble with
Thijs van den Broek (RU Nijmegen) Noncommuta ve geometry & supersymmetry The project Approach Applica on Preliminary results Outlook
R-parity & KO-dimension (1/2)
Problem the gaugino-sector (adjoint elements of ) incompa ble with
In fact parts of finite spectral triple possibly of different KO- dimensions
Thijs van den Broek (RU Nijmegen) Noncommuta ve geometry & supersymmetry The project Approach Applica on Preliminary results Outlook
R-parity & KO-dimension (1/2)
Problem the gaugino-sector (adjoint elements of ) incompa ble with
In fact parts of finite spectral triple possibly of different KO- dimensions
Solu on given: two spectral triples of KO-dimension (say)
an operator with:
Direct sum:
Thijs van den Broek (RU Nijmegen) Noncommuta ve geometry & supersymmetry The project Approach Applica on Preliminary results Outlook
R-parity & KO-dimension (2/2)
Onderstrepen: een manier Direct sum: om het te zien.
Use to ‘even out’ the KO dimensions:
three new signs (‘super-KO-dimension’?)
Thijs van den Broek (RU Nijmegen) Noncommuta ve geometry & supersymmetry The project Approach Applica on Preliminary results Outlook
R-parity & KO-dimension (2/2)
Onderstrepen: een manier Direct sum: om het te zien.
Use to ‘even out’ the KO dimensions:
three new signs (‘super-KO-dimension’?)
Example KO-dimensions 6 (SM) and 0 (gauginos) has:
i.e.
Role ‘R-parity’, where
Thijs van den Broek (RU Nijmegen) Noncommuta ve geometry & supersymmetry The project Approach Applica on Preliminary results Outlook
A supersymmetric spectral triple
Defini on We call an R-parity extended spectral triple:
a spectral triple that is extended with a grading sa sfying:
such that where
with only
We write:
Thijs van den Broek (RU Nijmegen) Noncommuta ve geometry & supersymmetry The project Approach Applica on Preliminary results Outlook
A supersymmetric spectral triple
Defini on We call an R-parity extended spectral triple:
a spectral triple that is extended with a grading sa sfying:
such that (...) Defini on An R-parity extended spectral triple is supersymmetric when: each element that transforms under the gauge group comes in both -values. all allowed components of the - part of the Dirac operator are nonzero.
Thijs van den Broek (RU Nijmegen) Noncommuta ve geometry & supersymmetry The project Approach Applica on Preliminary results Outlook
A supersymmetric spectral triple
Defini on We call an R-parity extended spectral triple:
a spectral triple that is extended with a grading sa sfying:
such that (...) Defini on An R-parity extended spectral triple is supersymmetric when: each element that transforms under the gauge group comes in both -values. all allowed components of the - part of the Dirac operator are nonzero. Hope (s ll) The ac on resul ng from such a spectral triple (via the spectral ac on principle) is automa cally supersymmetric.
Thijs van den Broek (RU Nijmegen) Noncommuta ve geometry & supersymmetry APPLICATIONAPPR The project Approach Applica on Preliminary results Outlook
Why the SM?
A nice way to look at things is provided by Chamseddine & Connes [2]:
Look for irreducible solu ons of a pair :
Chamseddine & Connes, Why the Standard Model, 0706.3688v1 [hep-th]
Thijs van den Broek (RU Nijmegen) Noncommuta ve geometry & supersymmetry The project Approach Applica on Preliminary results Outlook
Why the SM?
A nice way to look at things is provided by Chamseddine & Connes [2]:
Look for irreducible solu ons of a pair :
Either: ac ng on with
Chamseddine & Connes, Why the Standard Model, 0706.3688v1 [hep-th]
Thijs van den Broek (RU Nijmegen) Noncommuta ve geometry & supersymmetry The project Approach Applica on Preliminary results Outlook
Why the SM?
A nice way to look at things is provided by Chamseddine & Connes [2]:
Look for irreducible solu ons of a pair :
Either: ac ng on with
Or: ac ng on
with
Chamseddine & Connes, Why the Standard Model, 0706.3688v1 [hep-th]
Thijs van den Broek (RU Nijmegen) Noncommuta ve geometry & supersymmetry The project Approach Applica on Preliminary results Outlook
Why the SM?
