A x i o n T h o u g h t s : A x i o n T h o u - - PowerPoint PPT Presentation

SLIDE 1

A x i

• n

T h

• u

g h t s : A x i

• n

T h

• u

g h t s :

i . e . w h a t w e / I d

• n

’ t y e t u n d e r s t a n d a b

• u

t Q C D A x i

• n

D M i . e . w h a t w e / I d

• n

’ t y e t u n d e r s t a n d a b

• u

t Q C D A x i

• n

D M

G i

• v

a n n i V i l l a d

• r
• G

i

• v

a n n i V i l l a d

• r

SLIDE 2

A x i

• n

S

• l

u t i

• n

t

• t

h e S t r

• n

g C P P r

• b

l e m ! A x i

• n

S

• l

u t i

• n

t

• t

h e S t r

• n

g C P P r

• b

l e m !

SLIDE 3

A x i

• n

S

• l

u t i

• n

t

• t

h e S t r

• n

g C P P r

• b

l e m ! A x i

• n

S

• l

u t i

• n

t

• t

h e S t r

• n

g C P P r

• b

l e m !

P e c c e i Q u i n n ‘ 7 7 P e c c e i Q u i n n ‘ 7 7 We i n b e r g , Wi l c z e k ‘ 7 8 We i n b e r g , Wi l c z e k ‘ 7 8 ( K S V Z , D S F Z . . . ) ( K S V Z , D S F Z . . . )

SLIDE 4

A x i

• n

S

• l

u t i

• n

t

• t

h e S t r

• n

g C P P r

• b

l e m ! A x i

• n

S

• l

u t i

• n

t

• t

h e S t r

• n

g C P P r

• b

l e m !

V a f a Wi t t e n ' 8 4 V a f a Wi t t e n ' 8 4

P e c c e i Q u i n n ‘ 7 7 P e c c e i Q u i n n ‘ 7 7 We i n b e r g , Wi l c z e k ‘ 7 8 We i n b e r g , Wi l c z e k ‘ 7 8 ( K S V Z , D S F Z . . . ) ( K S V Z , D S F Z . . . )

SLIDE 5

A x i

• n

S

• l

u t i

• n

t

• t

h e S t r

• n

g C P P r

• b

l e m ! A x i

• n

S

• l

u t i

• n

t

• t

h e S t r

• n

g C P P r

• b

l e m !

V a f a Wi t t e n ' 8 4 V a f a Wi t t e n ' 8 4

P e c c e i Q u i n n ‘ 7 7 P e c c e i Q u i n n ‘ 7 7 We i n b e r g , Wi l c z e k ‘ 7 8 We i n b e r g , Wi l c z e k ‘ 7 8 ( K S V Z , D S F Z . . . ) ( K S V Z , D S F Z . . . )

SLIDE 6

f r

• m

1 8 1 . 8 1 2 7 I r a s t

• r

z a . R e d

• n

d

SLIDE 7

Q C D A x i

• n

Ma s s Q C D A x i

• n

Ma s s

We i n b e r g ‘ 7 8

SLIDE 8

1 5 1 1 . 2 8 6 7 – G r i l l i d i C

• r

t

• n

a e t a l . 1 5 1 2 . 6 7 4 6 – B

• n

a t i e t a l . 1 6 6 . 7 4 9 4 – B

• r

s a n y i e t a l . 1 8 1 2 . 1 8 – G

• r

g h e t t

• ,

G V

SLIDE 9

1 5 1 1 . 2 8 6 7 – G r i l l i d i C

• r

t

• n

a e t a l . 1 5 1 2 . 6 7 4 6 – B

• n

a t i e t a l . 1 6 6 . 7 4 9 4 – B

• r

s a n y i e t a l . 1 8 1 2 . 1 8 – G

• r

g h e t t

• ,

G V

SLIDE 10

1 5 1 1 . 2 8 6 7 – G r i l l i d i C

• r

t

• n

a e t a l . 1 5 1 2 . 6 7 4 6 – B

• n

a t i e t a l . 1 6 6 . 7 4 9 4 – B

• r

s a n y i e t a l . 1 8 1 2 . 1 8 – G

• r

g h e t t

• ,

G V

SLIDE 11

A x i

• n

D M

A b b

• t

t , D i n e , F i s c h l e r , A b b

• t

t , D i n e , F i s c h l e r , P r e s k i l l , P r e s k i l l , S i k i v i e , Wi s e , S i k i v i e , Wi s e , Wi l c z e k ‘ 8 3 Wi l c z e k ‘ 8 3

