“supersimetria y escalamiento anisotrÓpico; dos...
TRANSCRIPT
Departamento de Física
División de Ciencias e Ingenierías del Campus León Universidad de Guanajuato
“SUPERSIMETRIA Y ESCALAMIENTO ANISOTRÓPICO; DOS MANERAS DE GENERALIZAR LA
FÍSICA”
Dr. Octavio Obregón
) .. ..
ds
2 = �dt
2 + dx
2 + dy
2 + dz
2
NO ) x
2 + y
2 + z
2 = cte
( )x2+( )y2+( )z2 = cte
ds
2 = gµ⌫|{z}Interaccion
gravitacional
dx
µdx
⌫ )
8>>>><
>>>>:
µ, ⌫ = 0, . . . , 3x
0 = t
x
1 = x
x
2 = y
x
3 = z
Fuerzas
Fuerza de Coulomb
q1
d �
fotond
Bosones (Aµ)
Fermiones ( )
proton ( p
En General: “Interacciones”
Fuerza eléctrica
q2 q2
F = Kq1q2
(d+�)2
e ) electron
SimetríasNúcleo
=?...
. . . +isospın
F ⇠ BAhora que tal si
pero
=no tan facil
=
pero nuevas partıculas
B
. . . . . .
. . . . . .
Fotino
Selectron
F
F B
Regresamos a
gµ⌫
⇢Interaccion
gravitacional...B si Supersimetrıa . . . F gµ⌫ . . . µ
sistemas gravitatorios gµ⌫
ds2 = �dt2 + a(t)2⇥dr2 + r2d⌦2
⇤
a(t) radio del UNIVERSO
El UNIVERSO
Ademas � (o ⇤)
“EL SUPERUNIVERSO”
⇤⇤
(gµ⌫ , µ) & (�,�)
0
0.2
0.4
0.6
0.8
1
-1 -0.5 0 0.5 1
y
x
λ=3
A BC
E
IIIIIIIV
A
2-2
1.5
y
1-1
0.50
00x
0.5
1z
1
1.5
2
2
JCAP 1012:011,2010
Phys. Rev. D 80, 104020 (2009)
Phys. Rev. D 84, 024015 (2011)
Quantum Cosmology in Hořava-Lifshitz Gravity
O. Obregón
Motivation
- Self-consistent framework for quantum gravity
- Applications
1. Gravity duals (AdS/CFT)
2. Mathematical (Ricci Flows)
- Reproduce the observed gravitation phenomena
¿How close can we get with this idea?
Additional Motivation
Unification
Cosmology and BH
Problem of time
- Power-counting Renormalizable Ingredients
Anisotropic Scaling
Symmetries - DiffF(M)
Projectable metric N = N(t) Detailed Balance
Hořava Gravity (Minimal Version)
The Action:
Gravity with Anisotropic Scaling
Kinetic term Potential term
Quadratic in first time derivatives of gij
Invatiant under DiffF(M)
Of order 2z in spatial derivatives of gij
Invariant under DiffF(M)
Action in 3 dim
Action in 3+1 dim
κ, λ, μ. w and ΛW are coupling constants, and comparing the terms in yellow with GR
Detailed Balance
Misner parametrization
Wheeler-DeWitt Equation
Kantowski-Sachs Quantum Cosmological Model
GR Hořava
SdS (Hořava)
• Singularity t = 0
• ξ > 0, non-singular
• ξ = 0, 𝑡𝑠 =3
2Λ (singularity)
• ξ < 0, 2 singularities
SdS (GR)
• Singularity t = 0
• 𝑚 = 0, 𝑡ℎ =3
Λ (horizon)
• 2 horizons with 0 < Λ𝑚2 <1
9
𝑑𝑠2 = −Λ𝑡2
3+2ξ
𝑡+
3
4Λ𝑡2− 1
−1
𝑑𝑡2 +Λ𝑡2
3+2ξ
𝑡+
3
4Λ𝑡2− 1 𝑑𝑟2 + 𝑡2𝑑Ω2
WKB Approximation
SAdS (Hořava)
• Singularity t = 0
• −8 > 9Λξ2, 2 singularities
• −8 ≤ 9Λξ2 ≤ 0, unphysical
SAdS (GR)
• Singularity t = 0
• 𝑚 > 0, 1 Horizon
• 𝑚 < 0, Unphysical
- Quantum cosmology in Horava-Lifshitz gravity
Phys. Rev. D 86, 063502 (2012)
- A quantum cosmological model in Horava-Lifshitz gravity
AIP Conf. Proc. 1396, pp. 151-155 (2011)
Results available in...