6d SCFTs and F-theory: a bottom-up perspective · Iknow it’s not quite the Dave day yet,but let...
Transcript of 6d SCFTs and F-theory: a bottom-up perspective · Iknow it’s not quite the Dave day yet,but let...
I knowit’snotquitetheDavedayyet, butletmesayonething.
Davewasoriginallyapuremathematician.
Whenhewasaboutmyagerightnow, hestartedtolearnstringtheory,andbecameoneoftheleadingfiguresinthefield.
Isn’titamazing?
MaybeI shouldtrysomethingotherthanstringtheory,followinghisexample!
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I knowit’snotquitetheDavedayyet, butletmesayonething.
Davewasoriginallyapuremathematician.
Whenhewasaboutmyagerightnow, hestartedtolearnstringtheory,andbecameoneoftheleadingfiguresinthefield.
Isn’titamazing?
MaybeI shouldtrysomethingotherthanstringtheory,followinghisexample!
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I knowit’snotquitetheDavedayyet, butletmesayonething.
Davewasoriginallyapuremathematician.
Whenhewasaboutmyagerightnow, hestartedtolearnstringtheory,andbecameoneoftheleadingfiguresinthefield.
Isn’titamazing?
MaybeI shouldtrysomethingotherthanstringtheory,followinghisexample!
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Asyouknow, I’mnotreallyanF-theoryperson.
I don’tevenremembertheordersof (f, g,∆) inKodaira’stablebyheart!
I wasaskedtogiveareviewtalkfromanoutsiderpointofview,soit’sprobablyOK.
I guesstheideawaslikeinvitinganLQG persontotheStringsconference...
I alsoapologizeinadvancethatmytalkwillbeverysubjective,andwillnotcite/mentionmanyrelevantpapers,althoughI knowI should.
ButatleastI wouldliketoillustrate...
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Asyouknow, I’mnotreallyanF-theoryperson.
I don’tevenremembertheordersof (f, g,∆) inKodaira’stablebyheart!
I wasaskedtogiveareviewtalkfromanoutsiderpointofview,soit’sprobablyOK.
I guesstheideawaslikeinvitinganLQG persontotheStringsconference...
I alsoapologizeinadvancethatmytalkwillbeverysubjective,andwillnotcite/mentionmanyrelevantpapers,althoughI knowI should.
ButatleastI wouldliketoillustrate...
4/81
Asyouknow, I’mnotreallyanF-theoryperson.
I don’tevenremembertheordersof (f, g,∆) inKodaira’stablebyheart!
I wasaskedtogiveareviewtalkfromanoutsiderpointofview,soit’sprobablyOK.
I guesstheideawaslikeinvitinganLQG persontotheStringsconference...
I alsoapologizeinadvancethatmytalkwillbeverysubjective,andwillnotcite/mentionmanyrelevantpapers,althoughI knowI should.
ButatleastI wouldliketoillustrate...
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Q. Why6dSCFT?
A. When [Heckman-Morrison-Vafa 1312.5746] cameout, mystudentHiroyukiShimizugotinterested, soasanadviserI neededtostudyitandcomeupwithaprojecthecouldworkon.
A. I’vebeenstudying4d N=2 SUSY forquitesometime,and6dSCFTsfeltfamiliar
A. 6disthe maximal dimensionwhere superconformalgroupsareavailable. So, somethinginterestingmightbegoingon.
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Q. Why6dSCFT?
A. When [Heckman-Morrison-Vafa 1312.5746] cameout, mystudentHiroyukiShimizugotinterested, soasanadviserI neededtostudyitandcomeupwithaprojecthecouldworkon.
A. I’vebeenstudying4d N=2 SUSY forquitesometime,and6dSCFTsfeltfamiliar
A. 6disthe maximal dimensionwhere superconformalgroupsareavailable. So, somethinginterestingmightbegoingon.
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Q. Why6dSCFT?
A. When [Heckman-Morrison-Vafa 1312.5746] cameout, mystudentHiroyukiShimizugotinterested, soasanadviserI neededtostudyitandcomeupwithaprojecthecouldworkon.
A. I’vebeenstudying4d N=2 SUSY forquitesometime,and6dSCFTsfeltfamiliar
A. 6disthe maximal dimensionwhere superconformalgroupsareavailable. So, somethinginterestingmightbegoingon.
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Q. Why6dSCFT?
A. When [Heckman-Morrison-Vafa 1312.5746] cameout, mystudentHiroyukiShimizugotinterested, soasanadviserI neededtostudyitandcomeupwithaprojecthecouldworkon.