SLIDE 12

S c e n a r i

• I

: n

• P

Q r e s t

• r

a t i

• n

a f t e r i n fm a t i

• n

S c e n a r i

• I

: n

• P

Q r e s t

• r

a t i

• n

a f t e r i n fm a t i

• n

a a x x

SLIDE 13

S c e n a r i

• I

: n

• P

Q r e s t

• r

a t i

• n

a f t e r i n fm a t i

• n

S c e n a r i

• I

: n

• P

Q r e s t

• r

a t i

• n

a f t e r i n fm a t i

• n

a f t e r i n fm a t i

• n

a f t e r i n fm a t i

• n

a a x x H H

– 1 – 1

( w i t h i n H u b b l e ) ( w i t h i n H u b b l e )

SLIDE 14

T ≫ ΛQ

C D

S c e n a r i

• I

: S c e n a r i

• I

:

SLIDE 15

T ≫ ΛQ

C D

S c e n a r i

• I

: S c e n a r i

• I

:

SLIDE 16

1 5 1 2 . 6 7 4 6 – B

• n

a t i e t a l . 1 6 6 . 7 4 9 4 – B

• r

s a n y i e t a l . D I G A 1 8 7 . 7 9 5 4 B

• n

a t i e t a l .

F i n i t e T e m p e r a t u r e Q C D A x i

• n

Ma s s F i n i t e T e m p e r a t u r e Q C D A x i

• n

Ma s s

SLIDE 17

1 5 1 2 . 6 7 4 6 – B

• n

a t i e t a l . 1 6 6 . 7 4 9 4 – B

• r

s a n y i e t a l . D I G A 1 8 7 . 7 9 5 4 B

• n

a t i e t a l .

F i n i t e T e m p e r a t u r e Q C D A x i

• n

Ma s s F i n i t e T e m p e r a t u r e Q C D A x i

• n

Ma s s

SLIDE 18

?

D I G A / L a t t i c e D I G A / L a t t i c e

A B R A C A D A B R A Q U A X

L a t t i c e O l d L a t t i c e O l d D I G A / L a t t i c e D I G A / L a t t i c e

SLIDE 19

S c e n a r i

• I

I : S c e n a r i

• I

I : P Q r e s t

• r

a t i

• n

a f t e r i n fm a t i

• n

P Q r e s t

• r

a t i

• n

a f t e r i n fm a t i

• n

n

• f

r e e p a r a m e t e r s f r

• m

i n t i a l c

• n

d i t i

• n

s a b u n d a n c e c a l c u l a b l e ! ( i n p r i n c i p l e )

SLIDE 20

n

• f

r e e p a r a m e t e r s f r

• m

i n t i a l c

• n

d i t i

• n

s a b u n d a n c e c a l c u l a b l e ! ( i n p r i n c i p l e )

• m

i s a l i g n m e n t (

• m
• d

e )

( )

Mu l t i p l e c

• n

t r i b u t i

• n

s : Mu l t i p l e c

• n

t r i b u t i

• n

s :

ε

S c e n a r i

• I

I : S c e n a r i

• I

I : P Q r e s t

• r

a t i

• n

a f t e r i n fm a t i

• n

P Q r e s t

• r

a t i

• n

a f t e r i n fm a t i

• n

SLIDE 21

n

• f

r e e p a r a m e t e r s f r

• m

i n t i a l c

• n

d i t i

• n

s a b u n d a n c e c a l c u l a b l e ! ( i n p r i n c i p l e )

• m

i s a l i g n m e n t (

• m
• d

e )

( )

• m

i s a l i g n m e n t ( k

• m
• d

e s )

Mu l t i p l e c

• n

t r i b u t i

• n

s : Mu l t i p l e c

• n

t r i b u t i

• n

s :

ε

S c e n a r i

• I

I : S c e n a r i

• I

I : P Q r e s t

• r

a t i

• n

a f t e r i n fm a t i

• n

P Q r e s t

• r

a t i

• n

a f t e r i n fm a t i

• n

SLIDE 22

n

• f

r e e p a r a m e t e r s f r

• m

i n t i a l c

• n

d i t i

• n

s a b u n d a n c e c a l c u l a b l e ! ( i n p r i n c i p l e )

• m

i s a l i g n m e n t (

• m
• d

e )

( )

• m

i s a l i g n m e n t ( k

• m
• d

e s )

• t
• p
• l
• g

i c a l d e f e c t s ( s t r i n g s a n d d

• m

a i n w a l l s )

Mu l t i p l e c

• n

t r i b u t i

• n

s : Mu l t i p l e c

• n

t r i b u t i

• n

s :

ε

S c e n a r i

• I

I : S c e n a r i

• I

I : P Q r e s t

• r

a t i

• n

a f t e r i n fm a t i

• n

P Q r e s t

• r

a t i

• n

a f t e r i n fm a t i

• n

SLIDE 23

?

