String Phenomenology

Gary ShiuUniversity of Wisconsin

YITP@40 Symposium

YITP’s “Theory Space”

Strings/SUGRA

YITP

QCD/Collider Physics

Standard Model & Beyond

Cosmology

Statistical Mechanics

Neutrinos

+ a lot more ...

String Phenomenology

String Phenomenology

String Phenomenology

String Phenomenology

How do we test these ideas?

Cosmic Microwave Background

• Almost scale invariant, Gaussian primordial spectrum predicted by inflation: good agreement with data.

• A tantalizing upper bound on the energy density during inflation:

V ! M4GUT ! (1016GeV)4 i.e., H ! 1014GeV

WMAP

WMAP & Beyond

Can we learn from the CMB (or other cosmological measurements) details of string compactification?

LHC & Beyond

Can we learn from the LHC (and beyond) details of string compactification?

Flux Compactification

Energy !

1

8!

!

"

E2 + B

2#

Various p!cycles of M

Vn1,n2,···,nk(!i) ! moduli lifted

nj =

!!j

F

!j

Analogous to turning on a B-field:

Energy cost depends on detailed geometry:

W =

!M

G ! ΩIn Type IIB: Gukov, Vafa, Witten

[Dasgupta, Rajesh, Sethi]; [Greene, Schalm, GS]; [Giddings, Kachru, Polchinski]

Warped Throats

5UV

AdSIR

Klebanov, Strassler

e.g., warped deformed conifold

Fluxes back-react on the metric:

leads to Randall-Sundrum hierarchy Giddings, Kachru, Polchinski

Warped Throats

5UV

AdSIR

Klebanov, Strassler

e.g., warped deformed conifold

Fluxes back-react on the metric:

leads to Randall-Sundrum hierarchy Giddings, Kachru, Polchinski

A variety of warped throats with different isometries and IR behavior.

Standard-like D-brane Models

Marchesano, GS; Verlinde, Wijnholt;Cascales, Garcia del Moral, Quevedo, Uranga;Blumenhagen, Cvetic, GS, Marchesano; ...

Brane InflationDvali and Tye

...

Reviews:[Quevedo, hep-th/0210292];[Burgess, hep-th/0606020];[Tye, hep-th/0610221];[Cline, hep-th/0612129];[Kallosh,hep-th/0702059], ...

DD Inflation

Brane Inflation in Warped Throats

D3D3

Brane Inflation in Warped Throats

Slow-roll

D3D3

Brane Inflation in Warped ThroatsSilverstein, TongDBI

D3D3

Brane Inflation in Warped ThroatsSilverstein, TongDBI

D3D3

S = !

!

d4x"

!g

"

f(!)!1

#

1 ! f(!)!2! V (!) ! f(!)!1

$

Brane Inflation in Warped ThroatsSilverstein, TongDBI

D3D3

S = !

!

d4x"

!g

"

f(!)!1

#

1 ! f(!)!2! V (!) ! f(!)!1

$

!2 ! f(!)!1Speed limit:

Brane Inflation in Warped ThroatsSilverstein, TongDBI

D3D3

S = !

!

d4x"

!g

"

f(!)!1

#

1 ! f(!)!2! V (!) ! f(!)!1

$

! =1

!

1 ! f(")"2

!2 ! f(!)!1Speed limit:

Non-Gaussianities

0.20.4

0.60.8

0.2

0.4

0.6

0.8

0

0.1

0.2

0.20.4

0.60.8

0.20.4

0.6

0.8

0.2

0.4

0.6

0.8

0

1

2

3

0.20.4

0.6

0.8

Large 3-point correlations that are potentially observable.

Moreover, distinctive shape.

Slow-roll DBI

[Figures from Chen, Huang, Kachru, Shiu]

(fNL ! !) (fNL ! !2)

Non-Gaussianities

0.20.4

0.60.8

0.2

0.4

0.6

0.8

0

0.1

0.2

0.20.4

0.60.8

0.20.4

0.6

0.8

0.2

0.4

0.6

0.8

0

1

2

3

0.20.4

0.6

0.8

Large 3-point correlations that are potentially observable.

Moreover, distinctive shape.

