3173 Page 4 of 16 Eur. Phys. J. C (2014) 74:3173
a non-propagating torsion
˜
K
μνλρ
→ R
μνλρ
. The second
order curvature tensor and the irreducible curvature scalar
are worked out:
4
˜
K
μν
=−
2∂
λ
H
μν
λ
+ H
μρ
λ
H
λν
ρ
and
˜
K =−
1
4
H
μνλ
H
μνλ
. (7)
As a result, the effective curvature constructed in a non-
perturbative framework may be viewed as a generalized cur-
vature tensor. In a second order formalism the effective H
3
dynamics on a D
4
-brane may be approximated by
S
eff
D
4
=
1
3C
2
2
d
5
x
−det
˜
G
μν
˜
K. (8)
Generically the open string metric may arguably be re-
expressed in terms of the Poincaré dual field strength. It takes
the form
˜
G
μν
=
˜
G
z
μν
+ C
¯
H
μλρ
H
λρ
ν
, (9)
where
˜
G
z
μν
=
g
μν
− B
μλ
B
λ
ν
and B
μν
signify the global or
zero modes of the two form, which are i ndeed coupled to an
electromagnetic field F
linear
μν
. Under a two form gauge trans-
formation δ B
μν
=
∂
μ
ν
− ∂
ν
μ
the U(1) gauge invariance
underlying the curvature scalar
˜
K is worked out explicitly:
δ
˜
K =
3
2
δ
D
[μ
B
νλ]
H
μλν
=
1
2
δ
H
μνλ
+ H
μν
ρ
B
ρλ
+ H
νλ
ρ
B
ρμ
+H
λμ
ρ
B
ρν
H
μλν
=
3
2
H
μν
ρ
δ B
ρλ
H
μλν
=
3
2
H
μν
λ
H
μνρ
− H
μν
ρ
H
μνλ
∂
ρ
λ
. (10)
The U(1) gauge invariance, i.e. δ
˜
K = 0, may be achieved
by the notion of a metric (fluctuation) sourced by the local
degrees in a geometric torsion. A priori the gauge invariance
of the curvature scalar
˜
K seems to incorporate a condition on
the two form:
C (2πα
)H
αβ
μ
H
αβν
= f
μν
q
. (11)
Nevertheless the perturbation gauge theory ensures an
infinitesimally small global (two form) mode coupling in
a geometric torsion (5) and hence the condition may be
ignored. Then the emerging notion of a metric underlying
a propagating geometric torsion in the non-perturbative cur-
vature formalism is given by
f
q
μν
= C H
μαβ
¯
H
αβ
ν
. (12)
The symmetry under an interchange μ ↔ ν in the r.h.s.
ensures that the naive condition on a two form becomes
insignificant. Interestingly the emergent metric incorporates
the notion of space-time in the curvature scalar
˜
K and hence
justifies the open string effective metric arguably obtained in
Eq. (9)onaD
4
-brane.
3 Vacuum created pair of (D
¯
D)
3
-brane
It is remarkable to note that an effective space-time is vacuum
created on a pair of (D
¯
D)
3
-branes by a dynamical two form
in a U(1) gauge theory on a D
4
-brane. The vacuum refers to
a background black hole on a D
4
-brane which is well known
to be sourced by a global mode of a NS two form. Hence
a geometric torsion underlying the second order curvature
formalism is associated with a universe with a vacuum cre-
ated pair of (D
¯
D)
3
-branes. In fact, the dynamical space-time
without torsion in 4D has been argued to have begun at the
Big Bang singularity defined at a cosmological horizon in
a5D-brane world with torsion. It is noteworthy to remark
that the space-time curvature sourced by a geometric torsion
in 5D naturally incorporates an intrinsic angular momentum
on a vacuum created pair of (D
¯
D)
3
-branes. The world vol-
umes of a brane and an anti-brane are separated by an extra
fifth dimension transverse to each other. It may imply that
an observer in a D
3
-brane universe is inaccessible to an anti-
D
3
-brane universe or vice versa. Nevertheless the invisible
effect of an anti-D
3
-brane space-time is indeed compelling
on a 3-brane universe due to the hidden fifth dimension. Anal-
ysis may reveal that the brane universe geometry seems to be
influenced by a potential candidate for dark energy.
3.1 Quintessence
The CMB observations in cosmology ensure that the vac-
uum energy density is not a constant. The time variation
of the cosmological vacuum energy density in the early
epoch leading to a de Sitter geometry has been argued in
the i nflationary models. In this context a quintessence is
well known to describe a time varying, spatially homoge-
neous component of cosmic density with a negative pressure
and a positive energy density. In the recent past a slowly
rolling time dependent scalar field is believed to describe the
quintessence presumably due to its simplest form as a ten-
sor field which couples minimally to Einstein gravity. The
acceleration of the universe is parameterized by the cosmo-
logical equation of state: ω = P/ρ, where P =−T
i
i
< 0
and ρ = T
0
0
> 0, respectively, define the pressure and energy
density sourced by a scalar field. In the recent years the obser-
vational cosmology primarily has focused on the measure-
ment of ω sourced by a quintessence. It takes a bounded
value: −1 <ω<−1/3.
The quintessence energy density underlying geometric
torsion in the formalism may be seen to be sourced by a
123
剩余15页未读，继续阅读
weixin_38519849
- 粉丝: 5
- 资源: 973
我的内容管理
展开
最新资源
- 新型矿用本安直流稳压电源设计：双重保护电路
- 煤矿掘进工作面安全因素研究：结构方程模型
- 利用同位素位移探测原子内部新型力
- 钻锚机钻臂动力学仿真分析与优化
- 钻孔成像技术在巷道松动圈检测与支护设计中的应用
- 极化与非极化ep碰撞中J/ψ的Sivers与cos2φ效应：理论分析与COMPASS验证
- 新疆矿区1200m深孔钻探关键技术与实践
- 建筑行业事故预防：综合动态事故致因理论的应用
- 北斗卫星监测系统在电网塔形实时监控中的应用
- 煤层气羽状水平井数值模拟：交替隐式算法的应用
- 开放字符串T对偶与双空间坐标变换
- 煤矿瓦斯抽采半径测定新方法——瓦斯储量法
- 大倾角大采高工作面设备稳定与安全控制关键技术
- 超标违规背景下的热波动影响分析
- 中国煤矿选煤设计进展与挑战：历史、现状与未来发展
- 反演技术与RBF神经网络在移动机器人控制中的应用
资源上传下载、课程学习等过程中有任何疑问或建议，欢迎提出宝贵意见哦~我们会及时处理！
点击此处反馈