D I G A / L a t t i c e D I G A / L a t t i c e

A B R A C A D A B R A Q U A X

L a t t i c e O l d L a t t i c e O l d D I G A / L a t t i c e D I G A / L a t t i c e

SLIDE 24

P Q p h a s e t r a n s i t i

• n

P Q p h a s e t r a n s i t i

• n

s i m i l a r l y i f s i m i l a r l y i f H

≳ f

a

SLIDE 25

A x i

• n

i c S t r i n g s A x i

• n

i c S t r i n g s

SLIDE 26

A x i

• n

i c S t r i n g s A x i

• n

i c S t r i n g s

SLIDE 27

A x i

• n

i c S t r i n g s A x i

• n

i c S t r i n g s

radial core

SLIDE 28

A x i

• n

i c S t r i n g s A x i

• n

i c S t r i n g s

radial core axion field

SLIDE 29

A x i

• n

i c S t r i n g s A x i

• n

i c S t r i n g s

radial core axion field

SLIDE 30

f r e e s t r i n g s f r e e s t r i n g s

H

• 1

SLIDE 31

f r e e s t r i n g s f r e e s t r i n g s

H

• 1

SLIDE 32

f r e e s t r i n g s f r e e s t r i n g s s t r i n g r e c

• m

b i n a t i

• n

s t r i n g r e c

• m

b i n a t i

• n

H

• 1

SLIDE 33

f r e e s t r i n g s f r e e s t r i n g s s t r i n g r e c

• m

b i n a t i

• n

s t r i n g r e c

• m

b i n a t i

• n

H

• 1

s c a l i n g s

• l

u t i

• n

s c a l i n g s

• l

u t i

• n

ξ ξ = ( # s t r i n g s ) / ( H u b b l e P a t c h ) = ( # s t r i n g s ) / ( H u b b l e P a t c h )

SLIDE 34

f r e e s t r i n g s f r e e s t r i n g s s t r i n g r e c

• m

b i n a t i

• n

s t r i n g r e c

• m

b i n a t i

• n

H

• 1

s c a l i n g s

• l

u t i

• n

s c a l i n g s

• l

u t i

• n

ξ ξ = ( # s t r i n g s ) / ( H u b b l e P a t c h ) = ( # s t r i n g s ) / ( H u b b l e P a t c h )

d i fg e r e n c e g

• e

s i n r a d i a t i

• n

d i fg e r e n c e g

• e

s i n r a d i a t i

• n

SLIDE 35

@ @ H ~ m H ~ m

a a

( ( T T ~ ~ Λ Λ

Q C D Q C D

) )

SLIDE 36

@ @ H ~ m H ~ m

a a

( ( T T ~ ~ Λ Λ

Q C D Q C D

) ) N N

D W D W

= 1 c a s e = 1 c a s e

SLIDE 37

@ @ H ~ m H ~ m

a a

( ( T T ~ ~ Λ Λ

Q C D Q C D

) )