Slow-roll DBI

[Figures from Chen, Huang, Kachru, Shiu]

−54 < fNL < 114 (WMAP3) fNL ∼ 5 (PLANCK)

(fNL ! !) (fNL ! !2)

Probing the Warped Geometry

Exact KSMass Gap

AdSSpectral index depends on warp factor through:

GS, B. Underwood, PRL

Exact KS

Mass GapAdS

Probing the Warped Geometry

GS, B. Underwood, PRL

Running of spectral index:

Exact KS

AdS

Warped throats at the LHC & Beyond

Search for Warped KK GravitonsGS, Underwood, Walker, Zurek (to appear)

Much work on LHC signatures of KK gravitons for RS:

Davoudiasl, Hewett, Rizzo; Fitzpatrick, Kaplan, Randall, Wang; Agashe, Davoudiasl, Perez, Soni; ...

Couplings to KK gravitons only TeV suppressed

Warped KK Spectrum and CouplingsGS, Underwood, Walker, Zurek (to appear)

Warped KK Spectrum and CouplingsGS, Underwood, Walker, Zurek (to appear)

In comparison to RS, the KS geometry has:

Warped KK Spectrum and CouplingsGS, Underwood, Walker, Zurek (to appear)

• Smaller KK spacingIn comparison to RS, the KS geometry has:

Warped KK Spectrum and CouplingsGS, Underwood, Walker, Zurek (to appear)

• Smaller KK spacing

• Stronger & mode-dependent couplings

In comparison to RS, the KS geometry has:

Warped KK Spectrum and CouplingsGS, Underwood, Walker, Zurek (to appear)

• Smaller KK spacing

• Stronger & mode-dependent couplings

In comparison to RS, the KS geometry has:

KK Gravitons: Production and Decay

k2, n

k1, m

µ! (ij), n"

h~ n"

µ! ## : $ i %/2 &

mn ( m

2 # '

µ! + C

µ!, () k

1 ( k

2 ) )

*~ n"

ij ## : i + % &

ij &

mn ( k

1 • k

2 $ 2 m

2 # )

Ab )(k

2)

Aa ((k

1)

µ! (ij), n"

p

h~ n"

µ! ,, : $ i %/2 &

ab ( ( m

2 A + k

1 • k

2 ) C

µ!, () + D

µ!, () (k

1, k

2)

+ -$1

Eµ!, ()

(k1, k

2) )

*~ n"

ij ,, : i + % &

ij &

ab ( '

() m

2 A + -

$1 (k

1( p) + k

2) p() )

k2, n

k1, m

µ! (ij), n"

h~ n"

µ! .. : $ i %/8 &

mn ( /

µ (k

1! + k

2!) + /

! (k

1µ + k

2µ)

$ 2 'µ!

(k/1 + k/

2 $ 2 m

.) )

*~ n"

ij .. : i + % &

ij &

mn ( 3/4 k/

1 + 3/4 k/

2 $ 2 m

.)

Figure 4: Three-point vertex Feynman rules. The KK states are plot in double-sinusoidalcurves. The symbols Cµ!,"#, Dµ!,"#(k1, k2) and Eµ!,"#(k1, k2) are defined in Eqs. (A.10),(A.11) and (A.12) respectively. m!, mA and m$ are masses of the scalar, vector and

fermion. ! =!

23(n+2) , " =

!16#GN and $ is the gauge-fixing parameter.

26

k2, n

k1, m

µ! (ij), n"

h~ n"

µ! ## : $ i %/2 &

mn ( m

2 # '

µ! + C

µ!, () k

1 ( k

2 ) )

*~ n"

ij ## : i + % &

ij &

mn ( k

1 • k

2 $ 2 m

2 # )

Ab )(k

2)

Aa ((k

1)

µ! (ij), n"

p

h~ n"

µ! ,, : $ i %/2 &

ab ( ( m

2 A + k

1 • k

2 ) C

µ!, () + D

µ!, () (k

1, k

2)

+ -$1

Eµ!, ()

(k1, k

2) )

*~ n"

ij ,, : i + % &

ij &

ab ( '

() m

2 A + -

$1 (k

1( p) + k

2) p() )

k2, n

k1, m

µ! (ij), n"

h~ n"

µ! .. : $ i %/8 &

mn ( /

µ (k

1! + k

2!) + /

! (k

1µ + k

2µ)

$ 2 'µ!

(k/1 + k/

2 $ 2 m

.) )

*~ n"

ij .. : i + % &

ij &

mn ( 3/4 k/

1 + 3/4 k/

2 $ 2 m

.)

