3. The project Approach ApplicaNon 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)
Thijs van den Broek (RU Nijmegen) NoncommutaNve geometry & supersymmetry
Wednesday, May 30, 2012
4. The project Approach ApplicaNon 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)
How supersymmetric is the resulNng acNon?
(So: no superfields or anything...)
Thijs van den Broek (RU Nijmegen) NoncommutaNve geometry & supersymmetry
Wednesday, May 30, 2012
5. The project Approach ApplicaNon 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)
How supersymmetric is the resulNng acNon?
(So: no superfields or anything...)
Does it share the merits of ‘ordinary’ supersymmetry?
(E.g. hierarchy problem)
Thijs van den Broek (RU Nijmegen) NoncommutaNve geometry & supersymmetry
Wednesday, May 30, 2012
6. The project Approach ApplicaNon 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)
How supersymmetric is the resulNng acNon?
(So: no superfields or anything...)
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) NoncommutaNve geometry & supersymmetry
Wednesday, May 30, 2012
7. The project Approach ApplicaNon 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)
How supersymmetric is the resulNng acNon?
(So: no superfields or anything...)
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) NoncommutaNve geometry & supersymmetry
Wednesday, May 30, 2012
8. The project Approach ApplicaNon 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) NoncommutaNve geometry & supersymmetry
Wednesday, May 30, 2012
9. The project Approach ApplicaNon 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) NoncommutaNve geometry & supersymmetry
Wednesday, May 30, 2012
10. The project Approach ApplicaNon 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) NoncommutaNve geometry & supersymmetry
Wednesday, May 30, 2012
11. The project Approach ApplicaNon 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.
UnificaNon of coupling constants:
vs
Thijs van den Broek (RU Nijmegen) NoncommutaNve geometry & supersymmetry
Wednesday, May 30, 2012
12. The project Approach ApplicaNon Preliminary results Outlook
MoNvaNng example: super-‐QCD [1] (1/2)
Take:
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) NoncommutaNve geometry & supersymmetry
Wednesday, May 30, 2012
13. The project Approach ApplicaNon Preliminary results Outlook
MoNvaNng example: super-‐QCD [1] (1/2)
Take:
tensored with
where
‘quark’ ‘anNquark’
‘gluino’
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) NoncommutaNve geometry & supersymmetry
Wednesday, May 30, 2012
14. The project Approach ApplicaNon Preliminary results Outlook
MoNvaNng example: super-‐QCD [1] (2/2)
Inner fluctuaNons
parametrize (anN)squark
1TvdB, W. D. van Suijlekom, Physics Letters B 699 (2011), 119–122
Thijs van den Broek (RU Nijmegen) NoncommutaNve geometry & supersymmetry
Wednesday, May 30, 2012
15. The project Approach ApplicaNon Preliminary results Outlook
MoNvaNng example: super-‐QCD [1] (2/2)
Inner fluctuaNons
parametrize (anN)squark
Gauge group : superpartners
1TvdB, W. D. van Suijlekom, Physics Letters B 699 (2011), 119–122
Thijs van den Broek (RU Nijmegen) NoncommutaNve geometry & supersymmetry
Wednesday, May 30, 2012
16. The project Approach ApplicaNon Preliminary results Outlook
MoNvaNng example: super-‐QCD [1] (2/2)
Inner fluctuaNons
parametrize (anN)squark
Gauge group : superpartners
Spectral acNon , extra terms:
Inner product:
1TvdB, W. D. van Suijlekom, Physics Letters B 699 (2011), 119–122
Thijs van den Broek (RU Nijmegen) NoncommutaNve geometry & supersymmetry
Wednesday, May 30, 2012
17. The project Approach ApplicaNon Preliminary results Outlook
MoNvaNng example: super-‐QCD [1] (2/2)
Inner fluctuaNons
parametrize (anN)squark
Gauge group : superpartners
Spectral acNon , extra terms:
Inner product:
SUSY automaNcally broken: (minus) mass terms for squarks.
