SLIDE 1
Conformal Freeze-in
Sungwoo Hong Cornell
Utah Workshop: Leaving no stone unturned!
work in progress with Maxim Perelstein and Gowri Kurup
- I. Motivation / Question
* Universe consistent with QM + SR * Universe described by QFT
Conformal Freeze-in Sungwoo Hong Cornell work in progress with - - PowerPoint PPT Presentation
Conformal Freeze-in Sungwoo Hong Cornell work in progress with - - PowerPoint PPT Presentation
Conformal Freeze-in Sungwoo Hong Cornell work in progress with Maxim Perelstein and Gowri Kurup Utah Workshop: Leaving no stone unturned! I. Motivation / Question * Universe consistent with QM + SR * Universe described by QFT I. Motivation
SLIDE 2
SLIDE 3
- I. Motivation / Question
* Universe consistent with QM + SR * Universe described by QFT * Conventionally, cosmology via "particle" QFT
SLIDE 4
- I. Motivation / Question
* Universe consistent with QM + SR * Universe described by QFT * Conventionally, cosmology via "particle" QFT > mostly "particles" e.g. DM as massive particle DR as massless particle
SLIDE 5
- I. Motivation / Question
* Universe consistent with QM + SR * Universe described by QFT * Conventionally, cosmology via "particle" QFT > mostly "particles" e.g. DM as massive particle DR as massless particle > "Static" form of
SLIDE 6
- I. Motivation / Question
* In this talk, I will show a story where plays a crucial role in cosmology CFT
SLIDE 7
- I. Motivation / Question
* In this talk, I will show a story where plays a crucial role in cosmology * No notion of "particle" with scale-inv. CFT
SLIDE 8
- I. Motivation / Question
* In this talk, I will show a story where plays a crucial role in cosmology * No notion of "particle" with scale-inv. > mostly "non-particles" => hot CFT > "varying" form of CFT
SLIDE 9
- I. Motivation / Question
* In this talk, I will show a story where plays a crucial role in cosmology * No notion of "particle" with scale-inv. > mostly "non-particles" => hot CFT > "varying" form of > dynamical description of light DM => mass gap via SM phase transitions CFT
SLIDE 10
Outline
- II. Basic idea / Big picture
- III. Conformal Freeze-in
- IV. Light DM from COFI
SLIDE 11
- II. Basic idea / Big picture
Mpl
CFT R
T v
EW MeV (BBN) eV (CMB)
CFT
O
~
CFT
SM
O
CFT D-4
D = d + dCFT
SM
SLIDE 12
- II. Basic idea / Big picture
Mpl
CFT R
T v
EW MeV (BBN) eV (CMB)
CFT
O
~
CFT
SM
O
CFT D-4
D = d + dCFT
SM
* want to study SM <-> CFT dynamics at finite T
SLIDE 13
- II. Basic idea / Big picture
* In order to see (i) why this set up is useful (ii) possible challenges
SLIDE 14
- II. Basic idea / Big picture
Note : (i) For any QFT, exists. In particular, exists. T T
CFT
SLIDE 15
- II. Basic idea / Big picture
Note : (i) For any QFT, exists. In particular, exists. T T
CFT
homogeneity + isotropy => T =
- P
- P
- P
Scale invariance => = 1 3
CFT CFT
P
SLIDE 16
- II. Basic idea / Big picture
Note : (i-1) (i-2) d can be non-integer =>
CFT~ T
4
cf)
CFT
. + 3 H ( + P) = C
CFT CFT
cf) d > j + j +2-
CFT
1 2 j j ,0 1 2
= 1 3
CFT
P
SLIDE 17
- II. Basic idea / Big picture
(ii) possible challenges
CFT
O
~
CFT
SM
O
CFT D-4
SLIDE 18
- II. Basic idea / Big picture
(ii) possible challenges
CFT
O
~
CFT
SM
O
CFT D-4
* In usual particle case, (a) n = N/V well-defined, (b) SM <=> DS at finite T by scattering and/or (inverse) decay
SLIDE 19
- II. Basic idea / Big picture
(ii) possible challenges
CFT
O
~
CFT
SM
O
CFT D-4
* In usual particle case, (a) n = N/V well-defined, (b) SM <=> DS at finite T by
n + 3 H n = - < v> (n - n )
.
