YRM 2015 - JM ASHFAQUE
-
Upload
johar-m-ashfaque -
Category
Documents
-
view
158 -
download
1
Transcript of YRM 2015 - JM ASHFAQUE
Semi-Realistic Non-Supersymmetric HeteroticString Vacua
Johar M. Ashfaque
University of Liverpool
Johar M. Ashfaque YRM 2015, Oxford
The Fundamental Forces of Nature
Weak Nuclear Force
Strong Nuclear Force
Electromagnetism
Gravity
Johar M. Ashfaque YRM 2015, Oxford
Bosons & Fermions
Matter: Fermions
Interactions: Bosons
Johar M. Ashfaque YRM 2015, Oxford
Standard Model of Particle Physics
Johar M. Ashfaque YRM 2015, Oxford
Then Why String Theory?
Johar M. Ashfaque YRM 2015, Oxford
Then Why String Theory?
To incorporate GRAVITY with the Standard Model gaugegroup SU(3)× SU(2)× U(1).
Johar M. Ashfaque YRM 2015, Oxford
Why (Bosonic) String Theory Is Not The Complete Story?
Two major setbacks
The ground state of the spectrum always contains a tachyon.As a consequence, the vacuum is unstable.
Does not contain fermions. Where is the matter?
Johar M. Ashfaque YRM 2015, Oxford
Why (Bosonic) String Theory Is Not The Complete Story?
Two major setbacks
The ground state of the spectrum always contains a tachyon.As a consequence, the vacuum is unstable.
Does not contain fermions. Where is the matter?
Johar M. Ashfaque YRM 2015, Oxford
Why (Bosonic) String Theory Is Not The Complete Story?
Two major setbacks
The ground state of the spectrum always contains a tachyon.As a consequence, the vacuum is unstable.
Does not contain fermions. Where is the matter?
Johar M. Ashfaque YRM 2015, Oxford
Why Superstrings?
Supersymmetry is the symmetry that interchanges bosons andfermions.
Johar M. Ashfaque YRM 2015, Oxford
Superstring Theories
Johar M. Ashfaque YRM 2015, Oxford
Heterotic Strings
Heterotic strings are hybrid strings with either
left-moving sector being supersymmetric and right-movingsector being bosonic or
or vice versa
There are two heterotic string theories, one associated to thegauge group
E8 × E8
and the other toSO(32)
Johar M. Ashfaque YRM 2015, Oxford
Heterotic Strings
Heterotic strings are hybrid strings with either
left-moving sector being supersymmetric and right-movingsector being bosonic or
or vice versa
There are two heterotic string theories, one associated to thegauge group
E8 × E8
and the other toSO(32)
Johar M. Ashfaque YRM 2015, Oxford
The Basic Aim of Free Fermionic Construction
The Goal of the Free Fermionic Construction
4 Flat Space-Time Dimensions
N = 1 SUSY
3 generations of quarks and leptons
Johar M. Ashfaque YRM 2015, Oxford
Free-Fermionic Construction
The free-fermionic construction is based on the heterotic stringsand from here on, we will fix the left-moving sector to besupersymmetric and right-moving sector to be bosonic.
A torus has two non-contractible loops often referred to as the”toroidal” and ”poloidal” directions.
The left-moving and right-moving fermions acquire an integerphase when parallel transported along the two non-contractibleloops of the torus.