1TvdB, W. D. van Suijlekom, Physics Letters B 699 (2011), 119–122
Thijs van den Broek (RU Nijmegen) NoncommutaNve geometry & supersymmetry
Wednesday, May 30, 2012
19. The project Approach ApplicaNon Preliminary results Outlook
The approach
Problem: More realisNc situaNons: calculaNons get out of hand
More systemaNcal approach needed (cf. superfields)
Thijs van den Broek (RU Nijmegen) NoncommutaNve geometry & supersymmetry
Wednesday, May 30, 2012
20. The project Approach ApplicaNon Preliminary results Outlook
The approach
Problem: More realisNc situaNons: calculaNons get out of hand
More systemaNcal approach needed (cf. superfields)
Plan: 1) Define ‘supersymmetric spectral triple‘
2) Prove ‘susy spectral triple’ supersymmetric acNon
spectral acNon
3) MSSM as a special case
Thijs van den Broek (RU Nijmegen) NoncommutaNve geometry & supersymmetry
Wednesday, May 30, 2012
21. The project Approach ApplicaNon Preliminary results Outlook
Intermezzo: Krajewski diagrams
Finite spectral triple:
Krajewski diagram:
Thijs van den Broek (RU Nijmegen) NoncommutaNve geometry & supersymmetry
Wednesday, May 30, 2012
22. The project Approach ApplicaNon Preliminary results Outlook
Intermezzo: Krajewski diagrams
Finite spectral triple:
Krajewski diagram:
Thijs van den Broek (RU Nijmegen) NoncommutaNve geometry & supersymmetry
Wednesday, May 30, 2012
23. The project Approach ApplicaNon Preliminary results Outlook
Intermezzo: Krajewski diagrams
Finite spectral triple:
Krajewski diagram: ... ...
...
...
Thijs van den Broek (RU Nijmegen) NoncommutaNve geometry & supersymmetry
Wednesday, May 30, 2012
24. The project Approach ApplicaNon Preliminary results Outlook
Intermezzo: Krajewski diagrams
Finite spectral triple:
Krajewski diagram: ... ...
...
...
Thijs van den Broek (RU Nijmegen) NoncommutaNve geometry & supersymmetry
Wednesday, May 30, 2012
25. The project Approach ApplicaNon Preliminary results Outlook
Intermezzo: Krajewski diagrams
Finite spectral triple:
Krajewski diagram: ... ...
...
...
Thijs van den Broek (RU Nijmegen) NoncommutaNve geometry & supersymmetry
Wednesday, May 30, 2012
26. The project Approach ApplicaNon Preliminary results Outlook
Intermezzo: Krajewski diagrams
Finite spectral triple:
Grading
Krajewski diagram: ... ...
...
...
Thijs van den Broek (RU Nijmegen) NoncommutaNve geometry & supersymmetry
Wednesday, May 30, 2012
27. The project Approach ApplicaNon Preliminary results Outlook
Intermezzo: Krajewski diagrams
Finite spectral triple:
Grading
Krajewski diagram: ... ...
...
...
Thijs van den Broek (RU Nijmegen) NoncommutaNve geometry & supersymmetry
Wednesday, May 30, 2012
28. The project Approach ApplicaNon Preliminary results Outlook
Intermezzo: Krajewski diagrams
Finite spectral triple:
Grading
Dirac operator
Krajewski diagram: ... ...
...
...
Thijs van den Broek (RU Nijmegen) NoncommutaNve geometry & supersymmetry
Wednesday, May 30, 2012
29. The project Approach ApplicaNon Preliminary results Outlook
Intermezzo: Krajewski diagrams
Finite spectral triple:
Grading
Dirac operator
Krajewski diagram: ... ...
...
...
Thijs van den Broek (RU Nijmegen) NoncommutaNve geometry & supersymmetry
Wednesday, May 30, 2012
30. The project Approach ApplicaNon Preliminary results Outlook
Intermezzo: Krajewski diagrams
Finite spectral triple:
Grading
Dirac operator
Krajewski diagram: ... ...
...
...
Thijs van den Broek (RU Nijmegen) NoncommutaNve geometry & supersymmetry
Wednesday, May 30, 2012
31. The project Approach ApplicaNon Preliminary results Outlook
Intermezzo: Krajewski diagrams
Finite spectral triple:
Grading
Dirac operator
Krajewski diagram: ... ...