eq 2 2
SLIDE 20
- II. Basic idea / Big picture
(ii) possible challenges
CFT
O
~
CFT
SM
O
CFT D-4
* In cases with CFT, (a) n = N/V not defined, (b) SM <=> CFT at finite T requires
<O O >
CFT CFT
at finite T
SLIDE 21
- II. Basic idea / Big picture
CFT
O
~
CFT
SM
O
CFT D-4
CFT
O
~
eff
( )
SM SM SM SM SM SM
~ <O O >
CFT CFT
T=0 T=finite vs
SLIDE 22
- II. Basic idea / Big picture
(ii) possible challenges
CFT
O
~
CFT
SM
O
CFT D-4
* In cases with CFT, (a) n = N/V not defined,
CFT
. + 3 H ( + P) = + 4 H = C
CFT CFT CFT
.
SLIDE 23
- II. Basic idea / Big picture
(ii) possible challenges
CFT
O
~
CFT
SM
O
CFT D-4
* In cases with CFT, (a) (b) In d>2, general Not known (cf. holographic CFT)
CFT
. + 4 H = C
CFT
<O O >
CFT CFT
finite T
SLIDE 24
- II. Basic idea / Big picture
(ii) possible challenges
CFT
O
~
CFT
SM
O
CFT D-4
* In cases with CFT, (a) (b)
CFT
. + 4 H = C
CFT
Calculable case:
CFT SM
<<
SLIDE 25
(a) (b)
CFT
. + 4 H = C
CFT
Calculable case:
CFT SM
<< => backreaction CFT->SM can be ignored => C = C(SM->CFT)
- II. Basic idea / Big picture
SLIDE 26
(a) (b)
CFT
. + 4 H = C
CFT
Calculable case:
CFT SM
<< => backreaction CFT->SM can be ignored => C = C(SM->CFT)
* assume: No Pauli-blocking/stimulated emission
- II. Basic idea / Big picture
SLIDE 27
- III. Conformal Freeze-in
tot SM
= +
CFT tot
. + 3 H ( + P ) = 0
tot tot
* For concreteness, consider SM1 + SM2 -> CFT (only channel)
SLIDE 28
- III. Conformal Freeze-in
tot SM
= +
CFT tot
. + 3 H ( + P ) = 0
tot tot
* For concreteness, consider SM1 + SM2 -> CFT (only channel)
SM-{SM1,SM2}
. + 4 H = 0
SM-{SM1,SM2}
(RD)
SM1+SM2
. + 4 H = -n n < v E >
SM1+SM2
2 1 1+2->CFT 1+2
SLIDE 29
CFT
. + 4 H = +n n < v E >
CFT
2 1 1+2->CFT 1+2
- III. Conformal Freeze-in
SLIDE 30
CFT
. + 4 H = +n n < v E >
CFT
2 1 1+2->CFT 1+2
- III. Conformal Freeze-in
*As usual, Naive Dim. Analysis can teach us essence of relevant physics.
CFT
O
~
CFT
SM
O
CFT D-4
=> C ~ T
CFT
T
CFT 2D-8 2D-9 6 2
SLIDE 31
CFT
. + 4 H = +n n < v E >
CFT
2 1 1+2->CFT 1+2
- III. Conformal Freeze-in
*As usual, Naive Dim. Analysis can teach us essence of relevant physics.
CFT
O
~
CFT
SM
O
CFT D-4
=> C ~
CFT T CFT 2D-8 2D-3 2
SLIDE 32
CFT
. + 4 H = +n n < v E >
CFT
2 1 1+2->CFT 1+2
- III. Conformal Freeze-in
*As usual, Naive Dim. Analysis can teach us essence of relevant physics.
