Perturbative Vacua from IIB Matrix Model

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Perturbative Vacua from IIB Matrix Model

• ????(???)
• ????(??????)??????

2
???????????
Ishibashi-Kawai-Kitazawa-Tsuchiya,
Fukuma-Kawai-Kitazawa-Tsuchiya

• IIB????

IIB superstring
??
type IIB ????????????????
Motl, Banks-Seiberg, Dijkgraaf-Verlinde-Verlinde

• matrix string theory

IIA superstring
??
(cylinder ?? super Yang-Mills )
( fermionic terms)
??????????????????????????????????? ??????????????
?
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IIB??????large N ?moduli???
Naive reduced model
diagonal elements ????1???????
????????????????
supersymmetric ???(?????????????????)
IIB???????????????????????????????
1/N ??
large N ???? ???????????? moduli space ???
? 1/N ???????????????????????
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IIB?????1???????
???
???????????
???????????
??2N?
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Moduli space??perturbative vacuum
(??????quenching)
large N ????IIB????????????????????? ?????????????

?????(moduli space ???)????????????? large N
reduced model ?????????quench????
IIB?????
large N moduli
quench
????????????????????? ?????????0?????
IIA
super Yang-Mills

• ????quench

cylinder??
IIB on
(matrix string theory)
type IIA superstring

• ????quench

4dim. super Yang-Mills
??type IIB superstring
moduli space ??? string ? perturbative vacuum???
? 1/N ???????moduli????????
String????????????????????????
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quench
N??
????????
????quench?????????? ???????????????
4dim. super Yang-Mills
2dim. super Yang-Mills
cylinder??
(matrix string theory)
??type IIB superstring
type IIA superstring
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Gauge theories from IIB matrix model
ex. cylinder?? super Yang-Mills???
IIB matrix model
redefine
UV cut-off , fixed
t Hooft coupling, fixed
1
large N limit ?planar diagram??????
expansion
quench
( ?)
diagonal elements ?0
??Feynman rule ? super Yang-Mills ?Feynman
rule ???????
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Free energy ???
???????quench??IIB matrix model ?? cylinder??
super Yang-Mills ??????? ????free energy ?
??????????
?????free energy ????diagram????
IIB matrix model ???
Large N ?
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? factored out
???
??????? ????free energy??????
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Type IIA superstring from IIB Matrix Model
???
??????????????????
2
???
???? matrix string theory
????

• c ?IIB????????? ?????? ??????

• ??????????matrix string theory ? cut-off ?

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Large N limit
???????12??quench ?????????????????? ?????????
???????
large N ??????????????????????????? IIB???????????
??? planar diagram ????????
fixed
fixed
??????? ???????????????????????????????

• matrix string theory ? cut-off

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IIB matrix model??overall scale???????????? ??????
?????????????????????
????
????????
????
????
???? ???????????????????????large N ??
?????type IIA superstring ??????
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conclusion

• IIB?????large N ?????????????????
• moduli space????
• moduli ??????type IIA superstring ??????????
• AdS5 x S5 ??type IIB superstring
  ??????????moduli?
• string??????????????????????
• IIB???????????????????????????????
• ???????????0???????????(quench)???matrix string
  
• theory ??????????? type IIA superstring ???????
• ???????????????????????
• ?????large N ????????perturbative superstring
  ????