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Type IIA flux compactifications [Elektronische Ressource] : vacua, effective theories and cosmological challenges / vorgelegt von Simon Körs

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MTYPEISIMONIALudwig-Maximilians-UnivFLUXvCOMPausA2009CTIFICAsitTIONS:VvACUA,burgEFFECTIVEhen,THEORIESderANDerCOSMOLOGICALatCHALLENGESDissertationhenanorgelegtderonFKakultORSatHamfMurMaiPhysikmiiLMU1.PDhenhPrter:RalphProf.Dr.agDieterundlicLufung:Dr.ust,Blumenhagen,LMUMMTderhen2.henh30.7.2009ter:iiitheActhesis.knoLwledgmenItsanFirsthadoflikalltalks,IbhaavsharingeouldtoCathankandmersyandthesisevadvisoryMarcooutZagermann:bFmate.orTimmhismanFtinthankuedsuppKoortTsimpis,and,allt.theoryForinteacwhingOutsidemeemanmya,themmannallyythings,tespalsoeciallytoinrasetheideasbexplanationseginningmonofImeythosePh.D.pleasureAndwith:nallyP,er,forust,givingWmeZagermann.thewopptoortunitmemythetoofenforterahisulatingtheatevdinnerserytimephtoouldaskthankquestions.andIfriendsamindebtedtotoTPaulAndKoforerbeinger:hFpleasanorItlesswhourstofthankexplanations.WFfororhissharingandhisyideasduringandlastviewsths.ofurthermore,phwysicslikandtoforallhisItheintoalloratetheClaudioviezel,orationsaulwerbeDieterdidtogether.

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Published 01 January 2009
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M
TYPE

I
SIMON
IA
Ludwig-Maximilians-Univ
FLUX
v
COMP
aus
A
2009
CTIFICA
sit
TIONS:

V
v
A

CUA,
burg
EFFECTIVE
hen,
THEORIES
der
AND
er
COSMOLOGICAL
at
CHALLENGES

Dissertation
hen
an
orgelegt
der
on
F
K
akult
ORS
at
Ham
f
M


ur
Mai
Ph
ysikm
ii
LMU
1.
PD

hen
h
Pr
ter:
Ralph
Prof.

Dr.
ag
Dieter
undlic
L
ufung:

Dr.
ust,
Blumenhagen,
LMU
M
M


T

der
hen

2.
hen


h
30.7.2009
ter:
iii
the
Ac
thesis.
kno
L
wledgmen
I
ts
an
First
had
of
lik
all
talks,
I
b
ha
a
v
sharing
e
ould
to
Ca
thank
and
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ers
y
and
thesis
ev
advisor
y
Marco
out
Zagermann:
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F
mate.
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his
man

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tin
thank
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supp
Ko
ort
Tsimpis,
and
,

all
t.
theory
F

or
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teac
w
hing
Outside
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e
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m
y
a
,
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nally
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esp
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ecially
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in
rase
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ideas
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eginning
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nally
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ortunit
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to
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en
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ter
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ould
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pleasan
or


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tless
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t
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F
for
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sharing
and
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y
ideas
during
and
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views
ths.
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urthermore,
ph
w
ysics
lik
and
to
for
all
his
I

the
in
to
all
orate
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Claudio

viezel,
orations
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w
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e
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did

together.
Dimitrios
I
Timm
w
rase
an
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t
Finally
to
I
extend
ould
sp
e
ecial
thank
thanks
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to
b
Claudio
of
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string
viezel:
group
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the
or
k-Institut
explaining

to
h
me

all
stim
the
atmosphere
m
all
ysteries
seminars,
of

m
quia,
y
orkshops,

or
F
en
or
breaks.

of
ying
ysics,
me
w
during
lik
the
to
last
m
three
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y
all
ears
y
in
for
almost
eing
ev
h
erything
blast
that
hang
I
with.
did
o
inside
I
of
this
ph
ysics.iv.
Con
.
ten
.
ts
U(1)
1
.
In
.
tro
.

.
3
.
1.1
er
The
.
motiv
.
ation
.
for
.
string
.
theory
.
.
.
.
45
.
.
.
.
.
.
.
the
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
40
.
.
.
3.4.4
.
.
.
SU(2)
.
.
.
The
.
.
3
.
1.2
.
The
.
form
.
ulation

of
.
string
.
theory
.
.
.
.
.
.
Solutions
.
.
.
.
.
.
.
G
.
.
.
.
.
.
.
Sp(2)
.
.
.
.
.
.
.
U(1)
.
.
.
.
.
.
.
SU(2)
.
.
.
.
7
The
2
.
The
.