CFT
O
~
CFT
SM
O
CFT D-4
=> C ~
CFT T CFT 2D-8 2D-3 2
*Detailed calculation to determine O(1) factor
SLIDE 33
CFT
. + 4 H =
CFT
- III. Conformal Freeze-in
CFT T CFT 2D-8 2D-3 2
SLIDE 34
CFT
. + 4 H =
CFT
- III. Conformal Freeze-in
CFT T CFT 2D-8 2D-3 2
H = = g 1 2t
*
1/2 T 2 2
Mpl
(RD)
CFT
. + =
CFT
2 t A t
3/2-D
A=
(2g )
*
1/2 D-3/2
CFT 2D-8 D-3/2
Mpl
CFT 2
SLIDE 35
CFT
. + 4 H =
CFT
- III. Conformal Freeze-in
CFT T CFT 2D-8 2D-3 2
H = = g 1 2t
*
1/2 T 2
Mpl
(RD)
CFT
. + =
CFT
2 t A t
3/2-D
CFT = t (A/( -D) t + B)
- 2
9/2-D
9
2
SLIDE 36
- III. Conformal Freeze-in
CFT = t (A/( -D) t + B)
- 2
9/2-D
9
2
D=8/2 = 10 GeV
CFT
9
CFT = 1
A=
(2g )
*
1/2 D-3/2
CFT 2D-8 D-3/2
Mpl
CFT 2
R
T = 10 GeV
8
SLIDE 37
- III. Conformal Freeze-in
CFT = t (A/( -D) t + B)
- 2
9/2-D
9
2
D=8/2 = 10 GeV
CFT
9
CFT = 1
D=10/2 A=
(2g )
*
1/2 D-3/2
CFT 2D-8 D-3/2
Mpl
CFT 2
R
T = 10 GeV
8
SLIDE 38
- III. Conformal Freeze-in
CFT = t (A/( -D) t + B)
- 2
9/2-D
9
2
D<9/2
CFT << 1 =>
* We need :
=> d =non-integer
d > j + j +2-
CFT
1 2 j j ,0 1 2
CFT
CFT SM
<<
SLIDE 39
- III. Conformal Freeze-in
* Freeze-in ends via
(i) mass gaps
e.g.) SM mass: Dynamical mass gap:
mf
Gap
M
SLIDE 40
- III. Conformal Freeze-in
* Freeze-in ends via
(i) mass gaps
e.g.) SM mass: Dynamical mass gap:
mf
(ii) Phase transitions
e.g.) SM sector: EWPT, QCD-PT
Gap
M
SLIDE 41
- III. Conformal Freeze-in
* Freeze-in ends via
(i) mass gaps
e.g.) SM mass: Dynamical mass gap:
mf
Gap
(ii) Phase transitions
e.g.) SM sector: EWPT, QCD-PT CFT sector: conformality lost
M
SLIDE 42
- IV. Light DM from COFI
* We consider
SM
O = HQ q
SM
O = H H
(Q,q=quarks)
SLIDE 43
- IV. Light DM from COFI
* We consider
SM
O = HQ q
SM
O = H H
(i) SM PTs trigger COFI,
SLIDE 44
- IV. Light DM from COFI
* We consider
SM
O = HQ q
SM
O = H H
(i) SM PTs trigger COFI, (ii) SM PTs terminate COFI,
SLIDE 45
- IV. Light DM from COFI
* We consider
SM
O = HQ q
SM
O = H H
(i) SM PTs trigger COFI, (ii) SM PTs terminate COFI, (iii) SM PTs `generate' mass gap in CFT
SLIDE 46
- IV. Light DM from COFI
* We consider
SM
O = HQ q
SM
O = H H
(i) SM PTs trigger COFI, (ii) SM PTs terminate COFI, (iii) SM PTs `generate' mass gap in CFT (vi) COFI provides dynamical description for light (10 keV - 10 MeV) DM !
SLIDE 47
- IV. Light DM from COFI
SM
O = HQ q
(1) Mpl
CFT R
T v
EW MeV (BBN) eV (CMB)
CFT
O
~
CFT
SM
O
CFT D-4
D = d + dCFT
SM
SLIDE 48
- IV. Light DM from COFI
SM
O = HQ q
(1) Mpl
CFT R
T v
EW MeV (BBN) eV (CMB)
CFT
O
~
CFT
SM
O
CFT D-4
D = d + dCFT
SM
* two parameters:
CFT CFT D-4
dCFT ,
SLIDE 49
- IV. Light DM from COFI
SM
O = HQ q
(1) Mpl
CFT R
T v
EW MeV (BBN) eV (CMB)
CFT
O
~
CFT
SM
O
CFT D-4
D = d + dCFT
SM
* two parameters:
CFT CFT D-4
dCFT ,
Gap
M =>
SLIDE 50
- IV. Light DM from COFI
SM
O = HQ q
(1) Mpl
CFT R
T v
EW MeV (BBN) eV (CMB)
SLIDE 51
- IV. Light DM from COFI
SM
O = HQ q
(1) Mpl
CFT R
T v
EW MeV (BBN) eV (CMB)
CFT
O
~
CFT
SM
O
CFT D-4
D = d + dCFT
SM
< 9/2
SLIDE 52
- IV. Light DM from COFI
SM
O = HQ q
(1) Mpl
CFT R
T v
EW MeV (BBN) eV (CMB)
CFT
O
~
CFT
SM
O
CFT D-4
D = d + dCFT
SM
< 9/2 * T> v
EW
D > 4+1 = 5
SLIDE 53
- IV. Light DM from COFI
SM
O = HQ q
(1) Mpl
CFT R
T v
EW MeV (BBN) eV (CMB)
CFT
O
~
CFT
SM
O
CFT D-4
D = d + dCFT
SM
< 9/2 * T> v
EW
D > 4+1 = 5 => No (IR-dom) COFI !