A nice way to look at things is provided by Chamseddine & Connes [2]:
Look for irreducible solu ons of a pair :
Either: ac ng on with Incompa ble with
Or: ac ng on
with
Chamseddine & Connes, Why the Standard Model, 0706.3688v1 [hep-th]
Thijs van den Broek (RU Nijmegen) Noncommuta ve geometry & supersymmetry The project Approach Applica on Preliminary results Outlook
Why the SM?
A nice way to look at things is provided by Chamseddine & Connes [2]:
Look for irreducible solu ons of a pair :
Either: ac ng on with Incompa ble with
Or: ac ng on
with
Chamseddine & Connes, Why the Standard Model, 0706.3688v1 [hep-th]
Thijs van den Broek (RU Nijmegen) Noncommuta ve geometry & supersymmetry The project Approach Applica on Preliminary results Outlook
Why the SM Why the MSSM
Observa on: Given the solu on for the algebra we we can take not only but in addi on to that also the solu on for each of the two components of the algebra:
with
Thijs van den Broek (RU Nijmegen) Noncommuta ve geometry & supersymmetry The project Approach Applica on Preliminary results Outlook
Why the SM Why the MSSM
Observa on: Given the solu on for the algebra we we can take not only but in addi on to that also the solu on for each of the two components of the algebra:
with
There is an R-parity operator:
(From )
Thijs van den Broek (RU Nijmegen) Noncommuta ve geometry & supersymmetry The project Approach Applica on Preliminary results Outlook
Why the SM Why the MSSM
Observa on: Given the solu on for the algebra we we can take not only but in addi on to that also the solu on for each of the two components of the algebra:
with
SM par cles There is an R-parity operator:
(From )
Thijs van den Broek (RU Nijmegen) Noncommuta ve geometry & supersymmetry The project Approach Applica on Preliminary results Outlook
Why the SM Why the MSSM
Observa on: Given the solu on for the algebra we we can take not only but in addi on to that also the solu on for each of the two components of the algebra:
with
SM par cles “Gaugino’s” There is an R-parity operator:
(From )
Thijs van den Broek (RU Nijmegen) Noncommuta ve geometry & supersymmetry The project Approach Applica on Preliminary results Outlook
Why the SM Why the MSSM
Observa on: Given the solu on for the algebra we we can take not only but in addi on to that also the solu on for each of the two components of the algebra:
with
SM par cles “Gaugino’s” There is an R-parity operator:
(From )
(Krajewski diagrams: representa ons have a solid fill.)
Thijs van den Broek (RU Nijmegen) Noncommuta ve geometry & supersymmetry The project Approach Applica on Preliminary results Outlook
The supersymmetric spectral triple for the MSSM’
Three steps to the (MS)SM
Ini al situa on: 1.
Thijs van den Broek (RU Nijmegen) Noncommuta ve geometry & supersymmetry The project Approach Applica on Preliminary results Outlook
The supersymmetric spectral triple for the MSSM’
Three steps to the (MS)SM
Ini al situa on: 1.
Thijs van den Broek (RU Nijmegen) Noncommuta ve geometry & supersymmetry The project Approach Applica on Preliminary results Outlook
The supersymmetric spectral triple for the MSSM’
Three steps to the (MS)SM
Ini al situa on: 1.
Thijs van den Broek (RU Nijmegen) Noncommuta ve geometry & supersymmetry The project Approach Applica on Preliminary results Outlook
The supersymmetric spectral triple for the MSSM’
Three steps to the (MS)SM: A vs A^C
1.
2.
As the result of a grading:
Thijs van den Broek (RU Nijmegen) Noncommuta ve geometry & supersymmetry The project Approach Applica on Preliminary results Outlook
The supersymmetric spectral triple for the MSSM’
Three steps to the (MS)SM: A vs A^C
1.
2.
As the result of a grading:
Thijs van den Broek (RU Nijmegen) Noncommuta ve geometry & supersymmetry The project Approach Applica on Preliminary results Outlook
The supersymmetric spectral triple for the MSSM’
Three steps to the (MS)SM: A vs A^C
1.
