NYU AD 2020 H. Sati
Transcript of NYU AD 2020 H. Sati
![Page 1: NYU AD 2020 H. Sati](https://reader033.fdocuments.us/reader033/viewer/2022051922/628549f72fd89436743609e5/html5/thumbnails/1.jpg)
Urs Schreiber
(New York University, Abu Dhabi & Czech Academy of Science, Prague)
Microscopic brane physics from Cohomotopy
talk atM-Theory and Mathematics
NYU AD 2020
based on joint work with
H. Sati
ncatlab.org/schreiber/show/Microscopic+Brane+Physics+from+Cohomotopy
![Page 2: NYU AD 2020 H. Sati](https://reader033.fdocuments.us/reader033/viewer/2022051922/628549f72fd89436743609e5/html5/thumbnails/2.jpg)
0) Introduction
1) Microscopic Brane Charge
2) Orientifold Tadpole Cancellation
3) D6⊥D8D6⊥D8D6⊥D8 -Brane Intersections
4) Hanany-Witten Theory
5) Chan-Paton Data
6) BMN Matrix Model States
7) M2/M5 Brane Bound States
![Page 3: NYU AD 2020 H. Sati](https://reader033.fdocuments.us/reader033/viewer/2022051922/628549f72fd89436743609e5/html5/thumbnails/3.jpg)
(0)
Introduction
Open Problem M and Hypothesis H
back to top
3
![Page 4: NYU AD 2020 H. Sati](https://reader033.fdocuments.us/reader033/viewer/2022051922/628549f72fd89436743609e5/html5/thumbnails/4.jpg)
Open problem QCD
Confined QCD“Millennium problem”- QCD-cosmology- nucleosynthesis- form factors- · · ·
Flavored QCD“Flavor problem”
Hig
gsse
ctor - cosm. constant
- EW hierarchy- vacuum stability- Vcb-puzzle- flavour anomalies
Leptoquark=====⇒ GUT
- · · ·
Solution
???
![Page 5: NYU AD 2020 H. Sati](https://reader033.fdocuments.us/reader033/viewer/2022051922/628549f72fd89436743609e5/html5/thumbnails/5.jpg)
Open problem QCD’t Hooft doubling
Confined QCD“Millennium problem”- QCD-cosmology- nucleosynthesis- form factors- · · ·
Flavored QCD“Flavor problem”
Hig
gsse
ctor - cosm. constant
- EW hierarchy- vacuum stability- Vcb-puzzle- flavour anomalies
Leptoquark=====⇒ GUT
- · · ·
braneworld geometric engineering
AdS/QCD correspondence
Solution
??? ???
IIA super-gravitynear blackintersecting branes
flavor branes
colo
rbra
nes
. . .
![Page 6: NYU AD 2020 H. Sati](https://reader033.fdocuments.us/reader033/viewer/2022051922/628549f72fd89436743609e5/html5/thumbnails/6.jpg)
Open problem QCDsmall Nc ’t Hooft doubling
Nc = 3quark colors
Confined QCD“Millennium problem”- QCD-cosmology- nucleosynthesis- form factors- · · ·
Flavored QCD“Flavor problem”
Hig
gsse
ctor - cosm. constant
- EW hierarchy- vacuum stability- Vcb-puzzle- flavour anomalies
Leptoquark=====⇒ GUT
- · · ·
braneworld geometric engineering
AdS/QCD correspondence
Solution
??? ???
IIA super-gravitynear blackintersecting branes
flavor branes
colo
rbra
nes
. . .
![Page 7: NYU AD 2020 H. Sati](https://reader033.fdocuments.us/reader033/viewer/2022051922/628549f72fd89436743609e5/html5/thumbnails/7.jpg)
Open problem QCDsmall Nc ’t Hooft doubling
Nc = 3quark colors
Confined QCD“Millennium problem”- QCD-cosmology- nucleosynthesis- form factors- · · ·
Flavored QCD“Flavor problem”
Hig
gsse
ctor - cosm. constant
- EW hierarchy- vacuum stability- Vcb-puzzle- flavour anomalies
Leptoquark=====⇒ GUT
- · · ·
braneworld geometric engineering
AdS/QCD correspondence
Solution
??? ???
M-theorywith microscopicintersecting branes
flavor branes
colo
rbra
nes
. . .