T , H T , H ≳ ≳ f f

a a

H ~ m H ~ m

a a

( ( T T ~ ~ Λ Λ

Q C D Q C D

) ) t

• d

a y t

• d

a y s c a l i n g r e g i m e s c a l i n g r e g i m e l

• g

( l

• g

( m m

r r

/ / H H ) ) 1 ÷ 1 5 1 ÷ 1 5 ~ 7 ~ 7

N N

D W D W

= 1 c a s e = 1 c a s e

SLIDE 38

N ≈ 1 k – 4 k – 8 k

N u m e r i c a l S i m u l a t i

• n

N u m e r i c a l S i m u l a t i

• n

SLIDE 39

1 / m

r

1 / H

T h e B

• t

t l e N e c k T h e B

• t

t l e N e c k

SLIDE 40

1 / m

r

1 / H

T h e B

• t

t l e N e c k T h e B

• t

t l e N e c k

SLIDE 41

1 / m

r

~ R ~ t

1 / 2

1 / H

T h e B

• t

t l e N e c k T h e B

• t

t l e N e c k

f a t s t r i n g t r i c k

SLIDE 42

T h e S c a l i n g S

• l

u t i

• n

i s a n A t t r a c t i v e S

• l

u t i

• n

T h e S c a l i n g S

• l

u t i

• n

i s a n A t t r a c t i v e S

• l

u t i

• n

1 8 6 . 4 6 7 7 – G

• r

g h e t t

• ,

H a r d y , G V

SLIDE 43

S c a l i n g V i

• l

a t i

• n

S c a l i n g V i

• l

a t i

• n

1 8 6 . 4 6 7 7 – G

• r

g h e t t

• ,

H a r d y , G V A l s

• b

s e r v e d i n : 1 5 9 . 2 6 – F l e u r y , Mo

• r

e 1 8 6 . 5 5 6 6 – K a w a s a k i e t a l . 1 9 6 . 9 6 7 – B u s c h m a n n , F

• s

t e r , S a f d i p r e l i m i n a r y – R e d

• n

d

• ,

S a i k a w a , . . .

SLIDE 44

S c a l i n g V i

• l

a t i

• n

S c a l i n g V i

• l

a t i

• n

SLIDE 45

S c a l i n g V i

• l

a t i

• n

S c a l i n g V i

• l

a t i

• n

SLIDE 46

G

• r

g h e t t

• ,

H a r d y , G V

S c a l i n g V i

• l

a t i

• n

( 4 k s i m u l a t i

• n

) S c a l i n g V i

• l

a t i

• n

( 4 k s i m u l a t i

• n

)

SLIDE 47

Wh a t i s t h e l a r g e Wh a t i s t h e l a r g e ξ ξ b e h a v i

• r

? b e h a v i

• r

?

O r i g i n

• f

s c a l i n g v i

• l

a t i

• n

? O r i g i n

• f

s c a l i n g v i

• l

a t i

• n

? L a r g e r p h y s i c a l s i m u l a t i

• n

s s u g g e s t s

• m

e c u r v a t u r e ( l

• g

^ 2 ? ) L a r g e r p h y s i c a l s i m u l a t i

• n

s s u g g e s t s

• m

e c u r v a t u r e ( l

• g

^ 2 ? ) S c a l i n g v i

• l

a t i

• n
• b

s e r v e d a l s

• i

n l

• c

a l U ( 1 ) s t r i n g n e t w

• r

k s . . . S c a l i n g v i

• l

a t i

• n
• b

s e r v e d a l s

• i

n l

• c

a l U ( 1 ) s t r i n g n e t w

• r

k s . . .

SLIDE 48

L

• p

D i s t r i b u t i

• n

L

• p

D i s t r i b u t i

• n

1 8 6 . 4 6 7 7 – G

• r

g h e t t

• ,

H a r d y , G V

SLIDE 49

L

• p

D i s t r i b u t i

• n

L

• p

D i s t r i b u t i

• n

s c a l e i n v a r i a n t

1 8 6 . 4 6 7 7 – G

• r

g h e t t

• ,

H a r d y , G V S h

• r

t / L

• n

g s t r i n g r a t i

• a

l s

• b

s e r v e d b y : 1 8 6 . 5 5 6 6 – K a w a s a k i e t a l . 1 9 6 . 9 6 7 – B u s c h m a n n , F

• s

t e r , S a f d i

SLIDE 50

H m

r

k 1 / k

q

A x i

• n

S p e c t r a V S A x i

• n

N u m b e r A x i

• n

S p e c t r a V S A x i

• n

N u m b e r

SLIDE 51

H m

r

k 1 / k

q

A x i

• n

S p e c t r a V S A x i

• n

N u m b e r A x i

• n

S p e c t r a V S A x i

• n

N u m b e r

D a v i e s , S h e l l a r d , . . . D a v i e s , S h e l l a r d , . . .

q > 1

SLIDE 52

H m

r

k 1 / k

q

A x i

• n

S p e c t r a V S A x i

• n

N u m b e r A x i

• n

S p e c t r a V S A x i

• n

N u m b e r

D a v i e s , S h e l l a r d , . . . D a v i e s , S h e l l a r d , . . . S i k i v i e , . . . S i k i v i e , . . .