.
of
energy
this
4.1
thesis
.
11
.
2.1
.
T
the
yp
.
e
.
I
51
I
.
sup
.

.

.
kgrounds
.
with
.
ux
4.3.2
.
a
.
.
.
Summary
.
.
.
.
.
.
.
.
.
.
.
36
.

.
.
.
.
.
.
14
.
2.2
.
Flux
.

3.4.1
and
SU(3)
the
.
mo
.
duli
.
problem
.
.
.
.
.
.
3.4.2
.
(U(2)
.
solution
.
.
.
.
.
.
.
.
.
.
.
The
.
U(1)
18
.
2.3
.
Ination
.
in
.
string
.
theory
.
.
SU(2)
.
.
.
.
.
.
.
.
.
.
.
42
.

.
.
.
.
.
.
.
.
.
.
.
.
.
Lo
.
ysics
.

.

.
.
.
.
.
.
.
.
.
.
.
.
.
4.2
21
to
2.4
.
Non-sup
.

.
v
.
acua
.
.
The
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
4.3.1
.
the
.
.
.
.
.
.
.
.
.

.
asa
.
.
.
.
.
.
.
57
.
.
.
.
.
.
.
.
25
.
2.5
.
Outline
.
of
59
this
.
thesis
.
.
.
.
.
.
3.4
.
on
.
spaces
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
37
.
The
.
2
.
solution
.
.
.
.
.
.
.
.
.
.
.
.
27
.
3
.
Sup
.

.
t
.
yp
.
e
38
I
The
IA
S
AdS

4
)

.
29
.
3.1
.
Conditions
.
for
.
a
.
sup
.

.
v
.
acuum
.
.
.
.
3.4.3
.
SU(3)
.

.
solution
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
29
41
3.2
The


h
solution
y
.
of
.
scales
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
3.4.5
.
SU(3)
.
U(1)
.
solution
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
4
.
w
.
ph
.
I:
.
Kaluza-Klein
.
47
34
Kaluza-Klein
3.3
.
Solutions
.
on
.
nilmanifolds
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
47
.

.
Kaluza-Klein
.
w
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
4.3
.
nilmanifolds
34
.
3.3.1
.
The
.
T
.
6
.
solution
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
52
.
Kaluza-Klein
.
of
.
torus
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
54
.
Kaluza-Klein
.
of
.
Iw
.
w
.
.
.
.
35
.
3.3.2
.
The
.
Iw
.
asa
.
w
4.3.3
a
.
solution
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
..
vi
.
CONTENTS
The
5
.
Lo
.
w
.
energy
.
ph
Repro
ysics
.
I
.
I:
Classifying
Eectiv
.
e
.
sup
.
ergra
.
vit
on
y
.
61
.
5.1
.
Eectiv
.
e
.
sup
.
ergra
.
vit
.
y
.
.
.
.
.
.
7.1
.
.
.
.
.
.
.
Non-sup
.

.
.
.

.
.
.
U(1)
.
.
.
no-go
.
.
.
.
.
.
.
.
.
6.4.2
.
.
.
sup
.
U(1)
.
.
.
SU(2)
.
.
.
6.6
.
.
61
.
5.2
.
The
.
nilmanifolds
.
.
Non-sup
.
.
.
acua
.
.
.
.
.
.
.
.
.
U(1)
.
.
.
.
.
.
.
.
.
6.3.3
.
.
.
.
.
.
.
6.3.4
.
.
.
.
.
.
.
No
.
.
.
.
.
.
.

.
.
.
.
.
.
.
p
63
.
5.2.1
.
The
SU(2)
torus
.
p
.
oten
6.5
tial
.
.
90
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
on
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

.

.
.
.
.
.
on
.
.
.
.
63
7.3
5.2.2

The
.
Iw
.
asa
results
w
.
a
.
p
non-sup
oten
U(1))
tial
.
.
on
.
.
.
.
.
S
.
)
.
.
.
.
.
.
.
.
.
.
.
.
.
SU(3)
.
no-go
.
.
.
.
.
.
.
.
.
.
.
.
.
SU(3)
.
no-go
.
.
64
.
5.2.3
.
Summary
.
.
.
.
84
.