![Page 8: NYU AD 2020 H. Sati](https://reader033.fdocuments.us/reader033/viewer/2022051922/628549f72fd89436743609e5/html5/thumbnails/8.jpg)
Open problem QCD Open problem Msmall Nc ’t Hooft doubling
Confined QCD“Millennium problem”- QCD-cosmology- nucleosynthesis- form factors- · · ·
Flavored QCD“Flavor problem”
Hig
gsse
ctor - cosm. constant
- EW hierarchy- vacuum stability- Vcb-puzzle- flavour anomalies
Leptoquark=====⇒ GUT
- · · ·
braneworld geometric engineering
AdS/QCD correspondence
Solution
???
Hyp
othe
sis
H
M-theorywith microscopicintersecting branes
flavor branes
colo
rbra
nes
. . .
![Page 9: NYU AD 2020 H. Sati](https://reader033.fdocuments.us/reader033/viewer/2022051922/628549f72fd89436743609e5/html5/thumbnails/9.jpg)
Open problem QCD Open problem Msmall Nc ’t Hooft doubling
![Page 10: NYU AD 2020 H. Sati](https://reader033.fdocuments.us/reader033/viewer/2022051922/628549f72fd89436743609e5/html5/thumbnails/10.jpg)
Open problem QCD Open problem Msmall Nc ’t Hooft doubling
first consider large g2YMNc
+3 11d supergravity
![Page 11: NYU AD 2020 H. Sati](https://reader033.fdocuments.us/reader033/viewer/2022051922/628549f72fd89436743609e5/html5/thumbnails/11.jpg)
Open problem QCD Open problem Msmall Nc ’t Hooft doubling
first consider large g2YMNc
+3 11d supergravity
CovariantPhaseSpace11d SuGra
=
spacetimes
formalized as: GADE
–orbi R10, 1|32
–foldssuper-orbifold
(X )
equipped with: 0) gravity 1) C-field
formalized as: Pin+-structuresuper-vielbein
(E,Ψ) differential formsflux densities
(G4, G7)
subject to: Einstein equations Page equationG = T (Ψ, G4, G7) dG7 + 1
2G4 ∧G4 = 0
![Page 12: NYU AD 2020 H. Sati](https://reader033.fdocuments.us/reader033/viewer/2022051922/628549f72fd89436743609e5/html5/thumbnails/12.jpg)
Open problem QCD Open problem Msmall Nc ’t Hooft doubling
first consider large g2YMNc
+3 11d supergravity
CovariantPhaseSpace11d SuGra
=
spacetimes
formalized as: GADE
–orbi R10, 1|32
–foldssuper-orbifold
(X )
equipped with: 0) gravity 1) C-field
formalized as: Pin+-structuresuper-vielbein
(E,Ψ) differential formsflux densities
(G4, G7)
subject to: Einstein equations Page equation
equivalent to: super-torsion = 0Candiello-Lechner 93, Howe 97
flux is in rationalizedJ-twisted CohomotopySati 13, Fiorenza-Sati-S. 19a
![Page 13: NYU AD 2020 H. Sati](https://reader033.fdocuments.us/reader033/viewer/2022051922/628549f72fd89436743609e5/html5/thumbnails/13.jpg)
Open problem QCD Open problem Msmall Nc ’t Hooft doubling
& large g2YMNc
+3 11d supergravitycharge-quantizedin Cohomotopy
CovariantPhaseSpace11d SuGra
=
spacetimes
formalized as: GADE
–orbi R10, 1|32
–foldssuper-orbifold
(X )
equipped with: 0) gravity 1) C-field
formalized as: Pin+-structuresuper-vielbein
(E,Ψ) differential formsflux densities
(G4, G7)
subject to: Einstein equations Page equation
equivalent to: super-torsion = 0Candiello-Lechner 93, Howe 97
flux is in rationalizedJ-twisted CohomotopySati 13, Fiorenza-Sati-S. 19a
![Page 14: NYU AD 2020 H. Sati](https://reader033.fdocuments.us/reader033/viewer/2022051922/628549f72fd89436743609e5/html5/thumbnails/14.jpg)
Hypothesis HSati 13, Fiorenza-Sati-S. 19b,19c
CovariantPhaseSpaceM-Theory
=
spacetimes
formalized as: GADE
–orbi R10, 1|32
–foldssuper-orbifold
(X )
equipped with: 0) gravity 1) C-field
formalized as: Pin+-structuresuper-vielbein
(E,Ψ) differential formsflux densities
(G4, G7)
subject to: Einstein equations Page equation
formalized as: super-torsion = 0flux is in rationalizedJ-twisted CohomotopyFSS 19b,19c, SS 19a,19b,19c
![Page 15: NYU AD 2020 H. Sati](https://reader033.fdocuments.us/reader033/viewer/2022051922/628549f72fd89436743609e5/html5/thumbnails/15.jpg)
Discrepancies?