2.
As the result of a grading:
Thijs van den Broek (RU Nijmegen) Noncommuta ve geometry & supersymmetry The project Approach Applica on Preliminary results Outlook
The supersymmetric spectral triple for the MSSM’
Three steps to the (MS)SM: A vs A^C
1.
2.
As the result of a grading:
Thijs van den Broek (RU Nijmegen) Noncommuta ve geometry & supersymmetry The project Approach Applica on Preliminary results Outlook
The supersymmetric spectral triple for the MSSM’
Three steps to the (MS)SM: A vs A^C
1.
2.
As the result of a grading:
Thijs van den Broek (RU Nijmegen) Noncommuta ve geometry & supersymmetry The project Approach Applica on Preliminary results Outlook
The supersymmetric spectral triple for the MSSM’
Three steps to the (MS)SM: A vs A^C
1.
2.
As the result of a grading:
Thijs van den Broek (RU Nijmegen) Noncommuta ve geometry & supersymmetry The project Approach Applica on Preliminary results Outlook
The supersymmetric spectral triple for the MSSM’
Three steps to the (MS)SM:
1.
2.
3.
By adding a Majorana mass for the right handed neutrino
Thijs van den Broek (RU Nijmegen) Noncommuta ve geometry & supersymmetry The project Approach Applica on Preliminary results Outlook
The supersymmetric spectral triple for the MSSM’
Three steps to the (MS)SM:
1.
2.
3.
By adding a Majorana mass for the right handed neutrino
Thijs van den Broek (RU Nijmegen) Noncommuta ve geometry & supersymmetry The project Approach Applica on Preliminary results Outlook
The supersymmetric spectral triple for the MSSM’
Three steps to the (MS)SM:
1.
2.
3.
By adding a Majorana mass for the right handed neutrino Bino
Thijs van den Broek (RU Nijmegen) Noncommuta ve geometry & supersymmetry The project Approach Applica on Preliminary results Outlook
The supersymmetric spectral triple for the MSSM’
Three steps to the (MS)SM:
1.
2.
3.
By adding a Majorana mass for the right handed neutrino Bino
Gluino
Thijs van den Broek (RU Nijmegen) Noncommuta ve geometry & supersymmetry The project Approach Applica on Preliminary results Outlook
The supersymmetric spectral triple for the MSSM’
Three steps to the (MS)SM: Wino/Zino
1.
2.
3.
By adding a Majorana mass for the right handed neutrino Bino
Gluino
Thijs van den Broek (RU Nijmegen) Noncommuta ve geometry & supersymmetry The project Approach Applica on Preliminary results Outlook
The supersymmetric spectral triple for the MSSM’
Three steps to the (MS)SM: Higgsinos Wino/Zino
1.
2.
3.
By adding a Majorana mass for the right handed neutrino Bino
Gluino
Thijs van den Broek (RU Nijmegen) Noncommuta ve geometry & supersymmetry The project Approach Applica on Preliminary results Outlook
The supersymmetric spectral triple for the MSSM’
Three steps to the (MS)SM: Higgsinos Wino/Zino + new par cles
1.
2.
3.
By adding a Majorana mass for the right handed neutrino Bino
Gluino
Thijs van den Broek (RU Nijmegen) Noncommuta ve geometry & supersymmetry PRELIMINARYPrel RESULTS The project Approach Applica on Preliminary results Outlook
Gauge group | Unifica on
The gauge group:
is s ll
Thijs van den Broek (RU Nijmegen) Noncommuta ve geometry & supersymmetry The project Approach Applica on Preliminary results Outlook
Gauge group | Unifica on
The gauge group:
is s ll
We s ll have coupling constant unifica on:
Thijs van den Broek (RU Nijmegen) Noncommuta ve geometry & supersymmetry The project Approach Applica on Preliminary results Outlook
Gauge group | Unifica on
The gauge group:
is s ll
We s ll have coupling constant unifica on:
This happens only because we have more par cles than the MSSM itself provides!