.
.
.
.
.
.
.
.
.
.
.
85
.

.
.
.
.
.
.
.
.
.
.
.
.
.
85
.
alen
.
tials
.
.
.
.
.
.
.
.
.

.
SU(2)
.
.
.
.
.
.
.
.
64
.
5.3

The
v

.
spaces
.
.
SU(2)
.
U(1)
.
.
.
.
.
.
.
.
.
.
.
.
.
90
.
U(1)
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

.
ingredien
.
.
.
.
.
.
.
.
.
.
.
6.7
.
.
.
.
.
.
.
.
66
.
5.3.1
.
The
.
G
.
2
7
SU(3)
acua
p
the
oten
.
tial
.
.
.
.
.
.
96
.
v
.
2
.
.
.
.
.
.
.
.
.
.
.

.
Sp(2)
.
.
.
.
.
.
.
.
.
100
.
kno
.
.
.
.
.
.
.
.
.
.
.
7.3.2
66
v
5.3.2
S(U(2)
The
.
Sp(2)
.
S(U(2)
103

v
U(1))
U(1)
p
.
oten
.
tial
.
.
.
.
104
.
(U(2)
.
U(1)
.
no-go
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
84
.
The
.
U(1)
.
U(1)
.
.
67
.
5.3.3
.
The
.
SU(3)
.
U(1)
.

.
U(1)
.
p
.
oten
.
tial
.
.
.
.
84
.
The
.

.
SU(2)
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
6.3.5
.
SU(2)
.
SU(2)
.
.
.
.
69
.
5.3.4
.
The
.
SU(2)
.

.
SU(2)
.
p
.
oten
.
tial
.
.
6.4
.
SU(2)
.
SU(2)
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
6.4.1
.
inequiv
.
t
70
oten
5.3.5
.
The
.
SU(3)
.

.
U(1)
.
SU(2)
.
p
.
oten
.
tial
86
.
Small
.
for
.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
88
.

.
without
.

.
acuum
.
.
.
.
.
.
72
.
5.3.6
6.5.1
Summary
2
.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
6.5.2
.

.
3
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
73
.
6
.
Cosmology
91
75
A
6.1
t
A
extra
no-go
ts
theorem
.
without
.

.
uxes
.
.
.
.
.
.
.
.
.
.
.
.
.
.
92
.
Summary
.
.
.
.
.
.
.
.
.
.
.
.
.
.
76
.
6.2
.
A
.
mo
.
died
.
no-go
.
theorem
.
for
.

.
.
93
.
Non-sup
.
v
.
95
.
Generalizing
.
sup
.
solution
.
.
.
.
.
.
.
.
.
.
.
.
80
.
6.3
.
Cosmology
7.2
of


acua
.
G
.
SU(3)
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
99
.
Non-sup
.
v
.
on
.
S(U(2)
.
U(1))
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
7.3.1
.

.
wn
83
.
6.3.1
.
The
.
G
.
2
.
SU(3)
.
no-go
.
.
.
.
.
.
.
.
101
.
New
.

.
acua
.
Sp(2)
.

.
.
.
.
.
.
.
.
.
.
.
7.4
.

.
acua
.
SU(3)
.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
83
.
6.3.2
.
The
Sp(2)d
CONTENTS
.
1
.
8
.
Conclusions
geometries
107
.
A
.
T
.
yp
.
e
.
I
.
I
.
sup
.
ergra
.
vit
.
y
128
111
.
B
122
Generalized
.
geometry
.
113
.
B.1
.
N
.
=
.
1
.
AdS
.
4
127
susy
.
equations
.
.
.
.
.
.
on
.
133
.
.
.
.
.
T
.
C.1
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
C.2
.
.
.
.
.
.
.
.
.
.
.
.
.
.
114
.
B.2
Coset

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
A
.
tegrating
.
(3)
.
.
.
.
.
.
.
.
.
.
.
C
.
en-dimensional
.
125
.
Group-manifolds
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
116
.
B.3
.
Ho
.
w
125
to
Nilmanifolds
dress
.
smeared
.

.
with
.
orien
.
tifold
.
in
.
v
.
olutions
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
118
C.3
B.4
spaces
Eectiv
.
e
.
sup
.
ergra
.
vit
.
y
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
D
.
note
.
in
.
out
.

.
3
.
.