Salvageable?
Looks like M-theory?
Compare implicationsof Hypothesis Hto M-folklore.
today:
Adjust fine-printin Hypothesis H(e.g. differential refinement)
Solve1) Millennium problem2) Vacuum selection problem3) Flavor problem
...
(for later)
15
![Page 16: NYU AD 2020 H. Sati](https://reader033.fdocuments.us/reader033/viewer/2022051922/628549f72fd89436743609e5/html5/thumbnails/16.jpg)
Implications of Hypothesis H
on on on
curved but smoothspacetimes
flat but orbi-singularspacetimes
spacetimeswith horizons
FSS 19b, FSS 19c, GS20 BSS 18, SS 19a SS 19c
topologicalanomaly cancellation:
equivariantanomaly cancellation
Dp ⊥ D(p + 2)worldvolume QFT
- shifted C-field flux quantization- C-field tadpole cancellation- M5 Hopf-WZ level quantization- DMW anomaly cancellation- C-field integral eom...
- M5/MO5 anomaly cancellation- RR-field tadpole cancellation- no irractional D-brane charge
- fuzzy funnels- BLG 3-algebras- BMN matrix model- M2/M5 bound states- AdS3-holography- Coulomb branch indices- Hanany-Witten rules- ...
H. Sati’s talkD. Fiorenza’s talk my talk
at M-Theory and Mathematics 2020
16
![Page 17: NYU AD 2020 H. Sati](https://reader033.fdocuments.us/reader033/viewer/2022051922/628549f72fd89436743609e5/html5/thumbnails/17.jpg)
(1)
Microscopic Brane Charge
implied by
Hypothesis H with Pontrjagin-Thom Theorem
Sati-Schreiber 19a [arXiv:1909.12277]
back to top
17
![Page 18: NYU AD 2020 H. Sati](https://reader033.fdocuments.us/reader033/viewer/2022051922/628549f72fd89436743609e5/html5/thumbnails/18.jpg)
18
![Page 19: NYU AD 2020 H. Sati](https://reader033.fdocuments.us/reader033/viewer/2022051922/628549f72fd89436743609e5/html5/thumbnails/19.jpg)
19
![Page 20: NYU AD 2020 H. Sati](https://reader033.fdocuments.us/reader033/viewer/2022051922/628549f72fd89436743609e5/html5/thumbnails/20.jpg)
20
![Page 21: NYU AD 2020 H. Sati](https://reader033.fdocuments.us/reader033/viewer/2022051922/628549f72fd89436743609e5/html5/thumbnails/21.jpg)
21
![Page 22: NYU AD 2020 H. Sati](https://reader033.fdocuments.us/reader033/viewer/2022051922/628549f72fd89436743609e5/html5/thumbnails/22.jpg)
22
![Page 23: NYU AD 2020 H. Sati](https://reader033.fdocuments.us/reader033/viewer/2022051922/628549f72fd89436743609e5/html5/thumbnails/23.jpg)
23
![Page 24: NYU AD 2020 H. Sati](https://reader033.fdocuments.us/reader033/viewer/2022051922/628549f72fd89436743609e5/html5/thumbnails/24.jpg)
24
![Page 25: NYU AD 2020 H. Sati](https://reader033.fdocuments.us/reader033/viewer/2022051922/628549f72fd89436743609e5/html5/thumbnails/25.jpg)
25
![Page 26: NYU AD 2020 H. Sati](https://reader033.fdocuments.us/reader033/viewer/2022051922/628549f72fd89436743609e5/html5/thumbnails/26.jpg)
(2)
Orientifold Tadpole Cancellation
implied by
Hypothesis H with Equivariant Hopf Degree Theorem
Sati-Schreiber 19a [arXiv:1909.12277]
back to top
26
![Page 27: NYU AD 2020 H. Sati](https://reader033.fdocuments.us/reader033/viewer/2022051922/628549f72fd89436743609e5/html5/thumbnails/27.jpg)
27
![Page 28: NYU AD 2020 H. Sati](https://reader033.fdocuments.us/reader033/viewer/2022051922/628549f72fd89436743609e5/html5/thumbnails/28.jpg)
28
![Page 29: NYU AD 2020 H. Sati](https://reader033.fdocuments.us/reader033/viewer/2022051922/628549f72fd89436743609e5/html5/thumbnails/29.jpg)
29