q > 1 q = 1

SLIDE 53

H m

r

k 1 / k

q

A x i

• n

S p e c t r a V S A x i

• n

N u m b e r A x i

• n

S p e c t r a V S A x i

• n

N u m b e r

D a v i e s , S h e l l a r d , . . . D a v i e s , S h e l l a r d , . . . S i k i v i e , . . . S i k i v i e , . . .

q > 1 q = 1 q < 1

SLIDE 54

A x i

• n

S p e c t r a V S A x i

• n

N u m b e r A x i

• n

S p e c t r a V S A x i

• n

N u m b e r

I R d

• m

i n a t e d I R d

• m

i n a t e d s c a l e i n v a r i a n t s c a l e i n v a r i a n t U V d

• m

i n a t e d U V d

• m

i n a t e d

SLIDE 55

A x i

• n

S p e c t r u m A x i

• n

S p e c t r u m

m

r

/ 2

l

• g

( m

r

/ H ) = 4

2 π

1 8 6 . 4 6 7 7 – G

• r

g h e t t

• ,

H a r d y , G V

SLIDE 56

l

• g

( m

r

/ H ) = 4 l

• g

( m

r

/ H ) = 5

A x i

• n

S p e c t r u m A x i

• n

S p e c t r u m

1 8 6 . 4 6 7 7 – G

• r

g h e t t

• ,

H a r d y , G V

SLIDE 57

l

• g

( m

r

/ H ) = 4 l

• g

( m

r

/ H ) = 5 l

• g

( m

r

/ H ) = 6

A x i

• n

S p e c t r u m A x i

• n

S p e c t r u m

1 8 6 . 4 6 7 7 – G

• r

g h e t t

• ,

H a r d y , G V

SLIDE 58

l

• g

( m

r

/ H ) = 4 l

• g

( m

r

/ H ) = 5 l

• g

( m

r

/ H ) = 6 l

• g

( m

r

/ H ) = 3

A x i

• n

S p e c t r u m A x i

• n

S p e c t r u m

1 8 6 . 4 6 7 7 – G

• r

g h e t t

• ,

H a r d y , G V

SLIDE 59

l

• g

= 4 5 6 7 7 . 9

G

• r

g h e t t

• ,

H a r d y , G V

A x i

• n

S p e c t r u m @ 4 k A x i

• n

S p e c t r u m @ 4 k

SLIDE 60

A x i

• n

I n s t a n t a n e

• u

s S p e c t r u m A x i

• n

I n s t a n t a n e

• u

s S p e c t r u m

1 8 6 . 4 6 7 7 – G

• r

g h e t t

• ,

H a r d y , G V

SLIDE 61

A x i

• n

I n s t a n t a n e

• u

s S p e c t r u m A x i

• n

I n s t a n t a n e

• u

s S p e c t r u m

1 8 6 . 4 6 7 7 – G

• r

g h e t t

• ,

H a r d y , G V

SLIDE 62

A x i

• n

N u m b e r D e n s i t y A x i

• n

N u m b e r D e n s i t y

1 8 6 . 4 6 7 7 – G

• r

g h e t t

• ,

H a r d y , G V

SLIDE 63

A x i

• n

N u m b e r D e n s i t y → E x t r a p

• l

a t i

• n

A x i

• n

N u m b e r D e n s i t y → E x t r a p

• l

a t i

• n

SLIDE 64

A x i

• n

N u m b e r D e n s i t y → E x t r a p

• l

a t i

• n

A x i

• n

N u m b e r D e n s i t y → E x t r a p

• l

a t i

• n

SLIDE 65

A x i

• n

N u m b e r D e n s i t y → E x t r a p

• l

a t i

• n

A x i

• n

N u m b e r D e n s i t y → E x t r a p

• l

a t i

• n

SLIDE 66

A x i

• n

N u m b e r D e n s i t y → E x t r a p

• l

a t i

• n

A x i

• n

N u m b e r D e n s i t y → E x t r a p

• l

a t i

• n

SLIDE 67

A x i

• n

N u m b e r D e n s i t y → E x t r a p

• l

a t i

• n

A x i

• n

N u m b e r D e n s i t y → E x t r a p

• l

a t i

• n

SLIDE 68

A x i

• n

N u m b e r D e n s i t y → E x t r a p

• l

a t i

• n

A x i

• n

N u m b e r D e n s i t y → E x t r a p