...
...
Thijs van den Broek (RU Nijmegen) NoncommutaNve geometry & supersymmetry
Wednesday, May 30, 2012
32. The project Approach ApplicaNon Preliminary results Outlook
Intermezzo: Krajewski diagrams
Finite spectral triple:
Grading
Dirac operator ‘KO-‐dimension’
Krajewski diagram: ... ...
...
...
Thijs van den Broek (RU Nijmegen) NoncommutaNve geometry & supersymmetry
Wednesday, May 30, 2012
33. The project Approach ApplicaNon Preliminary results Outlook
Superpartners (1/2)
General scheme as in super-‐QCD:
ParIcle 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) NoncommutaNve geometry & supersymmetry
Wednesday, May 30, 2012
34. The project Approach ApplicaNon Preliminary results Outlook
Superpartners (2/2)
Gauge group:
:
ParIcle Superpartner
fermions: sfermions:
Hilbert space finite Dirac operator
gauge bosons: gauginos:
Dirac operator on Hilbert space (adjoint reps.)
Thijs van den Broek (RU Nijmegen) NoncommutaNve geometry & supersymmetry
Wednesday, May 30, 2012
35. The project Approach ApplicaNon Preliminary results Outlook
Superpartners (2/2)
Gauge group:
:
ParIcle Superpartner
fermions: sfermions:
Hilbert space finite Dirac operator
gauge bosons: gauginos:
Dirac operator on Hilbert space (adjoint reps.)
Thijs van den Broek (RU Nijmegen) NoncommutaNve geometry & supersymmetry
Wednesday, May 30, 2012
36. The project Approach ApplicaNon Preliminary results Outlook
Superpartners (2/2)
Gauge group:
:
ParIcle Superpartner
fermions: sfermions:
Hilbert space finite Dirac operator
gauge bosons: gauginos:
Dirac operator on Hilbert space (adjoint reps.)
Thijs van den Broek (RU Nijmegen) NoncommutaNve geometry & supersymmetry
Wednesday, May 30, 2012
37. The project Approach ApplicaNon Preliminary results Outlook
Superpartners (2/2)
Gauge group:
:
ParIcle Superpartner
fermions: sfermions:
Hilbert space finite Dirac operator
gauge bosons: gauginos:
Dirac operator on Hilbert space (adjoint reps.)
Thijs van den Broek (RU Nijmegen) NoncommutaNve geometry & supersymmetry
Wednesday, May 30, 2012
38. The project Approach ApplicaNon Preliminary results Outlook
Superpartners (2/2)
Gauge group:
:
ParIcle Superpartner
fermions: sfermions:
Hilbert space finite Dirac operator
gauge bosons: gauginos:
Dirac operator on Hilbert space (adjoint reps.)
Thijs van den Broek (RU Nijmegen) NoncommutaNve geometry & supersymmetry
Wednesday, May 30, 2012
39. The project Approach ApplicaNon Preliminary results Outlook
R-‐parity & KO-‐dimension (1/2)
Problem the gaugino-‐sector (adjoint elements of )
incompaNble with
Thijs van den Broek (RU Nijmegen) NoncommutaNve geometry & supersymmetry
Wednesday, May 30, 2012
40. The project Approach ApplicaNon Preliminary results Outlook
R-‐parity & KO-‐dimension (1/2)
Problem the gaugino-‐sector (adjoint elements of )
incompaNble with
In fact parts of finite spectral triple possibly of different KO-‐
dimensions
Thijs van den Broek (RU Nijmegen) NoncommutaNve geometry & supersymmetry
Wednesday, May 30, 2012
41. The project Approach ApplicaNon Preliminary results Outlook
R-‐parity & KO-‐dimension (1/2)
Problem the gaugino-‐sector (adjoint elements of )
incompaNble with
In fact parts of finite spectral triple possibly of different KO-‐
dimensions
SoluNon given:
two spectral triples
of KO-‐dimension (say)
an operator with:
Direct sum:
Thijs van den Broek (RU Nijmegen) NoncommutaNve geometry & supersymmetry
Wednesday, May 30, 2012
42. The project Approach ApplicaNon Preliminary results Outlook
R-‐parity & KO-‐dimension (2/2)
Direct sum:
Use to ‘even out’ the KO dimensions:
three new signs (‘super-‐KO-‐dimension’?)
