Infinite Symmetry in the high energy limit. Pei-Ming Ho 賀培銘 Physics, NTU Mar. 2006. Collaborators. Chuan-Tsung Chan (NCTS) 詹傳宗 Jen-Chi Lee (NCTU) 李仁吉 Shunsuke Teraguchi (NCTS/TPE) 寺口俊介 Yi Yang (NCTU) 楊毅. References.
Pei-Ming Ho 賀培銘
we take various limits:
Weak coupling limit strong coupling limit
Weak field limit (strong field limit?)
Low energy limit High energy limit
High energy limit: ( )
Gross, Wilczek (1973); Politzer (1973)
Closed string theory
Gross, Mende (1987,88); Gross (1988,89)
Open string theory
Gross, Manes (1989)
in string units. Creation/annih. op’s
A most generic spacetime field in the bosonic open string field theory is of the form:
Note that components of eP and eL scale like E1, eT scales like E0, and components of (eP-eL) scale like E-1.
k field theory is of the form:3
i.e., ignore 4-pt. fx’s subleading to a sibling.
(Families with larger M dominate.)
corresponding to gauge transformations
(how it scales with E when E )
At the lowest mass levels (m2 = -2, 0), there are no more than one independent physical states.
The lowest mass level as a nontrivial example is
m2 = 2.
Type I: [k-1 -1+ -2]0,k; k = 0.
= eL or eT
Type 2: ½[(+3kk)-1 -1+ 5k-2]0,k
= ½[5P-1P -1+ L-1L -1+ ]0,k
Decoupling of field theory is of the form:
zero norm states:
Count naïve order of E
and replace P L:
Solve the linear rel’s:
Leading order result:
These relations are new.
Gross and his collaborators’ computation was wrong.
s, t, u = Mandelstam variables:
s = 4E2, t -4E2 sin2, u -4E2 cos2 .
Zero norm states: field theory is of the form:
D(…, j) is almost the same as (…), but with the j-th row replaced by