View
215
Download
2
Category
Preview:
Citation preview
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 ?!
Recommended