Figure 4: Three-point vertex Feynman rules. The KK states are plot in double-sinusoidalcurves. The symbols Cµ!,"#, Dµ!,"#(k1, k2) and Eµ!,"#(k1, k2) are defined in Eqs. (A.10),(A.11) and (A.12) respectively. m!, mA and m$ are masses of the scalar, vector and

fermion. ! =!

23(n+2) , " =

!16#GN and $ is the gauge-fixing parameter.

26

Production:g

g

KK

q

q

KK

Decay:

k2, n

k1, m

µ! (ij), n"

h~ n"

µ! ## :$ i %/2 &mn ( m

2 # 'µ! + Cµ!, () k1

( k2

) )

*~ n"

ij ## :i + % &ij &mn ( k1 • k2 $ 2 m

2 # )

Ab )(k2)

Aa ((k1)

µ! (ij), n"

p

h~ n"

µ! ,, :$ i %/2 &

ab ( ( m

2 A + k1 • k2 ) Cµ!, () + Dµ!, () (k1, k2)

+ -$1

Eµ!, () (k1, k2) )

*~ n"

ij ,, :i + % &ij &

ab ( '() m

2 A + -

$1 (k1( p) + k2) p() )

k2, n

k1, m

µ! (ij), n"

h~ n"

µ! .. :$ i %/8 &mn ( /µ (k1! + k2!) + /! (k1µ + k2µ)

$ 2 'µ! (k/1 + k/2 $ 2 m.) )

*~ n"

ij .. :i + % &ij &mn ( 3/4 k/1 + 3/4 k/2 $ 2 m.)

Figure4:Three-pointvertexFeynmanrules.TheKKstatesareplotindouble-sinusoidalcurves.ThesymbolsCµ!,"#,Dµ!,"#(k1,k2)andEµ!,"#(k1,k2)aredefinedinEqs.(A.10),(A.11)and(A.12)respectively.m!,mAandm$aremassesofthescalar,vectorand

fermion.!=!

23(n+2),"=

!16#GNand$isthegauge-fixingparameter.

26

k2, n

k1, m

µ! (ij), n"

h~ n"

µ! ## :$ i %/2 &mn ( m

2 # 'µ! + Cµ!, () k1

( k2

) )

*~ n"

ij ## :i + % &ij &mn ( k1 • k2 $ 2 m

2 # )

Ab )(k2)

Aa ((k1)

µ! (ij), n"

p

h~ n"

µ! ,, :$ i %/2 &

ab ( ( m

2 A + k1 • k2 ) Cµ!, () + Dµ!, () (k1, k2)

+ -$1

Eµ!, () (k1, k2) )

*~ n"

ij ,, :i + % &ij &

ab ( '() m

2 A + -

$1 (k1( p) + k2) p() )

k2, n

k1, m

µ! (ij), n"

h~ n"

µ! .. :$ i %/8 &mn ( /µ (k1! + k2!) + /! (k1µ + k2µ)

$ 2 'µ! (k/1 + k/2 $ 2 m.) )

*~ n"

ij .. :i + % &ij &mn ( 3/4 k/1 + 3/4 k/2 $ 2 m.)

Figure4:Three-pointvertexFeynmanrules.TheKKstatesareplotindouble-sinusoidalcurves.ThesymbolsCµ!,"#,Dµ!,"#(k1,k2)andEµ!,"#(k1,k2)aredefinedinEqs.(A.10),(A.11)and(A.12)respectively.m!,mAandm$aremassesofthescalar,vectorand

fermion.!=!

23(n+2),"=

!16#GNand$isthegauge-fixingparameter.

26

KK KK

k2, n

k1, m

µ! (ij), n"

h~ n"

µ! ## :$ i %/2 &mn ( m

2 # 'µ! + Cµ!, () k1

( k2

) )

*~ n"

ij ## :i + % &ij &mn ( k1 • k2 $ 2 m

2 # )

Ab )(k2)

Aa ((k1)

µ! (ij), n"

p

h~ n"

µ! ,, :$ i %/2 &

ab ( ( m

2 A + k1 • k2 ) Cµ!, () + Dµ!, () (k1, k2)

+ -$1

Eµ!, () (k1, k2) )

*~ n"

ij ,, :i + % &ij &

ab ( '() m

2 A + -

$1 (k1( p) + k2) p() )

k2, n

k1, m

µ! (ij), n"

h~ n"

µ! .. :$ i %/8 &mn ( /µ (k1! + k2!) + /! (k1µ + k2µ)

$ 2 'µ! (k/1 + k/2 $ 2 m.) )

*~ n"

ij .. :i + % &ij &mn ( 3/4 k/1 + 3/4 k/2 $ 2 m.)