• l

a t i

• n

SLIDE 69

A x i

• n

N u m b e r D e n s i t y → E x t r a p

• l

a t i

• n

A x i

• n

N u m b e r D e n s i t y → E x t r a p

• l

a t i

• n

S h e l l a r d e t a l . ( S h e l l a r d e t a l . ( q q > 1 , > 1 , ξ ξ ~ 1 3 ) ~ 1 3 ) S i k i v i e e t a l . ( S i k i v i e e t a l . ( q = q = 1 , 1 , ξ ξ ~ 1 ) ~ 1 ) K a w a s a k i e t a l . ( K a w a s a k i e t a l . ( q > q > 1 , 1 , ξ ξ ~ 1 ) ~ 1 ) Mo

• r

e e t a l . ( Mo

• r

e e t a l . ( q = q = ? ? , , ξ ξ ~ 5 ) ~ 5 )

SLIDE 70

G

• r

g h e t t

• ,

H a r d y , G V

R u n n i n g

• f

t h e s p e c t r a l i n d e x ( i n 4 k ) R u n n i n g

• f

t h e s p e c t r a l i n d e x ( i n 4 k )

SLIDE 71

F a t C a s e : U V → I R d

• m

i n a t e d s p e c t r u m F a t C a s e : U V → I R d

• m

i n a t e d s p e c t r u m P h y s i c a l C a s e : s i m i l a r ? P h y s i c a l C a s e : s i m i l a r ? → → L a r g e b

• s

t

• f

a x i

• n

s f r

• m

s t r i n g s L a r g e b

• s

t

• f

a x i

• n

s f r

• m

s t r i n g s Wh a t h a p p e n s w h e n a x i

• n

s g e t a m a s s ? Wh a t h a p p e n s w h e n a x i

• n

s g e t a m a s s ?

P r

• b

a b l y s

• m

e s u p p r e s s i

• n
• f

t h e b

• s

t b e c a u s e

• f

n

• n
• l

i n e a r i t i e s P r

• b

a b l y s

• m

e s u p p r e s s i

• n
• f

t h e b

• s

t b e c a u s e

• f

n

• n
• l

i n e a r i t i e s

V e r y p l a u s i b l e t h a t i n t h i s s c e n a r i

• :

V e r y p l a u s i b l e t h a t i n t h i s s c e n a r i

• :

SLIDE 72

F a t C a s e : U V → I R d

• m

i n a t e d s p e c t r u m F a t C a s e : U V → I R d

• m

i n a t e d s p e c t r u m P h y s i c a l C a s e : s i m i l a r ? P h y s i c a l C a s e : s i m i l a r ? → → L a r g e b

• s

t

• f

a x i

• n

s f r

• m

s t r i n g s L a r g e b

• s

t

• f

a x i

• n

s f r

• m

s t r i n g s Wh a t h a p p e n s w h e n a x i

• n

s g e t a m a s s ? Wh a t h a p p e n s w h e n a x i

• n

s g e t a m a s s ?

P r

• b

a b l y s

• m

e s u p p r e s s i

• n
• f

t h e b

• s

t b e c a u s e

• f

n

• n
• l

i n e a r i t i e s P r

• b

a b l y s

• m

e s u p p r e s s i

• n
• f

t h e b

• s

t b e c a u s e

• f

n

• n
• l

i n e a r i t i e s

V e r y p l a u s i b l e t h a t i n t h i s s c e n a r i

• :

V e r y p l a u s i b l e t h a t i n t h i s s c e n a r i

• :

SLIDE 73

F a t C a s e : U V → I R d

• m

i n a t e d s p e c t r u m F a t C a s e : U V → I R d

• m

i n a t e d s p e c t r u m P h y s i c a l C a s e : s i m i l a r ? P h y s i c a l C a s e : s i m i l a r ? → → L a r g e b

• s

t

• f

a x i

• n

s f r

• m

s t r i n g s L a r g e b

• s

t

• f

a x i

• n

s f r

• m

s t r i n g s Wh a t h a p p e n s w h e n a x i

• n

s g e t a m a s s ? Wh a t h a p p e n s w h e n a x i

• n

s g e t a m a s s ?