A. I’vebeenstudying4d N=2 SUSY forquitesometime,and6dSCFTsfeltfamiliar
A. 6disthe maximal dimensionwhere superconformalgroupsareavailable. So, somethinginterestingmightbegoingon.
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Sketchoftheproofthat 6disthemaximaldimension:
1 Superconformalalgebrasare simple.
2 Fermionicpartsofthesuperconformalalgebrasare spinors.
3 Simple superalgebrasareclassified.
4 Fermionicpartsofalmostallofthemareinthe fundamental.
5 Needanaccidentalisomorphism spinors ≃ fundamental.
6 Themaximalcaseistherefore so(8), or so(6, 2) forourpurpose.
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6d N=(n, 0) SCFT correspondsto osp(6, 2|2n).
Openquestion
Showthat N=(n > 2, 0) SCFTsdon’texist.
cf. 5d N=1 SCFT correspondsto F (4), whosebosonicpartisso(7) ⊕ su(2) andthefermionicpartis spinor ⊗ doublet.
Theresimplyisno5d N>1 superconformalalgebra,sothere’snocorrespondingopenquestion.
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6d N=(n, 0) SCFT correspondsto osp(6, 2|2n).
Openquestion
Showthat N=(n > 2, 0) SCFTsdon’texist.
cf. 5d N=1 SCFT correspondsto F (4), whosebosonicpartisso(7) ⊕ su(2) andthefermionicpartis spinor ⊗ doublet.
Theresimplyisno5d N>1 superconformalalgebra,sothere’snocorrespondingopenquestion.
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Q. Howdoyoustudy6dSCFTs?
• Conformalbootstrap.• AnalysisoftheLagrangianonthetensorbranch.• AnalysisoftheLagrangianofthe S1 compactification.• BraneconstructionsinM,(massive)typeIIA,ortypeI• F-theory!
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M-theoryconstructionsandF-theory
↓
structureonthetensorbranchandF-theory
↓
massivetypeIIA constructionsandF-theory
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M-theoryconstructionsandF-theory
↓
structureonthetensorbranchandF-theory
↓
massivetypeIIA constructionsandF-theory
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A largeclassof6d N=(1, 0) SCFTscanbeobtainedbyputtingM5-branesontheALE singularities:
R6 ×
R1
C2/
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When Γ = Zk, wehave SU(k) gaugefieldsatthesingularity,andanM5justgivesabifundamentalof SU(k) × SU(k):
R6 ×
SU(k)
bifundamental
SU(k)
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Butsurprisingthingshappenwhen Γ isoftype Dk or Ek.[delZotto-Heckman-Tomasiello-Vafa, 1407.6359]
Forexample, take Γ oftype Dk andput1M5:
R6 ×
SO(2k)
nontrivialSCFT
SO(2k)
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TheM5becomestwofractionalM5s:
R6 ×
USp(2k−8)
bifund. bifund.
SO(2k)SO(2k)
Somehowthemiddleregionthegaugegroupis USp(2k − 8),andeachhalf-M5givesabifundamental.
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Similarly, when Γ isoftype E6, afullM5-branefractionates...
R6 ×
E6E6SU(3)
∅∅
into4fractionalM5s, andthegaugegroupsoccurinthesequence
E6, ∅, SU(3), ∅, E6.
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Ingeneral, wehave
A : doesn’tfractionate.
Dk : SO(2k), USp(2k − 8), SO(2k)
E6 : E6,∅, SU(3),∅, E6
E7 : E7,∅, SU(2), SO(7), SU(2),∅, E7
E8 : E8,∅,∅, SU(2), G2,∅, F4,∅, G2, SU(2),∅,∅, E8.
Mynaturalreactionwasthis:
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M-theoretically, youcangoasfollows[Ohmori-Shimizu-YT-Yonekura, 1503.06217, Sec. 3.1]:
Tostudythe tensorbranch ofthissystem,
R6 ×
G
M5
G
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LiftitbacktoM-theory:
R3 × ×
G
M2
G
We’renowinterestedinits Higgsbranch,sincewe’veeffectivelytakenthe3dmirror.
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AnM2candissolveintothe G gaugefieldasaninstantonon T 3 × R:
G
CS
0
1
TheplotbelowshowstheevolutionoftheChern-Simonsinvarianton T 3 ateachslice.