SLIDE 54
- IV. Light DM from COFI
SM
O = HQ q
(1) Mpl
CFT R
T v
EW MeV (BBN) eV (CMB)
CFT
O
~
CFT
SM
O
CFT D-4
D = d + dCFT
SM
< 9/2 * T< v
EW
CFT
O
~
CFT CFT D'-4
Q q
v
EW
CFT
2
SLIDE 55
- IV. Light DM from COFI
SM
O = HQ q
(1) Mpl
CFT R
T v
EW MeV (BBN) eV (CMB)
CFT
O
~
CFT
SM
O
CFT D-4
D = d + dCFT
SM
< 9/2 * T< v
EW
3+1 < D' < 9/2
CFT
O
~
CFT CFT D'-4
Q q
v
EW
CFT
2
SLIDE 56
- IV. Light DM from COFI
SM
O = HQ q
(1) Mpl
CFT R
T v
EW MeV (BBN) eV (CMB)
CFT
O
~
CFT
SM
O
CFT D-4
D = d + dCFT
SM
< 9/2 * T< v
EW
3+1 < D' < 9/2 => EWPT triggers COFI !
SLIDE 57
- IV. Light DM from COFI
SM
O = HQ q
(1) Mpl
CFT R
T v
EW MeV (BBN) eV (CMB)
<= No COFI (D>9/2) <= COFI via [Qq => CFT]
SLIDE 58
- IV. Light DM from COFI
SM
O = HQ q
(1) Mpl
CFT R
T v
EW MeV (BBN) eV (CMB)
<= No COFI (D>9/2) <= COFI via [Qq => CFT] When does COFI end ?
SLIDE 59
- IV. Light DM from COFI
SM
O = HQ q
(1) Mpl
CFT R
T v
EW MeV (BBN) eV (CMB)
<= No COFI (D>9/2) <= COFI via [Qq => CFT] When does COFI end ? When happens ?
CFT => DM
SLIDE 60
- IV. Light DM from COFI
SM
O = HQ q
(1)
: Mass gap via EWPT and QCDPT
CFT
O
~
CFT CFT D'-4
Q q
v
EW
CFT
2
(a) EWPT
SLIDE 61
- IV. Light DM from COFI
SM
O = HQ q
(1)
CFT
O
~
CFT CFT d -1
Q q
v
EW
CFT
2
(a) EWPT
CFT
: Mass gap via EWPT and QCDPT
SLIDE 62
- IV. Light DM from COFI
SM
O = HQ q
(1)
~
CFT CFT d -1
v
EW
CFT
2
(a) EWPT
CFT
: Mass gap via EWPT and QCDPT
(b) QCDPT
CFT
O
QCD
3
SLIDE 63
- IV. Light DM from COFI
SM
O = HQ q
(1)
~
CFT CFT d -1
v
EW
CFT
2
(a) EWPT
CFT
: Mass gap via EWPT and QCDPT
(b) QCDPT
CFT
O
QCD
3
=> relevant deformation to CFT !
