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


Bosons & Fermions

Matter: Fermions

Interactions: Bosons


Standard Model of Particle Physics


Then Why String Theory?


Then Why String Theory?

To incorporate GRAVITY with the Standard Model gaugegroup SU(3)× SU(2)× U(1).


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?


Why Superstrings?

Supersymmetry is the symmetry that interchanges bosons andfermions.


Superstring Theories


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)


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


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.


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


Rules for Modular Invariance

The ABK Rules[Antoniadis,Bachas,Kounnas, 1987]


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}.


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


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}


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


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)


THANK YOU!!!


YRM 2015 - JM ASHFAQUE

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