Heterotic Strings and Free-Fermionic Construction

1. First Year Development Workshop
Heterotic Strings and Free-Fermionic Construction
Johar M. Ashfaque
Supervisor: Alon Faraggi
University of Liverpool
May 11, 2014
Johar M. Ashfaque Supervisor: Alon Faraggi String Phenomenology

2. Introduction
The string phenomenology group here at the University of
Liverpool works on a wide range of projects.
Here, I will present a brief outline of the free-fermionic
construction highlighting only the key points.
Johar M. Ashfaque Supervisor: Alon Faraggi String Phenomenology

3. Motivation
To incorporate GRAVITY with the Standard Model gauge
group SU(3) SU(2) U(1).
Johar M. Ashfaque Supervisor: Alon Faraggi String Phenomenology

4. Why (Bosonic) String Theory Is Not The Whole Story?
Two major setbacks
Johar M. Ashfaque Supervisor: Alon Faraggi String Phenomenology

5. Why (Bosonic) String Theory Is Not The Whole Story?
Two major setbacks
The ground state of the spectrum always contains a tachyon.
As a consequence, the vacuum is unstable.
Johar M. Ashfaque Supervisor: Alon Faraggi String Phenomenology

6. Why (Bosonic) String Theory Is Not The Whole Story?
Two major setbacks
The ground state of the spectrum always contains a tachyon.
As a consequence, the vacuum is unstable.
Do not contain space-time fermions.
Johar M. Ashfaque Supervisor: Alon Faraggi String Phenomenology

7. Why Superstrings?
Supersymmetry is the symmetry that interchanges bosons and
fermions.
Johar M. Ashfaque Supervisor: Alon Faraggi String Phenomenology

8. Heterotic Superstrings
Heterotic strings are hybrid strings with either
Johar M. Ashfaque Supervisor: Alon Faraggi String Phenomenology

9. Heterotic Superstrings
Heterotic strings are hybrid strings with either
left-moving sector being supersymmetric and right-moving
sector being bosonic or
Johar M. Ashfaque Supervisor: Alon Faraggi String Phenomenology

10. Heterotic Superstrings
Heterotic strings are hybrid strings with either
left-moving sector being supersymmetric and right-moving
sector being bosonic or
left-moving sector being bosonic and right-moving sector
being supersymmetric.
Johar M. Ashfaque Supervisor: Alon Faraggi String Phenomenology

11. Heterotic Superstrings
Heterotic strings are hybrid strings with either
left-moving sector being supersymmetric and right-moving
sector being bosonic or
left-moving sector being bosonic and right-moving sector
being supersymmetric.
There are two heterotic string theories, one associated to the
gauge group
E8 E8
and the other to
SO(32)
or more precisely
Spin(32)=Z2
which is the double cover of SO(32).
Johar M. Ashfaque Supervisor: Alon Faraggi String Phenomenology

12. Aim
Our aim is to construct realistic models with
Johar M. Ashfaque Supervisor: Alon Faraggi String Phenomenology

13. Aim
Our aim is to construct realistic models with
4
at space-time dimensions,
Johar M. Ashfaque Supervisor: Alon Faraggi String Phenomenology

14. Aim
Our aim is to construct realistic models with
4
at space-time dimensions,
chiral matter

15. elds and
Johar M. Ashfaque Supervisor: Alon Faraggi String Phenomenology

16. Aim
Our aim is to construct realistic models with
4
at space-time dimensions,
chiral matter

17. elds and
N = 1 SUSY.
Johar M. Ashfaque Supervisor: Alon Faraggi String Phenomenology

18. Free-Fermionic Construction
The free-fermionic construction is based on the heterotic strings
and from here on, we will

19. x the left-moving sector to be
supersymmetric 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 integer
phase when parallel transported along the two non-contractible
loops of the torus.
Johar M. Ashfaque Supervisor: Alon Faraggi String Phenomenology

20. An Example: The NAHE Set
The NAHE set is the set of basis vectors
B = f1; S; b1; b2; b3g
where
; 1;:::;6; y1;:::;6; !1;:::;6jy1;:::;6; !1;:::;6; 1;:::;5; 1;2;3; 1;:::;8g;
1 = f 1;2
S = f 1;2
; 1;:::;6g;
; 1;2; y3;:::;6jy3;:::;6; 1;:::;5; 1g;
b1 = f 1;2
; 3;4; y1;2; !5;6jy1;2; !5;6; 1;:::;5; 2g;
b2 = f 1;2
; 5;6; !1;:::;4j!1;:::;4; 1;:::;5; 3g:
b3 = f 1;2
Johar M. Ashfaque Supervisor: Alon Faraggi String Phenomenology

21. THANKYOU!!!
Johar M. Ashfaque Supervisor: Alon Faraggi String Phenomenology