Thijs van den Broek (RU Nijmegen) Noncommuta ve geometry & supersymmetry The project Approach Applica on Preliminary results Outlook
Fermion doubling | Chiral anomalies
Copies of fermions exceed those of gaugino’s by a factor of four. Change inner product in:
Thijs van den Broek (RU Nijmegen) Noncommuta ve geometry & supersymmetry The project Approach Applica on Preliminary results Outlook
Fermion doubling | Chiral anomalies
Copies of fermions exceed those of gaugino’s by a factor of four. Change inner product in:
Hypercharges:
Thijs van den Broek (RU Nijmegen) Noncommuta ve geometry & supersymmetry The project Approach Applica on Preliminary results Outlook
Fermion doubling | Chiral anomalies
Copies of fermions exceed those of gaugino’s by a factor of four. Change inner product in:
Hypercharges:
All come in pairs of opposite charges: chiral anomalies cancel
Thijs van den Broek (RU Nijmegen) Noncommuta ve geometry & supersymmetry The project Approach Applica on Preliminary results Outlook
Comments on supersymmetry
NCG treats bosons & fermions differently
No auxiliary fields (on-shell descrip on)
Automa cally broken by sfermion masses
Thijs van den Broek (RU Nijmegen) Noncommuta ve geometry & supersymmetry The project Approach Applica on Preliminary results Outlook
Comments on supersymmetry
NCG treats bosons & fermions differently
No auxiliary fields (on-shell descrip on)
Automa cally broken by sfermion masses
Nonetheless: definitely susy-like proper es
Thijs van den Broek (RU Nijmegen) Noncommuta ve geometry & supersymmetry The project Approach Applica on Preliminary results Outlook
Comments on supersymmetry
NCG treats bosons & fermions differently
No auxiliary fields (on-shell descrip on)
Automa cally broken by sfermion masses
Nonetheless: definitely susy-like proper es
Try to prove susy modulo sfermion poten al terms:
1. prove susy for both solu ons given by C&C:
Thijs van den Broek (RU Nijmegen) Noncommuta ve geometry & supersymmetry The project Approach Applica on Preliminary results Outlook
Comments on supersymmetry
NCG treats bosons & fermions differently
No auxiliary fields (on-shell descrip on)
Automa cally broken by sfermion masses
Nonetheless: definitely susy-like proper es
Try to prove susy modulo sfermion poten al terms:
1. prove susy for both solu ons given by C&C:
2. prove that susy stays intact upon breaking
Thijs van den Broek (RU Nijmegen) Noncommuta ve geometry & supersymmetry OUTLOOKOUT The project Approach Applica on Preliminary results Outlook
Summary & Outlook
✓ ‘Supersymmetric spectral triple’ ? Supersymmetric ac on / explicit susy transforma ons
Thijs van den Broek (RU Nijmegen) Noncommuta ve geometry & supersymmetry The project Approach Applica on Preliminary results Outlook
Summary & Outlook
✓ ‘Supersymmetric spectral triple’ ? Supersymmetric ac on / explicit susy transforma ons ✓ Applied to SM-algebra gives MSSM’ ✓ Gauge group intact, anomaly free theory ✓ Coupling constant unifica on ? Role & effects extra par cles?
Thijs van den Broek (RU Nijmegen) Noncommuta ve geometry & supersymmetry The project Approach Applica on Preliminary results Outlook
Summary & Outlook
✓ ‘Supersymmetric spectral triple’ ? Supersymmetric ac on / explicit susy transforma ons ✓ Applied to SM-algebra gives MSSM’ ✓ Gauge group intact, anomaly free theory ✓ Coupling constant unifica on ? Role & effects extra par cles?
? Predic ons?
Thijs van den Broek (RU Nijmegen) Noncommuta ve geometry & supersymmetry The project Approach Applica on Preliminary results Outlook
Summary & Outlook
✓ ‘Supersymmetric spectral triple’ ? Supersymmetric ac on / explicit susy transforma ons ✓ Applied to SM-algebra gives MSSM’ ✓ Gauge group intact, anomaly free theory ✓ Coupling constant unifica on ? Role & effects extra par cles?
? Predic ons? For more (conclusive) results: stay tuned!
Thijs van den Broek (RU Nijmegen) Noncommuta ve geometry & supersymmetry