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SO(2k)
Threeholonomiesareknowntobegivenby
diag(+,+,+,−,−,−,−,+2k−7)
diag(+,−,−,+,+,−,−,+2k−7)
diag(−,+,−,+,−,+,−,+2k−7)
Originallynoticedby [Witten, hep-th/9712028].
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Goingbackthedualitychain, wehave
R3 × ×
½M5
USp(2k−8)SO(2k)SO(2k)
½M5
sinceweneedtotake4dS-duality/3dmirrorsymmetry:
SO(2k−7) ↔ USp(2k−8)
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Theanalysiscanbecarriedoutinasimilarmannerforany G,usingtheresultsin [Borel,Friedman,Morgan math.GR/9907007].
Whatneedstobedoneistheclassificationofflat G bundleson T 3
andthecomputationoftheirChern-Simonsinvariants.
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Example: G = E7.
Youcanconstructabundlewith CS = 1/2 asfollows. Take
diag(+,+,+,−,−,−,−)
diag(+,−,−,+,+,−,−)
diag(−,+,−,+,−,+,−)
in SO(7). Infacttheyarein G2.
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Youcanfractionatefurther, sincetheallowedCS invariantsare
CS = 0,1
4,1
3,1
2,2
3,3
4.
Wehave
CS
E7 USp(6) E7SU(2) SU(2) ∅∅
1
0
1/41/31/22/33/4
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Intheoriginaldualityframewehave
E7
E7SU(2)
∅
∅SU(2)
SO(7)1/4M5
1/12M5
1/6M5 1/6
M51/12M5
1/4M5
NotethattheM5chargesare notequallydistributed.
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InF-theory, theanalysisisdoneasfollows[Aspinwall-Morrison, hep-th/9705104]:
RecallthattheM-theoryconfiguration
R6 ×
G
M5
G
isdualto...
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ThisF-theoryconfiguration:
R6 ×
G
G
C2
wheretwoF-theory7-branesintersecttransversallyatapoint.
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I knowI don’thavetoreviewthefollowinginthisworkshop, butanyway.
Let’ssayweputtheellipticfibrationtotheWeierstrassform
y2 = x3 + fx + g
where f , g arefunctionsonthebase.
Let ∆ = 4f3 + 27g2 beitsdiscriminant.
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g G ord(f) ord(g) ord(∆)
Ik
(1 k0 1
)SU(k) 0 0 k
II
(1 1−1 0
)∅ ≥ 1 1 2
III
(0 1−1 0
)SU(2) 1 ≥ 2 3
IV
(0 1−1 −1
)SU(3) ≥ 2 2 4
I∗k
(−1 −k0 −1
)SO(2k + 8) 2 3 k + 6
IV ∗(−1 −11 0
)E6 ≥ 3 4 8
III∗(0 −11 0
)E7 3 ≥ 5 9
II∗(0 −11 1
)E8 ≥ 4 5 10
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So, supposetwo E7 7-branesintersect.
E7
E7
(3, 5, 9)
(3, 5, 9)
Here (3, 5, 9) meansthat (f, g,∆) vanishtotheseordersthere.
Attheintersection,
(3, 5, 9) + (3, 5, 9) = (6, 10, 18) ≥ (4, 6, 12).
A smoothellipticfibrationcan’texceed (4, 6, 12).
Soweblow-uptheintersectionpoint.
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Wenowgetthisconfiguration
E7
E7
(3, 5, 9)
(3, 5, 9)
(2, 4, 6)
where(2, 4, 6) = (3, 5, 9) + (3, 5, 9) − (4, 6, 12).
Lookingupthetable, thiscorrespondsto I∗0 with SO(8).
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A moredetailedanalysisshowsthatthereisan outer-automorphism actionof SO(8) aroundthis S2 of I∗
0 curve
E7
E7
(3, 5, 9)
(3, 5, 9)
(2, 4, 6)
SO(7)
giving SO(7).
Theintersectionof (2, 4, 6) and (3, 5, 9) isstillsingularsince
(2, 4, 6) + (3, 5, 9) ≥ (4, 6, 12).
Weneedtoblowup, repeat...
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whichreflectedpossiblechoicesofflat E7 connectionson T 3
CS
E7 USp(6) E7SU(2) SU(2) ∅∅
1
0
1/41/31/22/33/4
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Thecorrespondenceworksforany G = Ak, Dk and E6,7,8.
E7
E7SO(7)SU(2) SU(2)∅ ∅
CS
E7 USp(6) E7SU(2) SU(2) ∅∅
1
0
1/41/31/22/33/4
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HowonearthdoestheF-theoryknowtheflatconnectionson T 3?