![Page 30: NYU AD 2020 H. Sati](https://reader033.fdocuments.us/reader033/viewer/2022051922/628549f72fd89436743609e5/html5/thumbnails/30.jpg)
30
![Page 31: NYU AD 2020 H. Sati](https://reader033.fdocuments.us/reader033/viewer/2022051922/628549f72fd89436743609e5/html5/thumbnails/31.jpg)
31
![Page 32: NYU AD 2020 H. Sati](https://reader033.fdocuments.us/reader033/viewer/2022051922/628549f72fd89436743609e5/html5/thumbnails/32.jpg)
32
![Page 33: NYU AD 2020 H. Sati](https://reader033.fdocuments.us/reader033/viewer/2022051922/628549f72fd89436743609e5/html5/thumbnails/33.jpg)
33
![Page 34: NYU AD 2020 H. Sati](https://reader033.fdocuments.us/reader033/viewer/2022051922/628549f72fd89436743609e5/html5/thumbnails/34.jpg)
34
![Page 35: NYU AD 2020 H. Sati](https://reader033.fdocuments.us/reader033/viewer/2022051922/628549f72fd89436743609e5/html5/thumbnails/35.jpg)
The following four slides showtechnical detail of therealization of this mechanism forMO5-planes atADE-singularities in heterotic M-theory
Skip over technical detailahead to section (3).
35
![Page 36: NYU AD 2020 H. Sati](https://reader033.fdocuments.us/reader033/viewer/2022051922/628549f72fd89436743609e5/html5/thumbnails/36.jpg)
36
![Page 37: NYU AD 2020 H. Sati](https://reader033.fdocuments.us/reader033/viewer/2022051922/628549f72fd89436743609e5/html5/thumbnails/37.jpg)
37
![Page 38: NYU AD 2020 H. Sati](https://reader033.fdocuments.us/reader033/viewer/2022051922/628549f72fd89436743609e5/html5/thumbnails/38.jpg)
38
![Page 39: NYU AD 2020 H. Sati](https://reader033.fdocuments.us/reader033/viewer/2022051922/628549f72fd89436743609e5/html5/thumbnails/39.jpg)
(3)
D6⊥D8 -brane intersections
implied by
Hypothesis H with May-Segal Theorem
Sati-Schreiber 19c [arXiv:1912.10425]
back to top
39
![Page 40: NYU AD 2020 H. Sati](https://reader033.fdocuments.us/reader033/viewer/2022051922/628549f72fd89436743609e5/html5/thumbnails/40.jpg)
Cohomotopycocycle space
ππππ
boldface!
4(X) :=
pointedmapping space
Maps∗/(X,S4
)
π0
(ππππ4(X)
)=
Cohomotopycohomology
classes
= πnot
boldface
4(X) Cohomotopyset
π1
(ππππ4(X)
)=
Cohomotopygauge
transformations
π2
(ππππ4(X)
)=
Cohomotopygauge of gaugetransformations
...
40
![Page 41: NYU AD 2020 H. Sati](https://reader033.fdocuments.us/reader033/viewer/2022051922/628549f72fd89436743609e5/html5/thumbnails/41.jpg)
Cohomotopy cocycle spacevanishing at ∞ on Euclidean 3-space
ππππ4((R3)cpt
) hmtpy'←−−−−assign unit charge
in Cohomotopyto each point
Conf(R3,D1
)May-Segal theorem
configuration space of pointsin R3 × R1
which are:1) unordered
2) distinct after projection to R3
3) allowed to vanish to ∞ along R1
=
R3×0 R3×∞R3×∞
projection to R3point
in R3×R1point
disappearedto infinity
along R1
41
![Page 42: NYU AD 2020 H. Sati](https://reader033.fdocuments.us/reader033/viewer/2022051922/628549f72fd89436743609e5/html5/thumbnails/42.jpg)
ππππ4((Rd)cpt ∧ (R4−d)+
)oo hmtpy'
hence: a form of differential Cohomotopy
ππππ4diff
((Rd)cpt ∧ (R4−d)+
):=
assigns configuration spaces:
Conf(Rd,D4−d)
42
![Page 43: NYU AD 2020 H. Sati](https://reader033.fdocuments.us/reader033/viewer/2022051922/628549f72fd89436743609e5/html5/thumbnails/43.jpg)
Lemma:
43
![Page 44: NYU AD 2020 H. Sati](https://reader033.fdocuments.us/reader033/viewer/2022051922/628549f72fd89436743609e5/html5/thumbnails/44.jpg)
=
Lemma:
44