Thijs van den Broek (RU Nijmegen) NoncommutaNve geometry & supersymmetry
Wednesday, May 30, 2012
43. The project Approach ApplicaNon Preliminary results Outlook
R-‐parity & KO-‐dimension (2/2)
Direct sum:
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) NoncommutaNve geometry & supersymmetry
Wednesday, May 30, 2012
44. The project Approach ApplicaNon Preliminary results Outlook
A supersymmetric spectral triple
DefiniNon We call an R-‐parity extended spectral triple:
a spectral triple that is extended with a grading
saNsfying:
such that
where
with only
We write:
Thijs van den Broek (RU Nijmegen) NoncommutaNve geometry & supersymmetry
Wednesday, May 30, 2012
45. The project Approach ApplicaNon Preliminary results Outlook
A supersymmetric spectral triple
DefiniNon We call an R-‐parity extended spectral triple:
a spectral triple that is extended with a grading
saNsfying:
such that (...)
DefiniNon 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) NoncommutaNve geometry & supersymmetry
Wednesday, May 30, 2012
46. The project Approach ApplicaNon Preliminary results Outlook
A supersymmetric spectral triple
DefiniNon We call an R-‐parity extended spectral triple:
a spectral triple that is extended with a grading
saNsfying:
such that (...)
DefiniNon 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 (sNll) The acNon resulNng from such a spectral triple (via the spectral
acNon principle) is automaNcally supersymmetric.
Thijs van den Broek (RU Nijmegen) NoncommutaNve geometry & supersymmetry
Wednesday, May 30, 2012
48. The project Approach ApplicaIon Preliminary results Outlook
Why the SM?
A nice way to look at things is provided by Chamseddine & Connes [2]:
Look for irreducible soluNons of a pair :
Chamseddine & Connes, Why the Standard Model, 0706.3688v1 [hep-‐th]
Thijs van den Broek (RU Nijmegen) NoncommutaNve geometry & supersymmetry
Wednesday, May 30, 2012
49. The project Approach ApplicaIon Preliminary results Outlook
Why the SM?
A nice way to look at things is provided by Chamseddine & Connes [2]:
Look for irreducible soluNons of a pair :
Either: acNng on
with
Chamseddine & Connes, Why the Standard Model, 0706.3688v1 [hep-‐th]
Thijs van den Broek (RU Nijmegen) NoncommutaNve geometry & supersymmetry
Wednesday, May 30, 2012
50. The project Approach ApplicaIon Preliminary results Outlook
Why the SM?
A nice way to look at things is provided by Chamseddine & Connes [2]:
Look for irreducible soluNons of a pair :
Either: acNng on
with
Or: acNng on
with
Chamseddine & Connes, Why the Standard Model, 0706.3688v1 [hep-‐th]
Thijs van den Broek (RU Nijmegen) NoncommutaNve geometry & supersymmetry
Wednesday, May 30, 2012
51. The project Approach ApplicaIon Preliminary results Outlook
Why the SM?
A nice way to look at things is provided by Chamseddine & Connes [2]:
Look for irreducible soluNons of a pair :
Either: acNng on
with
IncompaNble with
Or: acNng on
with
Chamseddine & Connes, Why the Standard Model, 0706.3688v1 [hep-‐th]
Thijs van den Broek (RU Nijmegen) NoncommutaNve geometry & supersymmetry
Wednesday, May 30, 2012
52. The project Approach ApplicaIon Preliminary results Outlook
Why the SM?
