Download - YRM 2016 - JM ASHFAQUE
F-Theory GUTs & The LHC Diphoton Excess
JOHAR M. ASHFAQUE
University of Liverpool
Based on arXiv:1607.03076
JOHAR M. ASHFAQUE YRM 2016
The Standard Model of Particle Physics:SUp3q � SUp2q � Up1q
JOHAR M. ASHFAQUE YRM 2016
Then Why String Theory?
To incorporate GRAVITY with the Standard Model gaugegroup SUp3q � SUp2q � Up1ql jh n
SUp5ql jh nSOp10ql jh n
E6ÑSOp10q�Up1q
.
JOHAR M. ASHFAQUE YRM 2016
Why (Bosonic) String Theory Is Not The Complete Story?
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 2016
Why (Bosonic) String Theory Is Not The Complete Story?
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 2016
Why (Bosonic) String Theory Is Not The Complete Story?
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 2016
Superstring Theories
JOHAR M. ASHFAQUE YRM 2016
Heterotic Superstrings
There are two heterotic string theories, one associated to thegauge group
E8ljhnobservable
� E81ljhnhidden
and the other toSOp32q
or more preciselySpinp32q{Z2
which is the double cover of SOp32q.
JOHAR M. ASHFAQUE YRM 2016
The Importance of Geometry In Physics
Useful insight
Model Building
Low Energy Effective Models of String theory
Desire models with
4 flat space-time dimensions3 generations of matterN � 1 SUSY
JOHAR M. ASHFAQUE YRM 2016
How F-Theory Saves The Day?
How can we hope to say anything about particle physics giventhe complexity of string vacua?
Apparent unification of couplings in MSSM atMGUT � 1016 GeV
Ñ MSUSY ! MGUT ! MPlanck
JOHAR M. ASHFAQUE YRM 2016
The Idea
If we were to compactify type II-B theory on some manifold B thenthis could be expressed in terms of F-theory compactified on alarger manifold A with specific properties that A has the structureof a fibre bundle and is an elliptic fibration of the manifold B.
π : CYn�1 Ñ Bn
JOHAR M. ASHFAQUE YRM 2016
Model Building Elements
Each lower-dimensional subspace provides an important modelbuilding element
Dimension Ingredient Complex EnhancementsCodimension
10D Gravity - -
8D Gauge Theory 1 -
6D Matter 2 Rank 1
4D Yukawa Couplings 3 Rank 2
JOHAR M. ASHFAQUE YRM 2016
The SUp5q GUT: Pictorially
The six extra dimensions are compactified on B3 whereas theSUp5q degrees of freedom are localized on the submanifold SGUT .The gauge bosons live on the bulk of SGUT but the chiralmultiplets are localized on complex matter curves. At theintersection of two matter curves a Yukawa coupling develops.
JOHAR M. ASHFAQUE YRM 2016
The SUp5q Matter Curves: Viewing The Enhancements
�α1
� �α2
� �α3
� �α4l jh n
A4
� ñ �α1
� �α2
� �α3
� �α4
� �α5l jh n
A5
Or
�α1
� �α2
� �α3
� �α4l jh n
A4
� ñ �α1
� �α2
�
�α5
|�α3
� �α4l jh n
D5
JOHAR M. ASHFAQUE YRM 2016
The SUp5q Yukawa Points: Viewing The Enhancements
�α1
� �α2
� �α3
� �α4
� �α5l jh n
A5
� ñ �α1
� �α2
� �α3
� �α4
� �α5
� �α6l jh n
A6
Or
�α1
� �α2
� �α3
� �α4
� �α5l jh n
A5
� ñ �α1
� �α2
� �α3
�
�α6
|�α4
� �α5l jh n
D6
Or
�α1
� �α2
�
�α5
|�α3
� �α4l jh n
D5
� ñ �α1
� �α2
�
�α6
|�α3
� �α4
� �α5l jh n
E6
JOHAR M. ASHFAQUE YRM 2016
GUT Breaking Methods 1
Adjoint matter - undesirable phenomenology 7
No setup incorporating dynamical GUT breaking
Discrete Wilson lines on 7-brane world-volume. But discretesymmetries have fixed points leading to singularities on7-brane world-volume 7
GUT breaking by Up1q fluxes and is something specific toF-Theory 3
JOHAR M. ASHFAQUE YRM 2016
GUT Breaking Methods 1
Adjoint matter - undesirable phenomenology 7
No setup incorporating dynamical GUT breaking
Discrete Wilson lines on 7-brane world-volume. But discretesymmetries have fixed points leading to singularities on7-brane world-volume 7
GUT breaking by Up1q fluxes and is something specific toF-Theory 3
JOHAR M. ASHFAQUE YRM 2016
The SM Embedding In The 27
E6 Ñ SOp10q � Up1qζ
Ñ rSUp5q � Up1qζ1s � Up1qζ
Ñ rSUp3q � SUp2q � Up1qζ2s � Up1qζ1 � Up1qζ
27 �
$'''''''&'''''''%
16 12
FL � FR � pQ, uc , dc , L, ec ,Nq
�Q uc
ec
���dc
L
�� N
10�1 D � h � pD,D,H,Hq
�DH
���DH
�
12 S Ñ S
JOHAR M. ASHFAQUE YRM 2016
Recently At The LHC...
D D, HS
g
g
γ
γ
Figure: (D � Dq P 10 of SOp10q contribute to the diphoton signalobserved at the LHC.
JOHAR M. ASHFAQUE YRM 2016
THANK YOU !!!
JOHAR M. ASHFAQUE YRM 2016