Notethat [Aspinwall-Morrison, hep-th/9705104] appearedbefore [Borel,Friedman,Morgan math.GR/9907007].
F-theoryworksinmysteriousways.
Openquestion
TheF-theoryshouldknowtheCS invariantsoftheflatconnections,buthow?
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HowonearthdoestheF-theoryknowtheflatconnectionson T 3?
Notethat [Aspinwall-Morrison, hep-th/9705104] appearedbefore [Borel,Friedman,Morgan math.GR/9907007].
F-theoryworksinmysteriousways.
Openquestion
TheF-theoryshouldknowtheCS invariantsoftheflatconnections,buthow?
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M-theoryconstructionsandF-theory
↓
structureonthetensorbranchandF-theory
↓
massivetypeIIA constructionsandF-theory
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We’reactivatingscalarsinthetensormultiplet.
E7
E7
E7
E7SO(7)SU(2) SU(2)∅ ∅
Ongenericpointsonthetensorbranch, wejusthave
• tensormultiplets• vectormultiplets• hypermultiplets
soonecanapplyamoretraditionalfield-theoreticalanalysis.
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Caveat: weareassumingthatallnontrivialSCFTshavetensorbranch.
Openquestion
Showthatifa6dSCFT doesnothaveanytensorbranch,itisatheoryoffreehypermultiplets.
Openquestion
Showthatifa4d N=2 SCFT doesnothaveanyCoulombbranch,itisatheoryoffreehypermultiplets.
Comments:
• Ifyoubelieveevery6dSCFT comesfromF-theoreticsingularities,thentheanswerisyes:3-dimCY singularitiescanalwaysberesolved.
• Bootstrap?
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E7
E7SO(7)SU(2) SU(2)∅ ∅
InF-theory, each P1 isassociatedto
• a tensor multiplet• a string comingfromD3wrappedthere,whosetensionisgivenbythescalarinthetensormultiplet
• possiblya gaugemultiplet, whoseinversecouplingsquaredisalsogivenbythescalarinthetensormultiplet
• When ∃ gaugemultiplet, the string isthe instanton-string.
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E7
E7SO(7)SU(2) SU(2)∅ ∅
InF-theory, eachintersectionoftwo P1 supporting G1 and G2 givesaparticularhypermultipletchargedunder G1 × G2.
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Soyoucantrytowork bottom-up: whatisthepossiblestructureof
• tensors Hi, i = 1, . . . , nT
• vectorsfor Ga, a = 1, . . . , nV
• hyperschargedunder∏
Ga
ongenericpointsofthetensorbranchofa6dSCFT?
Strongconstraintscomefromthe anomalycancellation.
Animportantroleisplayedbythe Diracpairing ⟨·, ·⟩onthechargelattice Λ ≃ ZnT ofthestrings.
Notethatin6d, thepairingis symmetric.
SCFT requiresittobe positivedefinite.
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Beforegettingfurther, I shouldsaytheanalysisthatfollowswouldbe ratherdefective.
• There’s noguarantee thatagivenanomaly-freecombinationcomesfroma6dSCFT thatreallyexists.
• Theanalysisdoesnottellusanythingaboutthe modelswheretherearenovectors.
I willcomebacktothefirstpointlater.
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Onthesecondpoint:
Thereshouldbeawaytounderstandbetterthe modelsthatdo nothavevectormultipletsonthetensorbranch.
Sofar, knownexamplesare
• ADE N=(2, 0) theories, and• E-string theoryanditshigher-rankanalogues, whichare N=(1, 0).
Whydoes N=(2, 0) theoriesclassifiedby ADE?
Wheredoesthe E8 symmetry comefrom, for N=(1, 0) examples?
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Whydoes N=(2, 0) theoriesclassifiedbyADE?
Thereisaniceargument [Henningson, hep-th/0405056] showingthatthe anomalycancellationonthestringworldsheet requiresthatthechargelatticeofany N=(2, 0) theoryshouldbea simply-lacedrootlattice.
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Essentialpointsofhisideaareasfollows.
• Takethestringofchargevector q ∈ Λ.• ThestringbreakshalftheSUSY.Nambu-Goldstonemodesbecomeworldsheetfields.Theyarechiral, andthereforeanomalous.
• Italsocouplestotheself-dualfieldsinthebulk.Thisgivestheanomalyinflowproportionalto ⟨q, q⟩.
• Thecancellationrequires ⟨q, q⟩ = 2.• So Λ isanintegrallatticegeneratedbyelementsof (length)2 = 2.