A nice way to look at things is provided by Chamseddine & Connes [2]:
Look for irreducible soluNons of a pair :
Either: acNng on
with
IncompaNble with
Or: acNng on
with
Chamseddine & Connes, Why the Standard Model, 0706.3688v1 [hep-‐th]
Thijs van den Broek (RU Nijmegen) NoncommutaNve geometry & supersymmetry
Wednesday, May 30, 2012
53. The project Approach ApplicaIon Preliminary results Outlook
Why the SM Why the MSSM
ObservaNon:
Given the soluNon for the algebra we we can take not
only but in addiNon to that also the soluNon
for each of the two components of the algebra:
with
Thijs van den Broek (RU Nijmegen) NoncommutaNve geometry & supersymmetry
Wednesday, May 30, 2012
54. The project Approach ApplicaIon Preliminary results Outlook
Why the SM Why the MSSM
ObservaNon:
Given the soluNon for the algebra we we can take not
only but in addiNon to that also the soluNon
for each of the two components of the algebra:
with
There is an R-‐parity operator:
(From )
Thijs van den Broek (RU Nijmegen) NoncommutaNve geometry & supersymmetry
Wednesday, May 30, 2012
55. The project Approach ApplicaIon Preliminary results Outlook
Why the SM Why the MSSM
ObservaNon:
Given the soluNon for the algebra we we can take not
only but in addiNon to that also the soluNon
for each of the two components of the algebra:
with
SM parNcles
There is an R-‐parity operator:
(From )
Thijs van den Broek (RU Nijmegen) NoncommutaNve geometry & supersymmetry
Wednesday, May 30, 2012
56. The project Approach ApplicaIon Preliminary results Outlook
Why the SM Why the MSSM
ObservaNon:
Given the soluNon for the algebra we we can take not
only but in addiNon to that also the soluNon
for each of the two components of the algebra:
with
SM parNcles “Gaugino’s”
There is an R-‐parity operator:
(From )
Thijs van den Broek (RU Nijmegen) NoncommutaNve geometry & supersymmetry
Wednesday, May 30, 2012
57. The project Approach ApplicaIon Preliminary results Outlook
Why the SM Why the MSSM
ObservaNon:
Given the soluNon for the algebra we we can take not
only but in addiNon to that also the soluNon
for each of the two components of the algebra:
with
SM parNcles “Gaugino’s”
There is an R-‐parity operator:
(From )
(Krajewski diagrams: representaNons have a solid fill.)
Thijs van den Broek (RU Nijmegen) NoncommutaNve geometry & supersymmetry
Wednesday, May 30, 2012
58. The project Approach ApplicaIon Preliminary results Outlook
The supersymmetric spectral triple for the MSSM’
Three steps to the (MS)SM
IniNal situaNon:
1.
Thijs van den Broek (RU Nijmegen) NoncommutaNve geometry & supersymmetry
Wednesday, May 30, 2012
59. The project Approach ApplicaIon Preliminary results Outlook
The supersymmetric spectral triple for the MSSM’
Three steps to the (MS)SM
IniNal situaNon:
1.
Thijs van den Broek (RU Nijmegen) NoncommutaNve geometry & supersymmetry
Wednesday, May 30, 2012
60. The project Approach ApplicaIon Preliminary results Outlook
The supersymmetric spectral triple for the MSSM’
Three steps to the (MS)SM
IniNal situaNon:
1.
Thijs van den Broek (RU Nijmegen) NoncommutaNve geometry & supersymmetry
Wednesday, May 30, 2012
61. The project Approach ApplicaIon 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) NoncommutaNve geometry & supersymmetry
Wednesday, May 30, 2012
62. The project Approach ApplicaIon 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) NoncommutaNve geometry & supersymmetry
Wednesday, May 30, 2012
63. The project Approach ApplicaIon 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) NoncommutaNve geometry & supersymmetry
Wednesday, May 30, 2012
64. The project Approach ApplicaIon 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) NoncommutaNve geometry & supersymmetry
Wednesday, May 30, 2012
65. The project Approach ApplicaIon 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) NoncommutaNve geometry & supersymmetry
Wednesday, May 30, 2012
66. The project Approach ApplicaIon 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) NoncommutaNve geometry & supersymmetry
Wednesday, May 30, 2012
67. The project Approach ApplicaIon 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) NoncommutaNve geometry & supersymmetry
Wednesday, May 30, 2012
68. The project Approach ApplicaIon 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) NoncommutaNve geometry & supersymmetry
Wednesday, May 30, 2012
69. The project Approach ApplicaIon 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) NoncommutaNve geometry & supersymmetry
Wednesday, May 30, 2012
70. The project Approach ApplicaIon 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) NoncommutaNve geometry & supersymmetry
Wednesday, May 30, 2012
71. The project Approach ApplicaIon 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) NoncommutaNve geometry & supersymmetry
Wednesday, May 30, 2012
72. The project Approach ApplicaIon 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) NoncommutaNve geometry & supersymmetry
Wednesday, May 30, 2012
73. The project Approach ApplicaIon Preliminary results Outlook
The supersymmetric spectral triple for the MSSM’
Three steps to the (MS)SM: Higgsinos Wino/Zino
+ new parNcles
1.