Figure4:Three-pointvertexFeynmanrules.TheKKstatesareplotindouble-sinusoidalcurves.ThesymbolsCµ!,"#,Dµ!,"#(k1,k2)andEµ!,"#(k1,k2)aredefinedinEqs.(A.10),(A.11)and(A.12)respectively.m!,mAandm$aremassesofthescalar,vectorand

fermion.!=!

23(n+2),"=

!16#GNand$isthegauge-fixingparameter.

26

KK

g

g

q, !+

q, !!

W, Z, !

W, Z, !

KK Gravitons: Production and Decay

k2, n

k1, m

µ! (ij), n"

h~ n"

µ! ## : $ i %/2 &

mn ( m

2 # '

µ! + C

µ!, () k

1 ( k

2 ) )

*~ n"

ij ## : i + % &

ij &

mn ( k

1 • k

2 $ 2 m

2 # )

Ab )(k

2)

Aa ((k

1)

µ! (ij), n"

p

h~ n"

µ! ,, : $ i %/2 &

ab ( ( m

2 A + k

1 • k

2 ) C

µ!, () + D

µ!, () (k

1, k

2)

+ -$1

Eµ!, ()

(k1, k

2) )

*~ n"

ij ,, : i + % &

ij &

ab ( '

() m

2 A + -

$1 (k

1( p) + k

2) p() )

k2, n

k1, m

µ! (ij), n"

h~ n"

µ! .. : $ i %/8 &

mn ( /

µ (k

1! + k

2!) + /

! (k

1µ + k

2µ)

$ 2 'µ!

(k/1 + k/

2 $ 2 m

.) )

*~ n"

ij .. : i + % &

ij &

mn ( 3/4 k/

1 + 3/4 k/

2 $ 2 m

.)

Figure 4: Three-point vertex Feynman rules. The KK states are plot in double-sinusoidalcurves. The symbols Cµ!,"#, Dµ!,"#(k1, k2) and Eµ!,"#(k1, k2) are defined in Eqs. (A.10),(A.11) and (A.12) respectively. m!, mA and m$ are masses of the scalar, vector and

fermion. ! =!

23(n+2) , " =

!16#GN and $ is the gauge-fixing parameter.

26

k2, n

k1, m

µ! (ij), n"

h~ n"

µ! ## : $ i %/2 &

mn ( m

2 # '

µ! + C

µ!, () k

1 ( k

2 ) )

*~ n"

ij ## : i + % &

ij &

mn ( k

1 • k

2 $ 2 m

2 # )

Ab )(k

2)

Aa ((k

1)

µ! (ij), n"

p

h~ n"

µ! ,, : $ i %/2 &

ab ( ( m

2 A + k

1 • k

2 ) C

µ!, () + D

µ!, () (k

1, k

2)

+ -$1

Eµ!, ()

(k1, k

2) )

*~ n"

ij ,, : i + % &

ij &

ab ( '

() m

2 A + -

$1 (k

1( p) + k

2) p() )

k2, n

k1, m

µ! (ij), n"

h~ n"

µ! .. : $ i %/8 &

mn ( /

µ (k

1! + k

2!) + /

! (k

1µ + k

2µ)

$ 2 'µ!

(k/1 + k/

2 $ 2 m

.) )

*~ n"

ij .. : i + % &

ij &

mn ( 3/4 k/

1 + 3/4 k/

2 $ 2 m

.)

Figure 4: Three-point vertex Feynman rules. The KK states are plot in double-sinusoidalcurves. The symbols Cµ!,"#, Dµ!,"#(k1, k2) and Eµ!,"#(k1, k2) are defined in Eqs. (A.10),(A.11) and (A.12) respectively. m!, mA and m$ are masses of the scalar, vector and

fermion. ! =!

23(n+2) , " =

!16#GN and $ is the gauge-fixing parameter.