Johar M. Ashfaque YRM 2015, Oxford
The Free Fermionic Construction
A general boundary condition basis vector is of the form
α ={ψ1,2, χi , y i , ωi |y i , ωi , ψ
1,...,5, η1,2,3, φ
1,...,8}
where i = 1, ..., 6
ψ1,...,5
- SO(10) gauge group
φ1,...,8
- SO(16) gauge group
Johar M. Ashfaque YRM 2015, Oxford
Rules for Modular Invariance
The ABK Rules[Antoniadis,Bachas,Kounnas, 1987]
Johar M. Ashfaque YRM 2015, Oxford
The NAHE Set: A Toy Model
The NAHE set is the set of basis vectors
B = {1,S,b1,b2,b3}
where
1 = {ψ1,2µ , χ1,...,6, y1,...,6, ω1,...,6|y1,...,6, ω1,...,6, ψ1,...,5, η1,2,3, φ1,...,8},
S = {ψ1,2µ , χ1,...,6},
b1 = {ψ1,2µ , χ1,2, y3,...,6|y3,...,6, ψ1,...,5, η1},
b2 = {ψ1,2µ , χ3,4, y1,2, ω5,6|y1,2, ω5,6, ψ1,...,5, η2},
b3 = {ψ1,2µ , χ5,6, ω1,...,4|ω1,...,4, ψ1,...,5, η3}.
Johar M. Ashfaque YRM 2015, Oxford
Primarily
Seek string models which closely resemble the MSSM with
4D N = 1 theory
N = 1→ N = 0
with SM gauge group embedding
3 generations of quarks and leptons
minimum of 1 Higgs doublet pair
Johar M. Ashfaque YRM 2015, Oxford
Primarily
Seek string models which closely resemble the MSSM with
4D N = 1 theory
N = 1→ N = 0
with SM gauge group embedding
3 generations of quarks and leptons
minimum of 1 Higgs doublet pair
Johar M. Ashfaque YRM 2015, Oxford
Primarily
Seek string models which closely resemble the MSSM with
4D N = 1 theory
N = 1→ N = 0
with SM gauge group embedding
3 generations of quarks and leptons
minimum of 1 Higgs doublet pair
Johar M. Ashfaque YRM 2015, Oxford
Primarily
Seek string models which closely resemble the MSSM with
4D N = 1 theory
N = 1→ N = 0
with SM gauge group embedding
3 generations of quarks and leptons
minimum of 1 Higgs doublet pair
Johar M. Ashfaque YRM 2015, Oxford
Primarily
Seek string models which closely resemble the MSSM with
4D N = 1 theory
N = 1→ N = 0
with SM gauge group embedding
3 generations of quarks and leptons
minimum of 1 Higgs doublet pair
Johar M. Ashfaque YRM 2015, Oxford
An Explicit Non-Supersymmetric Tachyon-Free Model
1 = {ψµ, χ1,..,6, y1,...,6, ω1,...,6|y1,...,6, ω1,...,6, ψ1,...,5
, η1,2,3, φ1,...,8}
S = {ψµ, χ1,..,6}
b1 = {ψµ, χ1,2, y3,...,6|y3,...,6, ψ1,...,5
, η1}
b2 = {ψµ, χ3,4, y1,2, ω5,6|y1,2, ω5,6, ψ1,...,5
, η2}
b3 = {ψµ, χ5,6, ω1,...,4|ω1,...,4, ψ1,...,5
, η3}
α = {y1,...,6, ω1,...,6|ω1, y2, ω3, y4,5, ω6, ψ1,2,3
, φ1,...,4}
β = {y2, ω2, y4, ω4|y1,...,4, ω5, y6, ψ1,2,3
, φ1,...,4}
γ = {y1, ω1, y5, ω5|ω1,2, y3, ω4, y5,6, ψ1,2,3
= 12 ,
η1,2,3 = 12 , φ
2,...,7= 1
2}
Johar M. Ashfaque YRM 2015, Oxford
The Observable Sector: Left-Right Symmetric
SO(10)
α, β��
SO(6)× SO(4)
γ
��SU(3)C × U(1)C × SU(2)L × SU(2)R
Johar M. Ashfaque YRM 2015, Oxford
The Hidden Sector
SO(16)
α, β��
SO(8)× SO(8)
γ
��U(1)× SU(3)H1 × U(1)H1 × SU(3)H2 × U(1)H2 × U(1)
Johar M. Ashfaque YRM 2015, Oxford
THANK YOU!!!
Johar M. Ashfaque YRM 2015, Oxford