2.
3.
By adding a Majorana mass
for the right handed neutrino Bino
Gluino
Thijs van den Broek (RU Nijmegen) NoncommutaNve geometry & supersymmetry
Wednesday, May 30, 2012
75. The project Approach ApplicaNon Preliminary results Outlook
Gauge group | UnificaNon
The gauge group:
is sNll
Thijs van den Broek (RU Nijmegen) NoncommutaNve geometry & supersymmetry
Wednesday, May 30, 2012
76. The project Approach ApplicaNon Preliminary results Outlook
Gauge group | UnificaNon
The gauge group:
is sNll
We sNll have coupling constant unificaNon:
Thijs van den Broek (RU Nijmegen) NoncommutaNve geometry & supersymmetry
Wednesday, May 30, 2012
77. The project Approach ApplicaNon Preliminary results Outlook
Gauge group | UnificaNon
The gauge group:
is sNll
We sNll have coupling constant unificaNon:
This happens only because we have more parNcles than the MSSM itself
provides!
Thijs van den Broek (RU Nijmegen) NoncommutaNve geometry & supersymmetry
Wednesday, May 30, 2012
78. The project Approach ApplicaNon 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) NoncommutaNve geometry & supersymmetry
Wednesday, May 30, 2012
79. The project Approach ApplicaNon 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) NoncommutaNve geometry & supersymmetry
Wednesday, May 30, 2012
80. The project Approach ApplicaNon 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) NoncommutaNve geometry & supersymmetry
Wednesday, May 30, 2012
81. The project Approach ApplicaNon Preliminary results Outlook
Comments on supersymmetry
NCG treats bosons & fermions differently
No auxiliary fields (on-‐shell descripNon)
AutomaNcally broken by sfermion masses
Thijs van den Broek (RU Nijmegen) NoncommutaNve geometry & supersymmetry
Wednesday, May 30, 2012
82. The project Approach ApplicaNon Preliminary results Outlook
Comments on supersymmetry
NCG treats bosons & fermions differently
No auxiliary fields (on-‐shell descripNon)
AutomaNcally broken by sfermion masses
Nonetheless: definitely susy-‐like properIes
Thijs van den Broek (RU Nijmegen) NoncommutaNve geometry & supersymmetry
Wednesday, May 30, 2012
83. The project Approach ApplicaNon Preliminary results Outlook
Comments on supersymmetry
NCG treats bosons & fermions differently
No auxiliary fields (on-‐shell descripNon)
AutomaNcally broken by sfermion masses
Nonetheless: definitely susy-‐like properIes
Try to prove susy modulo sfermion potenNal terms:
1. prove susy for both soluNons given by C&C:
Thijs van den Broek (RU Nijmegen) NoncommutaNve geometry & supersymmetry
Wednesday, May 30, 2012
84. The project Approach ApplicaNon Preliminary results Outlook
Comments on supersymmetry
NCG treats bosons & fermions differently
No auxiliary fields (on-‐shell descripNon)
AutomaNcally broken by sfermion masses
Nonetheless: definitely susy-‐like properIes
Try to prove susy modulo sfermion potenNal terms:
1. prove susy for both soluNons given by C&C:
2. prove that susy stays intact upon breaking
Thijs van den Broek (RU Nijmegen) NoncommutaNve geometry & supersymmetry
Wednesday, May 30, 2012