String Field Theories

Oct. 18, 2010at ： YITP, Kyoto University 　　　　　　　 Taichiro Kugo

History of SFT – personal view

　 1974 　 Kaku and Kikkawa 　　　　　　（加来 - 吉川）　　 First SFT 　　 Light-cone gauge SFT

String length

Gave much impact to physics societyGauge symmetry is not manifestSuccess of QCD (local field theory) → has soon faded away, unfortunately

BRS （ T) symmetry 1978 Operator Formalism of YM Kugo and Ojima Gupta-Bleuler-Nakanishi-Lautru

p

1982 Fujikawa: BRS quantization of String Anomaly of conformal and ghost number 1983 Kato and Ogawa

Kato-Ogawa, “Covariant Quantization of String based on BRS Invariance” Nucl.Phys.B212(1983)443

Infinite number of conditions

A Single condition

Toward String Field Theories Single Condition QB Φ ＝０　→　 kinetic term should be

Interaction term 　 should be midpoint type:

1983 – 1984 Kato, Ogawa, Uehara and TK We gave seminar talks in a few University seminars

Tetsuo Goto, “Picture of Extended Particles”(Iwanami, 1978)

Chapter5. String Model§5.5 String-string Interaction

Midpoint Interaction

Unfortunately,we could have confidence on the correctness neither of the Kinetic term nor of the Interaction term.

Huge gauge invariance → 　 how to gauge-fix?　　 Bizarre midpoint interaction → 　 reproduce Koba-Nielsen?

Soon Siegel’s paper appeared 1984 July Gauge fixed and Free theory

We could not convince ourselves to the last and gave up publication of our work

Important Lesson: If you find a natural theory, then publish it even you cannot prove its validity.

Interacting gauge SFTs : 1986 Witten: Cubic SFT Goto-Witten-type vertex

open bosonic open NSR superstring

HIKKO (Hata-Itoh-Kugo-Kunitomo-Ogawa) bosonic open LC-type vertex

bosonic closed : cubic

Problems: GW-type vertex NSR superstring Colliding X2 problem (C.Wendt, 1989)

・ 1990 Modified Cubic SFT (0-picture NS) Preitschopf-Thorn-Yost Aref’eva-Medvedev-Zubarev gauge-fixing problem (Kernel of PC ops X,Y)

・ 1995 WZW-like superSFT Berkovitz problem in R-sector

Closed string Non-polynomial SFT

Saadi-ZwiebachKugo-Kunitomo-Suehiro ’90 Tree level actionPolyhedral vertices

B.Zwiebach ’93Quantum Action

Problems: LC-type vertex HIKKO ： unphysical α

１）　　　　　　　　 (identify) HIKKO Consistent gauge theory, but non-covariant 2) Covariantized LC SFT Unphysical quartet variables: α + 1(bosonic) + 2(fermionic) Siegel-Zwiebach, Neveu-West, Uehara, Kugo

Cubic SFT for closed string!

But, it is difficult to discuss vacuum energyVertex depends on the string length ratio

Cf: a single field condensation can be discussed in the cubic vertexDilaton condensation: Yoneya(787), Kawano(’92)

Nongeometrical vertex?

BSFT (Boundary SFT) Witten

There are no propagator and no vertices explicitly at least

It is not a SFT in the usual sense.

Insight on Non-perturbative Aspects from SFT At eraly stage　・ SFT is a gauge theory with Huge gauge symmetry　・ Pregeometrical SFT (Purely cubic action)

　　 QB : only object specifying space-time metric

　　 Spontaneous generation of space-time and motion　　　 Yoneya,Friedan(‘85), HIKKO(‘86), Strominger et al.

T-duality 　 and gauge symmetry 1992 Kugo-Zwiebach based on 　 HIKKO

Remarkable Success of SFT

Exact solution by Schnabl (Nov. 2005)

classical solutions and technique

explosive progress made by

Okawa, Ellwood, Fuchs, Kroyter, Rastelli, Zwiebach, Aref’eva, ….

Stagnancy after that, at the moment ?!

We should study by SFT D-branes matrix models : SFT D-instanton complementary D-particle D-string

S-duality U-duality M-theory AdS/CFT

May give hints On a new formulation of SFT

I hope that this workshop, this series of workshops, give a breakthrough for the SFT approach to string theory