SLIDE 64
- IV. Light DM from COFI
SM
O = HQ q
(1)
~
CFT CFT d -1
v
EW
CFT
2
(a) EWPT
CFT
: Mass gap via EWPT and QCDPT
(b) QCDPT
CFT
O
QCD
3
< >
Gap
M
~
d -1
CFT
Gap
M
d -1
CFT
Gap
M
~
4
(c) Conf. lost
SLIDE 65
- IV. Light DM from COFI
SM
O = HQ q
(1)
(a) EWPT
: Mass gap via EWPT and QCDPT
(b) QCDPT
Gap
M
~
(c) Conf. lost
CFT
CFT d
v
EW
2
CFT
QCD
3
4-dCFT
1
SLIDE 66
- IV. Light DM from COFI
SM
O = HQ q
(1) Mpl
CFT R
T v
EW MeV (BBN) eV (CMB)
<= No COFI (D>9/2) <= COFI via [Qq => CFT]
Gap
M
COFI ends at max{ , }
QCD
CFT => DM
at
Gap
M
SLIDE 67
- IV. Light DM from COFI
SM
O = HQ q
(1)
SLIDE 68
- IV. Light DM from COFI
SM
O = HQ q
(1)
CFT,0= CFT
QCD
4
Gap
M
3
Gap
M
T
QCD
SLIDE 69
- IV. Light DM from COFI
SM
O = HQ q
(1)
SLIDE 70
- IV. Light DM from COFI
SM
O = HQ q
(1)
SLIDE 71
- IV. Light DM from COFI
SM
O = HQ q
(1)
SLIDE 72
SM
O = H H
- IV. Light DM from COFI
(2) Mpl
CFT R
T v
EW MeV (BBN) eV (CMB)
<= D=2+d < 9/2
CFT CFT
O
~
CFT
SM
O
CFT D-4
SLIDE 73
SM
O = H H
- IV. Light DM from COFI
(2) Mpl
CFT R
T v
EW MeV (BBN) eV (CMB)
<= COFI via [HH => CFT]
CFT
O
~
CFT
SM
O
CFT D-4
SLIDE 74
SM
O = H H
- IV. Light DM from COFI
(2) Mpl
CFT R
T v
EW MeV (BBN) eV (CMB)
<= h out of bath
CFT
O
~
CFT
SM
O
CFT D-4
<= COFI via [HH => CFT]
SLIDE 75
SM
O = H H
- IV. Light DM from COFI
(2) Mpl
CFT R
T v
EW MeV (BBN) eV (CMB)
<= "No COFI (no h)"
CFT
O
~
CFT
SM
O
CFT D-4
<= COFI via [hh => CFT]
SLIDE 76
SM
O = H H
- IV. Light DM from COFI
(2) Mpl
CFT R
T v
EW MeV (BBN) eV (CMB)
<= "No COFI (no h)"
CFT
O
~
CFT
SM
O
CFT D-4
<= COFI via [hh => CFT]
Gap
M
"COFI ends at max{ , }"
CFT => DM
at
Gap
M
v
EW
SLIDE 77
SM
O = H H
- IV. Light DM from COFI
(2)
Gap
M
~
CFT
CFT d -2
v
EW
CFT
4-dCFT
1
2/2
SLIDE 78
SM
O = H H
- IV. Light DM from COFI
(2)
SLIDE 79
SM
O = H H
- IV. Light DM from COFI
(2)
SLIDE 80
<more observables/constraints>
- 1. SN bounds
- 2. rare meson decay (visible/invisible)
- 3. beam dump
- 4. Higgs inv. decay
- 5. BBN
- 6. CMB (spectral distorsion)
- 7. CMB (ionization of neutral H)
SLIDE 81
Thank You !
SLIDE 82
UV Completion
SLIDE 83
Mpl
R
T v
EW MeV (BBN) eV (CMB)
UV Completion
CFT
MU
BZ
O
~
BZ
SM
O
D1-4
MU
D1 = d + d >4
BZ SM
SLIDE 84
Mpl
R
T v
EW MeV (BBN) eV (CMB)
UV Completion
CFT
MU
BZ
O
~
BZ
SM
O
D1-4
MU
D1 = d + d >4
BZ SM
=-b + b
1 2 2 3
g 4 =
2
SLIDE 85
Mpl
R
T v
EW MeV (BBN) eV (CMB)
UV Completion
CFT
MU
BZ
O
~