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Howabout N=(1, 0) examples?
Openquestion
Giveanargumentthatifagenuine N=(1, 0) SCFT doesnothaveanyvectormultipletongenericpointsonthetensorbranch,itistheE-stringoritshigher-rankanalogue.
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Thefirststepwouldbetostudytherank-1case.
AssumethattheDiracpairingofthechargelattice Λ ≃ Z isminimal.
Thenitseemsthatthecancellationoftheworldsheetanomalyrequiresthat ∃ aleft-moving c = 8 modular-invariantsector,showingthatitautomaticallyhas E8 symmetry.
Anybodyinterestedinfillinginthegaps?
Orisitalreadygivenintheliterature?
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Letuscomebacktothesetup:
• tensors Hi, i = 1, . . . , nT
• vectorsfor Ga, a = 1, . . . , nV
• hyperschargedunder∏
Ga
Letusfurtherassume nT = nV .Instantonstringsarechargedunderthetensors, sowehave
dHa = c2(Ga).
Thiscontributestotheanomalyby
I tensor8 =1
2Ωabc2(Ga)c2(Gb)
where Ωab istheintegralDiracpairingofthechargelattice.
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A sidecomment:
TheIIB F5 alsosatisfies dF5 = (something), andthereforethereis
IGS12 =1
2(something)2
whichisnotusuallydiscussed. Isitzero?
Ifitisn’t, itruinstheanomalycancellationofIIB supergravity.
Yes, since (something) = H3 ∧ G3.
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A sidecomment:
TheIIB F5 alsosatisfies dF5 = (something), andthereforethereis
IGS12 =1
2(something)2
whichisnotusuallydiscussed. Isitzero?
Ifitisn’t, itruinstheanomalycancellationofIIB supergravity.
Yes, since (something) = H3 ∧ G3.
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Comingbackto6d, thetotalanomalyshouldvanish:
0 =1
2Ωabc2(Ga)c2(Gb) +
∑a
Ivector8 (Ga) +∑
Ihyper8
FirstanalyzedbySeiberg [hep-th/9609161] for nV = nT = 1.
For SU(2) with 2Nf half-hypersinthedoublet, wehave
0 =1
2Ω c2
2 −32 − 2Nf
24c2
2
Weneed 32 > 2Nf , because Ω > 0.
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For SU(2) with Nf half-hypersinthedoublet, wehave
0 =1
2Ωc2
2 −32 − 2Nf
24c2
2
Weneed 32 > 2Nf , because Ω > 0.
BershadskyandVafain [hep-th/9703167] pointedoutthattherearemoreconstraints.
• F-theoryconstructionsonlygave Nf = 4 and = 10. Why?• In6d, there’saglobalanomalyassociatedto π6(SU(2)) = Z12,anditrequires 32 − 2Nf = 0 mod 12.
• Also, Ω needstobeaninteger, whichgivesthesamecondition.
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HowonearthdoestheF-theoryknowtheglobalanomalyassociatedtothesubtlehomotopygroup π6(SU(2)) = Z12?
F-theoryworksinmysteriousways.
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Wecanextendthefield-theoreticalanalysistogeneral nT = nV ,witharbitrary
∏Ga andarbitraryhypers.
[Heckman-Morrison-Rudelius-Vafa 1502.05405][Bhardwaj, 1502.06594]
Oneexampleis nT = nV = 2, G = su(2) × so(8),withahalf-hyperin 2 ⊗ 8V andfullspinorsin 8S ⊕ 8C .
Thisisfreeofbothlocalandglobalanomalies, withthechargepairing(2 −1−1 3
)
But thisisneverrealizedinF-theory!Isthereafield-theoreticalwaytoseethis?
Yes. [Ohmori-Shimizu-YT-Yonekura, 1508.00915, AppendixA]
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Thismodeltriestogaugethe so(8) flavorsymmetryofthe6dmodel
su(2) and 4 doubletsonthetensorbranch.
ThepointisthatthisSCFT onlyhas so(7) ⊂ so(8)where8doubletstransformasaspinorof so(7).
Soyoucan’tgauge so(8).
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Toseethatthereisonly so(7), compactifyon T 2 the6dmodel
su(2) and 4 doubletsonthetensorbranch.
Youget
4d N=2 su(2)G with 4 doublets
+ anadditional su(2)T comingfromthe6dtensor.
TheWeylgroupof su(2)T istheS-dualityofthis4d N=2 su(2)G with 4 doublets, andmaps 8V to 8S .
