2019 1 15 IPMU

Mdonic Supertensor Models

work in progress with Mukund RangumaniSean Cellini Eller in

Melanie tensor model is a new type ofSolvable model when the melanie Feynman diagramdominate in the large N limit I will alsoargue later that supersymmetry is inevitablefor the model to be interesting in d ⼆二 2

Motivation and background

Solve QFT iprutuvbatun theory ⼀一 Feynman diagram

resum to all ordersihoft large N limit1 vector like models 中 ī 1 N

L Ìzizi ÌliifN one t R

tshfh.t.itsohiiǖble diagramN i_fhgr.eeSchwinger_Dyson equations

⼀一⽉月 rs

GD t Q DEDtSolvable in any dimensions

Otherexamples Chern Simons vector models

I dl

a Matrix like models fixing不 j NP N x N matrix

L ÌT 2中⼦子中 好 不 中4

N planar diagrams

tnoh 四⼀一 ⼗十 an t

SD equs do not truncate Only solvablein special cases by other techniques

Solvable example i N 4SYM.to matrix model

New large N limit GunnWittenCarrozza Tanasa klebanov

Tarnopolskyfiia.ir1 N r 1 f 1Ìni ⼗十 年年 g f9 4 中4 tiiflib pipits

中 ⼀一 中tetrahedron

Q 中

Each pair of fields has one index contractedbetween them

large N with 5 P 三 5 fixedtriple line notation

⼆二 千

N ⼆二 ⼗十 1_tgp J

large N limit is dominated by

mdonicdigmmsgocsingle line notation

Nonmdouie diagrams

frfr

gN Entnlg g4N4 TT

SD equation of 2 pt function

器

GO ⼀一 ⼗十⼀一 回 ⼀一 ⼗十Other type of interactions

DT DID

四 CDD

⽽而世

pillow double sum

pillow and double sum ruin mdouic dominance

gnif

Lore of Q FTRG flow generates all possibleinteractions allowed by symmetryresolution i supersymmetry

Non_renormalization theorem

For theories with 4 supercharges hdomorphyprevents the superpotential beingrenrmdized

UV theory w RGmdonic superpotential

7 IRSCFT

want marginal or relevant couplings

mdonic quartic and higherad X3 di quartic marginally irrelevantxzdquartic slxtic

2 d N 2，2did superfields 五 if

it M a bit N

superpotential Wig 三下 ⽟玉 的 五 iji jT T

I 2

LiMN

五⼀一 五

large N M with Jj NM fixed⼆二 mdouk dominance

Commentsl Same large N limit as the 2dsusy SYKmodel C with random couplingstudied byMurugan Stanford_

witten and Bwlycheva1706.05362 1801.09006

2 Two point function

中⼆二 0 ⼗十 年年 王 中 tdft

freetheory

3 Four point function solved by ladder

1 our pond function solved by ladderdiagrams

⼆二 ⼗十 ⼆二 ⼗十 ⽫皿 t

central charge c ǏNMdouble twist operator spectrumE J 2 n 2Op t ECn Jccn 丁 0 I 他 J

王 2 zm更更or

4 Chaos exponent I ⼆二 0.6䛒 s 哥

王 to 更更 laxl 五 t 以五比 ffeht5IR SCFTBulk dud Ads string theory

with finite tension

o Noncompact moduli space2W

2W

Ei⼆二

李 吾 王 i Ij Ftemeq

1 五 nilpotent matrix王 五 ⼆二 EM ⼆二 0

2 丟 入 G 王 z XG

王了了 ⼆二 五4 ⼆二 ⼆二 五m ⼆二 0

continuum in the spectrumof IRCFT

lifting the flat directions requires⼈人 gauge the SUM sym2 break the 0 Mlsymby anisotropic deformation

Gauge the SUN

symdt 上

71Tg 9YM

z

Mdoùe coupling J g N Mt Hooft coupling ⼩小 9in N

g gym I

Choosing g GYM mdouic coupling ismuch larger than it Hoft coupling

J giM sg.im N Dstill melanie after guying

Anisotropic deformation

W ftrliltījaijtr 王香⽟玉利利ai Gāji cx parameters

⼦子 P

Mdonlc dominance most of aīj to

large IR conformal manifold

Higgs branch i

Ftermqiaft 就aij求求我 oD tnmeqi 本 𤣰 五⽉月 ⼆二 0

Higgsbranch is a symplectic quotient

F term eq Dtmeq SUNholomorphic quotient

F

temegYSUN.clhlo h Ul UMU

holomorphicquotnf MUM UMUlsymplectic

quotient

Conjecture i symplectic quotient is compact forgeneric aij_

example i N M 2 a ⼆二9221 Gn⼆二921⼆二 a

PtaYXYIPtaxyx oattl.co odetx dt Y 0

不刈 Xt at MY不 叫 Yt at XY X ⼆二 0

⼈人 X Y 0

2 Xx Y and I ⼆二 0

x x 火 ⼦子

iii é é71

GP

holomorphic quotient GP U

Dtnneg lxityp.nosymplectic quotient

compact generic a

non compact a 0 ⼠士 I N

Coulomb branch

twisted chiral superfield

G idI io X_tQTCD iE.lt

品⼀一

區 oi 㮺sgtnV

IDP IFFttrco.ci

V It tr Go 中 6⼗十中 t d中 G中了了

classical Coulomb branch i中 f

oai.j

Nou.compact N 1 dimension

assuming i G t Gj for ītjCi to V i

integrating out W bosonsand charged matters

effective twisted superpotential Hiring0609032Ū Mtifiilhgki i 1

N 12 llty N_n Gi

El

N I

Theta angles for UG⼼心

Qī Im䂬i 2 Mtj N_n

Q Q.it 2⺎兀兀

flat directions are preserved

Kill the flat directions by consider SUMANForexample SUMEz.ES 0 3

N i Mtl a 1104.2853 Hori

compactness Qbare ⼆二 0 M evenQbare 三 ⼤大 M odd

Future directions⼈人 compute elliptic gems

Nez done

z generalizationM

xeMz

3 embed in string theorybrane construction