P r

• b

a b l y s

• m

e s u p p r e s s i

• n
• f

t h e b

• s

t b e c a u s e

• f

n

• n
• l

i n e a r i t i e s P r

• b

a b l y s

• m

e s u p p r e s s i

• n
• f

t h e b

• s

t b e c a u s e

• f

n

• n
• l

i n e a r i t i e s

V e r y p l a u s i b l e t h a t i n t h i s s c e n a r i

• :

V e r y p l a u s i b l e t h a t i n t h i s s c e n a r i

• :

SLIDE 74

F a t C a s e : U V → I R d

• m

i n a t e d s p e c t r u m F a t C a s e : U V → I R d

• m

i n a t e d s p e c t r u m P h y s i c a l C a s e : s i m i l a r ? P h y s i c a l C a s e : s i m i l a r ? → → L a r g e b

• s

t

• f

a x i

• n

s f r

• m

s t r i n g s L a r g e b

• s

t

• f

a x i

• n

s f r

• m

s t r i n g s Wh a t h a p p e n s w h e n a x i

• n

s g e t a m a s s ? Wh a t h a p p e n s w h e n a x i

• n

s g e t a m a s s ?

P r

• b

a b l y s

• m

e s u p p r e s s i

• n
• f

t h e b

• s

t b e c a u s e

• f

n

• n
• l

i n e a r i t i e s P r

• b

a b l y s

• m

e s u p p r e s s i

• n
• f

t h e b

• s

t b e c a u s e

• f

n

• n
• l

i n e a r i t i e s

V e r y p l a u s i b l e t h a t i n t h i s s c e n a r i

• :

V e r y p l a u s i b l e t h a t i n t h i s s c e n a r i

• :

SLIDE 75

Wh a t h a p p e n s n e x t ? Wh a t h a p p e n s n e x t ? H a r d t

• t

e l l r e l i a b l y . . . H a r d t

• t

e l l r e l i a b l y . . .

S i m u l a t i

• n

s w i t h D W + S t r i n g s S i m u l a t i

• n

s w i t h D W + S t r i n g s v e r y f a r f r

• m

p h y s i c a l p a r a m e t e r s [ O ( 1 v e r y f a r f r

• m

p h y s i c a l p a r a m e t e r s [ O ( 1

3 3

) a w a y ] ) a w a y ] D y n a m i c s

• f

s t r i n g s a t l

• g

~ f e w D y n a m i c s

• f

s t r i n g s a t l

• g

~ f e w v e r y v e r y d i fg e r e n t f r

• m

t h a t a t l

• g

~ 7 d i fg e r e n t f r

• m

t h a t a t l

• g

~ 7 Ma y b e s a m e f

• r

D W Ma y b e s a m e f

• r

D W V e r y r i c h p h e n

• a

f t e r w a r d s (

• s

c i l l

• n

s , m i n i c l u s t e r s , b

• s

e s t a r s , e t c …) , V e r y r i c h p h e n

• a

f t e r w a r d s (

• s

c i l l

• n

s , m i n i c l u s t e r s , b

• s

e s t a r s , e t c …) , b u t v e r y h a r d t

• e

s t i m a t e r e l i a b l y b u t v e r y h a r d t

• e

s t i m a t e r e l i a b l y

SLIDE 76

Wh a t h a p p e n s n e x t ? Wh a t h a p p e n s n e x t ? H a r d t

• t

e l l r e l i a b l y . . . H a r d t

• t

e l l r e l i a b l y . . .

S i m u l a t i

• n

s w i t h D W + S t r i n g s S i m u l a t i

• n

s w i t h D W + S t r i n g s v e r y f a r f r

• m

p h y s i c a l p a r a m e t e r s [ O ( 1 v e r y f a r f r

• m

p h y s i c a l p a r a m e t e r s [ O ( 1

3 3

) a w a y ] ) a w a y ] D y n a m i c s

• f

s t r i n g s a t l

• g

~ f e w D y n a m i c s

• f

s t r i n g s a t l

• g

~ f e w v e r y v e r y d i fg e r e n t f r

• m

t h a t a t l

• g

~ 7 d i fg e r e n t f r

• m

t h a t a t l

• g

~ 7 Ma y b e s a m e f

• r

D W Ma y b e s a m e f

• r

D W V e r y r i c h p h e n

• a

f t e r w a r d s (

• s

c i l l

• n

s , m i n i c l u s t e r s , b

• s

e s t a r s , e t c …) , V e r y r i c h p h e n

• a

f t e r w a r d s (

• s

c i l l

• n

s , m i n i c l u s t e r s , b

• s

e s t a r s , e t c …) , b u t v e r y h a r d t

• e

s t i m a t e r e l i a b l y b u t v e r y h a r d t

• e

s t i m a t e r e l i a b l y

SLIDE 77

Wh a t h a p p e n s n e x t ? Wh a t h a p p e n s n e x t ? H a r d t

• t

e l l r e l i a b l y . . . H a r d t

• t

e l l r e l i a b l y . . .

