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a-ゲージにおける ゲージ不変量の数値計算soken.editorial/sokendenshi/...まとめ...
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a-ゲージにおける ゲージ不変量の数値計算 岸本 功（理研） 高橋智彦氏（奈良女大理）との共同研究 arXiv.0812.nnnn[hep-th], to appear
Transcript of a-ゲージにおける ゲージ不変量の数値計算soken.editorial/sokendenshi/...まとめ...
a-ゲージにおけるゲージ不変量の数値計算
岸本 功（理研）高橋智彦氏（奈良女大理）との共同研究
arXiv.0812.nnnn[hep-th], to appear
結果
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! ! ! ! ! ! !
!
!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""
""""""""""
" " "
"
"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""
#######################################################################################################################################
######################################################################################################
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$$$$$$
$
$
$
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
&&
0.88 0.90 0.92 0.94 0.96 0.98 1.00 1.020.88
0.90
0.92
0.94
0.96
0.98
1.00
(2,6)
(4,12)
(6,18)
(8,24)(10,30)(12,36)
Schnabl解
2!2g2
V26S[!]
2!
V26OV (!)
横軸の量:(規格化した) 開弦の場の理論の作用
S[!] = !1g2
!12
"!, QB!# +13
"!, ! $ !#"
!!! = QB" + ! ! " " " ! !ゲージ変換：
2!2g2S[!]/V26
運動方程式： QB! +! ! ! =0
縦軸の量2!OV (!)/V26 :(規格化した) gauge invariant overlap
OV (!) = !!̂(1c, 2)|"V "1c |!"2
|!V ! = "126
!µ!"µ!1"̄!
!1c1c̄1|0!
!!OV (!) = 0これはゲージ不変：
on-shell閉弦状態
a-ゲージ(b0M + a b0c0Q̃)|!! = 0
QB = Q̃ + c0L0 + b0M
a = 0 b0|!! = 0特に
のときSiegelゲージ
b0c0Q̃|!! = 0a = ! のときLandauゲージ
[浅野-加藤(2006)]
解の構成初期値：
Q!nA ! QB + !n " A # (#1)|A|A " !n
!0 =64
81!
3c1|0"
(b0M + a b0c0Q̃)!n+1 = 0
c0b0(Q!n!n+1 ! !n " !n) = 0
により !n !" !n+1
収束すれば c0b0(QB!! + !! ! !!) = 0
レベルトランケーションにより数値計算。
運動方程式(BRST不変性)の中の の係数
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!
!
!
!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""
"""""
"
""""""""""""""""""""""""""""""""""""
""""""""""""""""""""""""""""""""""""""
#############################################################################################################
#
#
########################################################################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
$$$$
$
$$$$
$
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&
!10 !5 0 5 100.000
0.005
0.010
0.015
0.020
0.025
0.030
0.035(2,6)
(4,12)
(6,18)(8,24)
(10,30)(12,36)
b0c0(QB! +! ! !)
a
c!2c1|0!
まとめ• a-ゲージの数値解を（レベルトランケーションで(10,30),(12,24)近似まで）構成し、ゲージ不変量（作用およびgauge invariant overlap）を計算した。
• 「BRST不変性」についても確かめた。• どのゲージの解も、Schnablの解析解と同じ値をほぼ再現する。• これらの数値解は全てSchnabl解とゲージ同値でuniqueな非摂動論的真空を表す解である、という期待と整合する。