![Page 45: NYU AD 2020 H. Sati](https://reader033.fdocuments.us/reader033/viewer/2022051922/628549f72fd89436743609e5/html5/thumbnails/45.jpg)
Consequence: assumingHypothesis H:
differential Cohomotopy cocycle spacereflecting D6⊥D8 -charges
45
![Page 46: NYU AD 2020 H. Sati](https://reader033.fdocuments.us/reader033/viewer/2022051922/628549f72fd89436743609e5/html5/thumbnails/46.jpg)
(4)
Hanany-Witten Theory
implied by
Hypothesis H with Fadell-Husseini Theorem
Sati-Schreiber 19c [arXiv:1912.10425]
back to top
46
![Page 47: NYU AD 2020 H. Sati](https://reader033.fdocuments.us/reader033/viewer/2022051922/628549f72fd89436743609e5/html5/thumbnails/47.jpg)
higher co-observables on D6⊥D8 -intersections
H•
topologicalphase space
t[c]
Ωc ππππ4diff
' H•
(t
Nf∈NConf1,· · ·, Nf
(R3))
(by the above)
' ⊕Nf∈NApb
NfFadell-Husseini
theorem
are algebra of horizontal chord diagrams:
47
![Page 48: NYU AD 2020 H. Sati](https://reader033.fdocuments.us/reader033/viewer/2022051922/628549f72fd89436743609e5/html5/thumbnails/48.jpg)
Horizontal chord diagrams form algebra under concatenation of strands.
tik tij = tiktij
This is universal enveloping algebra of the infinitesimal braid Lie algebra (Kohno):
[tij, tkl] = 0
[tij, tik + tjk] = 0
48
![Page 49: NYU AD 2020 H. Sati](https://reader033.fdocuments.us/reader033/viewer/2022051922/628549f72fd89436743609e5/html5/thumbnails/49.jpg)
Consider the subspace of skew-symmetric co-observables,
denote elements as follows:
49
![Page 50: NYU AD 2020 H. Sati](https://reader033.fdocuments.us/reader033/viewer/2022051922/628549f72fd89436743609e5/html5/thumbnails/50.jpg)
In the subspace of skew-symmetric co-observables we find:
the 2T relationsbecome theordering constraint
=form of anynon-vanishing element
skew-symmetrybecomes thes-rule
the 4T relationsbecome thebreaking rule
50
![Page 51: NYU AD 2020 H. Sati](https://reader033.fdocuments.us/reader033/viewer/2022051922/628549f72fd89436743609e5/html5/thumbnails/51.jpg)
these are the rules of Hanany-Witten theoryfor NS5 ⊥ Dp ⊥ D(p + 2)-brane intersections
if we identify horizontal chord diagrams as follows:
51
![Page 52: NYU AD 2020 H. Sati](https://reader033.fdocuments.us/reader033/viewer/2022051922/628549f72fd89436743609e5/html5/thumbnails/52.jpg)
(5)
Chan-Paton data
implied by
Hypothesis H with Bar-Natan’ theorem
Sati-Schreiber 19c [arXiv:1912.10425]
back to top
52
![Page 53: NYU AD 2020 H. Sati](https://reader033.fdocuments.us/reader033/viewer/2022051922/628549f72fd89436743609e5/html5/thumbnails/53.jpg)
higher co-states on D6⊥D8 -intersections
H•
topologicalphase space
t[c]
Ωc ππππ4diff
' H•(t
Nf∈NConf1,· · ·, Nf
(R3))
(by the above)
' ⊕Nf∈NWpb
NfKohno & Cohen-Gitler
theorem
are horizontal weight systems:
53
![Page 54: NYU AD 2020 H. Sati](https://reader033.fdocuments.us/reader033/viewer/2022051922/628549f72fd89436743609e5/html5/thumbnails/54.jpg)
All horizontal weight systems w : Apb → C come from Chan-Paton data:1) metric Lie representations ρ 2) stacks of coincident strands 3) winding monodromies:
w
Bar-Natantheorem
54
![Page 56: NYU AD 2020 H. Sati](https://reader033.fdocuments.us/reader033/viewer/2022051922/628549f72fd89436743609e5/html5/thumbnails/56.jpg)
(6)
BMN Matrix Model States
implied by
Hypothesis H
back to top
56
![Page 57: NYU AD 2020 H. Sati](https://reader033.fdocuments.us/reader033/viewer/2022051922/628549f72fd89436743609e5/html5/thumbnails/57.jpg)
