D3诱导的几何膨胀模型与超重力
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"D3诱导几何膨胀"
这篇学术文章探讨了由抗D3麸皮（antidyon D3-branes）与本体几何中的模场（moduli fields）相互作用所引发的一种有效超重力膨胀模型。这个模型的核心是几何描述，其中Kähler函数扮演着至关重要的角色，因为它包含了理论的全部几何信息。在该理论构造中，非零的二等分弯曲（bisectional curvature）是一个关键要素，它对模型的形成起到了重要作用。
超重力膨胀模型是一种利用超弦理论或超引力理论来解释宇宙早期膨胀阶段的物理模型。抗D3麸皮在这里作为激发因子，其与模场的相互作用产生了膨胀效应。文章中提出的新的几何形式主义引入了无能的超场（nilpotent superfield）来代表抗D3麸皮，这为现有的基于超重力的膨胀模型提供了强大的概括手段。这种新方法允许模型轻易地整合任意的哈勃参数（Hubble parameter）、宇宙常数以及引力质量值。
文章通过展示多项式混沌膨胀的广义形式、α吸引子类型的T模型以及E模型来具体阐述这一概念。这些模型都是膨胀理论中常见的模型类型，它们描述了粒子在不同条件下的动力学行为。此外，作者还提出了一种多阶段的宇宙吸引子机制，称为级联膨胀，这可能意味着宇宙的演化经历了多个连续的膨胀阶段。
这篇研究由Renata Kallosh、Andrei Linde、Diederik Roest和Yusuke Yamada合作完成，他们分别来自斯坦福大学的理论物理研究所和物理学系，以及格罗宁根大学的范斯温德伦粒子物理和重力研究所。文章在2017年由Springer出版，并在JHEP期刊上发表，表明了其在高能物理和宇宙学领域的学术价值。通过这种深入的研究，科学家们对宇宙早期状态的理解得到了进一步的深化，也为未来探索宇宙的起源和演化提供了新的理论工具。
JHEP07(2017)057
2 Geometric inflation features
2.1 D3-brane induced geometry
We will explain here that the most general K¨ahler invariant K¨ahler function G depending
on multiple Calabi-Yau moduli and on a nilpotent multiplet S can be reduced to the form
we show in eq. (1.2). An equivalent form is to use
K(T
i
, T
i
; S, S) = K
0
(T
i
, T
i
) + S + S + G
SS
(T
i
, T
i
)SS , W = W
0
, (2.1)
where the gravitino mass, in general is given by the following expression:
|m
3/2
(T
i
, T
i
)|
2
= e
G
0
(T
i
,T
i
)
= e
K
0
(T
i
,T
i
)
|W
0
|
2
. (2.2)
The linear terms in the K¨ahler function and potential are directly related to spontaneous
SUSY breaking and hence an integral aspect of our set-up.
We will start with the observation [41, 42] that the most general supergravity theory
with a number of unconstrained chiral multiplets T
i
and a single nilpotent superfield S is
given by
K = K
0
(T
i
, T
i
) + K
S
(T
i
, T
i
)S + K
S
(T
i
, T
i
)S + G
SS
(T
i
, T
i
)SS ,
W = g(T
i
) + f(T
i
)S, (2.3)
where K
S
,
K
S
and G
SS
are non-holomorphic functions while f and g are holomorphic.
These are the most general Taylor expansions of the K¨ahler and superpotential due to the
nilpotency condition S
2
= 0.
These general expressions can be simplified without loss of generality by a number of
redefinitions. First of all, one can use a K¨ahler transformation acting as
W → W × F , K → K − log |F|
2
, (2.4)
to set W = W
0
by choosing F = W
0
/(g + fS). The resulting K¨ahler potential is given by
K
0
= K
0
0
(T
i
, T
i
) + K
0
S
(T
i
, T
i
)S + K
0
S
(T
i
, T
i
)S + G
SS
(T
i
, T
i
)SS, (2.5)
in terms of the redefined variables K
0
0
= K
0
+ 2 log(|g|/|W
0
|), and K
0
S
= K
S
+ f/g. In this
frame, the supersymmetry breaking is set by K
0
S
which we assume to be non-vanishing due
to the nilpotency of S.
We can subsequently use the field redefinition K
0
S
S = S. Note that K
0
S
is not holomor-
phic, and hence this field redefinition breaks the complex manifold structure. However, at
least in the bosonic part of the theory
1
this is not a problem for the following reason. The
geometry spanned by the physical scalars is given by the K¨ahler manifold with a projection
S = 0, since the bosonic component of S is a fermion bilinear, i.e.,
ds
2
= G
ij
dT
i
dT
j
|
dS=S=0
. (2.6)
1
The fermionic action will be affected by this change only in the part depending on the goldstino, a
fermion in the nilpotent multiplet, χ
S
. But in the unitary gauge, χ
S
= 0, in which this fermion is absent,
there will be no changes. In our models with G
T
i
= 0 in this gauge the gravitino decouples from the
fermions in T
i
multiplets and the gauge with χ
S
= 0 is simple.
– 4 –
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