So, onlythe so(7) ⊂ so(8) s.t. 8C → 7 + 1 iscompatible.
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Anotherwayistocompactifyon S1 the6dmodel
su(2) and 4 doubletsonthetensorbranch.
Youget
5d N=1 su(2)G with 4 doublets
+ anadditional su(2)T comingfromthe6dtensor.
5d su(2)G with 4 doublets hasanenhanced so(10) flavorsymmetry,andthe su(2)T gaugesthe so(3) subgroup,whichcomesfromtheenhancedinstantonnumbersymmetry.
Thecommutantisclearly so(7), since so(3) ⊕ so(7) ⊂ so(10).
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M-theoryconstructionsandF-theory
↓
structureonthetensorbranchandF-theory
↓
massivetypeIIA constructionsandF-theory
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Wecanalsouse(massive)IIA toengineer6dSCFTs.[Brunner-Karch, hep-th/9712143] [Hanany-Zaffaroni, hep-th/9712145]
Twoexamples:
n D6s
NS5½NS5
O8−+ 16 D8s
n − 8 D6s
gives su(n) withan antisymmetric and n + 8 fundamentals, and
n D6s
NS5½NS5
O8+
n − 8 D6s
gives su(n) witha symmetric and n − 8 fundamentals.
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Theyarefreefromanomalies, bothlocalandglobal.
However, itsohappensthattheF-theoreticatomicclassification[Heckman-Morrison-Rudelius-Vafa, 1502.05405] includes
su(n) withan antisymmetric and n + 8 fundamentals
but doesnotinclude
su(n) witha symmetric and n − 8 fundamentals.
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Thisconundrumwasnoticedbymanypeoplesimultaneously,intheUS,inCanada, inJapan, andmaybeelsewheretoo.
I didn’tnoticeitmyself, butI learnedaboutitfrommultiplesources.
Doesthemodel
su(n) witha symmetric and n − 8 fundamentals.
havesomesecretinconsistency?
No. ClassificationsinF-theorysofarforgottoinclude O7+.[workinprogress, withBhardwaj, MorrisonandTomasiello]
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Youcantakeeither
n D6s
NS5½NS5
O8−+ 16 D8s
n − 8 D6s
or
n D6s
NS5½NS5
O8+
n − 8 D6s
andcompactifyonetransversedirection,thentaketheT-dualtogototheIIB.
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IntheF-theorylanguage, wehave
In
transversetangent
I 4* In−8
or
transversetangent
In
In−8“ I4* ”
What’sthis “I∗4”?
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ThepointisthatinF-theory, thereare two distincttypesof I∗
n singularitieswhen n ≥ 4.
• I∗n with so(2n + 8) symmetry, deformabletobesmooth.
• “I∗n” with usp(2n − 8) symmetry, deformableonlydownto “I∗
4”.
Thelatterisfrozenbyamysteriousdiscreteflux[Witten, hep-th/9712028].
YoumightworrythatotherKodairatypesmighthavefrozenversions,butthatdoesn’thappen[YT, 1508.06679].
F-theorygeometrizesmostofthefieldtheoryphenomena,butitstillneedssomeadditionaldata. cf. T-brane.
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Summary
• 6dSCFTscanbestudiedinmanyways.
• Varioussubtlefield-theoreticalfeaturesarealwaysencodedinF-theory, butinmysteriousways.
–Propertiesof ADE Instantonson R × T 3
–Globalanomaly π6(SU(2)) = Z12
–Reductionofflavorsymmetry so(8) ⊃ so(7)of nT = 1 su(2) with 4 doublets
–Issueson O+-planes
• Therearemanyopenquestions.
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Openquestion
Doesevery6dSCFT comefromF-theory?
Openquestion
Doesevery4d N=2 SCFT comefromstringtheory?
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Openquestion
Doesevery6dSCFT comefromF-theory?
Openquestion
Doesevery4d N=2 SCFT comefromstringtheory?
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cf. AsfarasI know, thereisneitherastringyrealizationof
• 4d N=2 SU(7) or SU(8) with 3-indexantisymmetric• 4d N=2 Sp(3) or Sp(4) with 3-indexantisymmetric• 4d N=2 SO(13) or SO(14) with spinor
northeSeiberg-Wittensolutionstothem. DoesF-theoryhelp?
NotethatalmostexactlythesamelistofgroupsweregivenbyDaveonthe1stdayoftheworkshop, assubtlecasesinTate’salgorithm.Anyrelation?
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