ρ ∈ su(2)C MetricReps equivalently identified with:
0) configuration of concentric fuzzy 2-spheres
1) fuzzy funnel state in DBI model for Dp⊥D(p + 2)
2) susy state in BMN matrix model for M2/M5
corresponding weight systems w(ρ,σ)
: Apb → C are:
0) radius fluctuation amplitudes of fuzzy 2-spheres
1)
2)invariant multi-trace observables in
DBI modelBMN model
57
![Page 58: NYU AD 2020 H. Sati](https://reader033.fdocuments.us/reader033/viewer/2022051922/628549f72fd89436743609e5/html5/thumbnails/58.jpg)
,0) Radius fluctuation observables on N -bit fuzzy 2-spheres S2
Nare N ∈ su(2)CMetricReps weight systems on chord diagrams:
58
![Page 59: NYU AD 2020 H. Sati](https://reader033.fdocuments.us/reader033/viewer/2022051922/628549f72fd89436743609e5/html5/thumbnails/59.jpg)
1,2) weight system wρ is the observable aspect of matrix model state ρ:
linear combinations offinite-dim suC-representations
Span(su(2)CMetricReps
)naive funnel- / susy-states of
DBI model / BMN matrix model
ρ 7→wρ//
weight systems onhorizontal chord diagrams
Wpb
states of DBI model / BMN matrix modeas observed by invariant multi-trace observables
59
![Page 60: NYU AD 2020 H. Sati](https://reader033.fdocuments.us/reader033/viewer/2022051922/628549f72fd89436743609e5/html5/thumbnails/60.jpg)
(7)
M2/M5 Brane Bound States
implied by
Hypothesis H
back to top
60
![Page 61: NYU AD 2020 H. Sati](https://reader033.fdocuments.us/reader033/viewer/2022051922/628549f72fd89436743609e5/html5/thumbnails/61.jpg)
Given a sequence of susy states in the BMN matrix model
M2/M5-brane state(finite-dim su(2)C-rep)︷ ︸︸ ︷
(V, ρ) := ⊕i︸︷︷︸
stacks of coincident branes(direct sum over irreps)
(M2/M5-brane charge in ith stack
(ith irrep with multiplicity)︷ ︸︸ ︷N
(M2)
i ·N(M5)
i
)∈ su(2)CMetricReps/∼
this is argued to converge to macroscopic M2- or M5-branesdepending on how the sequence behaves in the large N limit:
Stacks of macroscopic...
M2-branes M5-branes
If for all i N(M5)
i →∞ N(M2)
i →∞(
the relevantlarge N limit)
)
with fixed N(M2)
i N(M5)
i
(the number of coincident branes
in the ith stack
)
and fixed N(M2)i /N N
(M5)i /N
(the charge/light-cone momentum
carried by the ith stack
)
61
![Page 62: NYU AD 2020 H. Sati](https://reader033.fdocuments.us/reader033/viewer/2022051922/628549f72fd89436743609e5/html5/thumbnails/62.jpg)
Given a sequence of susy states in the BMN matrix model
M2/M5-brane state(finite-dim su(2)C-rep)︷ ︸︸ ︷
(V, ρ) := ⊕i︸︷︷︸
stacks of coincident branes(direct sum over irreps)
(M2/M5-brane charge in ith stack
(ith irrep with multiplicity)︷ ︸︸ ︷N
(M2)
i ·N(M5)
i
)∈ su(2)CMetricReps/∼
the large Nlimit does not exist
here:
Span(su(2)CMetricReps
) ρ 7→wρ//
butdoes exist in weight systems
Wpb
if we normalize by the scale of the fuzzy 2-sphere geometry:
4π 22n((N
(M5))2−1)1/2+n wN
(M5)
︸ ︷︷ ︸Single M2-brane state in BMN model
(multiple of suC-weight system)
∈ Wpb
states as seen by multi-trace observables(weight systems on chord diagrams)
62
![Page 63: NYU AD 2020 H. Sati](https://reader033.fdocuments.us/reader033/viewer/2022051922/628549f72fd89436743609e5/html5/thumbnails/63.jpg)
M2/M5-brane bound statesas emergent under Hypothesis H
63
![Page 64: NYU AD 2020 H. Sati](https://reader033.fdocuments.us/reader033/viewer/2022051922/628549f72fd89436743609e5/html5/thumbnails/64.jpg)
End.
back to top
64