BZ
SM
O
D1-4
MU
D1 = d + d >4
BZ SM
=-b + b
1 2 2 3
g 4 =
2
Nc b1= 3 ( - )=
11 2
c
N Nf
Nc 3 Nc b2=- 8
2
2 ( )
34 3 - 1 2
c
N Nf( )
c
N N -1
c
2 2
2 20 3
+
SLIDE 86
Mpl
R
T v
EW MeV (BBN) eV (CMB)
UV Completion
CFT
MU
BZ
O
~
BZ
SM
O
D1-4
MU
D1 = d + d >4
BZ SM
=-b + b
1 2 2 3
g 4 =
2
Nc b1= 3 ( - )=
11 2
c
N Nf
Nc 3 Nc b2=- 8
2
2 ( )
34 3 - 1 2
c
N Nf( )
c
N N -1
c
2 2
2 20 3
+
>0
SLIDE 87
Mpl
R
T v
EW MeV (BBN) eV (CMB)
UV Completion
CFT
MU
BZ
O
~
BZ
SM
O
D1-4
MU
D1 = d + d >4
BZ SM
=-b + b
1 2 2 3
g 4 =
2
Nc b1= 3 ( - )=
11 2
c
N Nf
Nc 3 Nc b2=- 8
2
2 ( )
34 3 - 1 2
c
N Nf( )
c
N N -1
c
2 2
2 20 3
+
>0 >0
SLIDE 88
Mpl
R
T v
EW MeV (BBN) eV (CMB)
UV Completion
CFT
MU
BZ
O
~
BZ
SM
O
D1-4
MU
D1 = d + d >4
BZ SM
=-b + b
1 2 2 3
g 4 =
2
Nc b1= 3 ( - )=
11 2
c
N Nf
Nc 3 Nc b2=- 8
2
2 ( )
34 3 - 1 2
c
N Nf( )
c
N N -1
c
2 2
2 20 3
+
>0 >0
c
N Nf 34 13 11 2
< <
SLIDE 89
Mpl
R
T v
EW MeV (BBN) eV (CMB)
UV Completion
CFT
MU
BZ
O
~
BZ
SM
O
D1-4
MU
D1 = d + d >4
BZ SM
=-b + b
1 2 2 3
g 4 =
2
Nc b1= 3 ( - )=
11 2
c
N Nf
Nc 3 Nc b2=- 8
2
2 ( )
34 3 - 1 2
c
N Nf( )
c
N N -1
c
2 2
2 20 3
+
>0 >0
*Nc ~ Nc b1
b2 ~ 16 75
SLIDE 90
Mpl
R
T v
EW MeV (BBN) eV (CMB)
UV Completion
CFT
MU
BZ
O
~
BZ
SM
O
D1-4
MU
D1 = d + d >4
BZ SM
* Note: D1 > 4, integer !
SLIDE 91
Mpl
R
T v
EW MeV (BBN) eV (CMB)
UV Completion
CFT
MU
BZ
O
~
BZ
SM
O
D1-4
MU
BZ
O
BZ BZ
=
SM
O
SM SM
=
* Note: D1 = 6
D1 = d + d >4
BZ SM
SLIDE 92
Mpl
R
T v
EW MeV (BBN) eV (CMB)
UV Completion
CFT
MU
BZ
O
~
BZ
SM
O
D1-4
MU
BZ
O
BZ BZ
=
SM
O
SM SM
=
* Note: D1 = 6
D1 = d + d >4
BZ SM
SLIDE 93
Mpl
R
T v
EW MeV (BBN) eV (CMB)
UV Completion
CFT
MU
BZ
O
~
BZ
SM
O
D1-4
MU
BZ
O
BZ BZ
=
SM
O
=
D1 = d + d >4
BZ SM
SM SM
BZ
O ~
CFT
O
CFT d -d
BZ CFT
SLIDE 94
Mpl
R
T v
EW MeV (BBN) eV (CMB)
UV Completion
CFT
MU
BZ
O
~
BZ
SM
O
D1-4
MU
BZ
O
BZ BZ
=
SM
O
=
D1 = d + d >4
BZ SM
CFT
O
~
CFT
SM
O
CFT D2-4
SM SM
BZ
O ~
CFT
O
CFT d -d
BZ CFT
SLIDE 95
Mpl
R
T v
EW MeV (BBN) eV (CMB)
UV Completion
CFT
MU
BZ
O
~
BZ
SM
O
D1-4
MU
BZ
O
BZ BZ
=
SM
O
=
D1 = d + d >4
BZ SM
CFT
O
~
CFT
SM
O
CFT D2-4
* D2 = d + d < 9/2
CFT SM
=> d - d < 0 => 1 < d < 3/2
CFT
BZ
CFT
non-integer
SM SM
SLIDE 96
Mpl
R
T v
EW MeV (BBN) eV (CMB)
UV Completion
CFT
MU
BZ
O
~
BZ
SM
O
D1-4
MU
BZ
O
BZ BZ
=
SM
O
=
D1 = d + d >4
BZ SM
CFT
O
~
CFT
SM
O
CFT D2-4
* D2 = d + d < 9/2
CFT SM
*
CFT BZ CFT
MU
D1-4
=
BZ CFT
MU
2
=
<< 1
SM SM