S i m u l a t i

• n

s w i t h D W + S t r i n g s S i m u l a t i

• n

s w i t h D W + S t r i n g s v e r y f a r f r

• m

p h y s i c a l p a r a m e t e r s [ O ( 1 v e r y f a r f r

• m

p h y s i c a l p a r a m e t e r s [ O ( 1

3 3

) a w a y ] ) a w a y ] D y n a m i c s

• f

s t r i n g s a t l

• g

~ f e w D y n a m i c s

• f

s t r i n g s a t l

• g

~ f e w v e r y v e r y d i fg e r e n t f r

• m

t h a t a t l

• g

~ 7 d i fg e r e n t f r

• m

t h a t a t l

• g

~ 7 Ma y b e s a m e f

• r

D W Ma y b e s a m e f

• r

D W V e r y r i c h p h e n

• a

f t e r w a r d s (

• s

c i l l

• n

s , m i n i c l u s t e r s , b

• s

e s t a r s , e t c …) , V e r y r i c h p h e n

• a

f t e r w a r d s (

• s

c i l l

• n

s , m i n i c l u s t e r s , b

• s

e s t a r s , e t c …) , b u t v e r y h a r d t

• e

s t i m a t e r e l i a b l y b u t v e r y h a r d t

• e

s t i m a t e r e l i a b l y

SLIDE 78

Wh a t h a p p e n s n e x t ? Wh a t h a p p e n s n e x t ? H a r d t

• t

e l l r e l i a b l y . . . H a r d t

• t

e l l r e l i a b l y . . .

S i m u l a t i

• n

s w i t h D W + S t r i n g s S i m u l a t i

• n

s w i t h D W + S t r i n g s v e r y f a r f r

• m

p h y s i c a l p a r a m e t e r s [ O ( 1 v e r y f a r f r

• m

p h y s i c a l p a r a m e t e r s [ O ( 1

3 3

) a w a y ] ) a w a y ] D y n a m i c s

• f

s t r i n g s a t l

• g

~ f e w D y n a m i c s

• f

s t r i n g s a t l

• g

~ f e w v e r y v e r y d i fg e r e n t f r

• m

t h a t a t l

• g

~ 7 d i fg e r e n t f r

• m

t h a t a t l

• g

~ 7 Ma y b e s a m e f

• r

D W Ma y b e s a m e f

• r

D W V e r y r i c h p h e n

• a

f t e r w a r d s (

• s

c i l l

• n

s , m i n i c l u s t e r s , b

• s

e s t a r s , e t c …) , V e r y r i c h p h e n

• a

f t e r w a r d s (

• s

c i l l

• n

s , m i n i c l u s t e r s , b

• s

e s t a r s , e t c …) , b u t v e r y h a r d t

• e

s t i m a t e r e l i a b l y b u t v e r y h a r d t

• e

s t i m a t e r e l i a b l y

SLIDE 79

C

• n

c l u s i

• n

s : C

• n

c l u s i

• n

s :

S t i l l a l

• t

t

• b

e u n d e r s t

• d

. . . S t i l l a l

• t

t

• b

e u n d e r s t

• d

. . . → → F a r a w a y f r

• m

a r e l i a b l e c

• m

p u t a t i

• n
• f

t h e a x i

• n

a b u n d a n c e F a r a w a y f r

• m

a r e l i a b l e c

• m

p u t a t i

• n
• f

t h e a x i

• n

a b u n d a n c e ( f e a s i b l e ? ) n e a r

• t

e r m g

• a

l : ( f e a s i b l e ? ) n e a r

• t

e r m g

• a

l : l

• w

e r b

• u

n d f r

• m

s t r i n g s p r

• d

u c t i

• n

l

• w

e r b

• u

n d f r

• m

s t r i n g s p r

• d

u c t i

• n

( a f t e r e d u c a t e d g u e s s e s

• f

e x t r a p

• l

a t e d s c a l i n g p r

• p

e r t i e s ) ( a f t e r e d u c a t e d g u e s s e s

• f

e x t r a p

• l

a t e d s c a l i n g p r

• p

e r t i e s )