26

Production:g

g

KK

q

q

KK

Decay:

k2, n

k1, m

µ! (ij), n"

h~ n"

µ! ## :$ i %/2 &mn ( m

2 # 'µ! + Cµ!, () k1

( k2

) )

*~ n"

ij ## :i + % &ij &mn ( k1 • k2 $ 2 m

2 # )

Ab )(k2)

Aa ((k1)

µ! (ij), n"

p

h~ n"

µ! ,, :$ i %/2 &

ab ( ( m

2 A + k1 • k2 ) Cµ!, () + Dµ!, () (k1, k2)

+ -$1

Eµ!, () (k1, k2) )

*~ n"

ij ,, :i + % &ij &

ab ( '() m

2 A + -

$1 (k1( p) + k2) p() )

k2, n

k1, m

µ! (ij), n"

h~ n"

µ! .. :$ i %/8 &mn ( /µ (k1! + k2!) + /! (k1µ + k2µ)

$ 2 'µ! (k/1 + k/2 $ 2 m.) )

*~ n"

ij .. :i + % &ij &mn ( 3/4 k/1 + 3/4 k/2 $ 2 m.)

Figure4:Three-pointvertexFeynmanrules.TheKKstatesareplotindouble-sinusoidalcurves.ThesymbolsCµ!,"#,Dµ!,"#(k1,k2)andEµ!,"#(k1,k2)aredefinedinEqs.(A.10),(A.11)and(A.12)respectively.m!,mAandm$aremassesofthescalar,vectorand

fermion.!=!

23(n+2),"=

!16#GNand$isthegauge-fixingparameter.

26

k2, n

k1, m

µ! (ij), n"

h~ n"

µ! ## :$ i %/2 &mn ( m

2 # 'µ! + Cµ!, () k1

( k2

) )

*~ n"

ij ## :i + % &ij &mn ( k1 • k2 $ 2 m

2 # )

Ab )(k2)

Aa ((k1)

µ! (ij), n"

p

h~ n"

µ! ,, :$ i %/2 &

ab ( ( m

2 A + k1 • k2 ) Cµ!, () + Dµ!, () (k1, k2)

+ -$1

Eµ!, () (k1, k2) )

*~ n"

ij ,, :i + % &ij &

ab ( '() m

2 A + -

$1 (k1( p) + k2) p() )

k2, n

k1, m

µ! (ij), n"

h~ n"

µ! .. :$ i %/8 &mn ( /µ (k1! + k2!) + /! (k1µ + k2µ)

$ 2 'µ! (k/1 + k/2 $ 2 m.) )

*~ n"

ij .. :i + % &ij &mn ( 3/4 k/1 + 3/4 k/2 $ 2 m.)

Figure4:Three-pointvertexFeynmanrules.TheKKstatesareplotindouble-sinusoidalcurves.ThesymbolsCµ!,"#,Dµ!,"#(k1,k2)andEµ!,"#(k1,k2)aredefinedinEqs.(A.10),(A.11)and(A.12)respectively.m!,mAandm$aremassesofthescalar,vectorand

fermion.!=!

23(n+2),"=

!16#GNand$isthegauge-fixingparameter.

26

KK KK

k2, n

k1, m

µ! (ij), n"

h~ n"

µ! ## :$ i %/2 &mn ( m

2 # 'µ! + Cµ!, () k1

( k2

) )

*~ n"

ij ## :i + % &ij &mn ( k1 • k2 $ 2 m

2 # )

Ab )(k2)

Aa ((k1)

µ! (ij), n"

p

h~ n"

µ! ,, :$ i %/2 &

ab ( ( m

2 A + k1 • k2 ) Cµ!, () + Dµ!, () (k1, k2)

+ -$1

Eµ!, () (k1, k2) )

*~ n"

ij ,, :i + % &ij &

ab ( '() m

2 A + -

$1 (k1( p) + k2) p() )

k2, n

k1, m

µ! (ij), n"

h~ n"

µ! .. :$ i %/8 &mn ( /µ (k1! + k2!) + /! (k1µ + k2µ)

$ 2 'µ! (k/1 + k/2 $ 2 m.) )

*~ n"

ij .. :i + % &ij &mn ( 3/4 k/1 + 3/4 k/2 $ 2 m.)

Figure4:Three-pointvertexFeynmanrules.TheKKstatesareplotindouble-sinusoidalcurves.ThesymbolsCµ!,"#,Dµ!,"#(k1,k2)andEµ!,"#(k1,k2)aredefinedinEqs.(A.10),(A.11)and(A.12)respectively.m!,mAandm$aremassesofthescalar,vectorand

fermion.!=!

23(n+2),"=

!16#GNand$isthegauge-fixingparameter.

26

KK

g

g

q, !+

q, !!

W, Z, !

W, Z, !

KK Graviton Resonances

• Closer spacing between resonances

• Higher and broader peaks:

• Relative heights between different KK resonances! ! !

!4! ! "

!2MKK

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