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