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


Then Why String Theory?

To incorporate GRAVITY with the Standard Model gaugegroup SUp3q � SUp2q � Up1ql jh n

SUp5ql jh nSOp10ql jh n

E6ÑSOp10q�Up1q

.


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?


Superstring Theories


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.


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


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


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


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


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.


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


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


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


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

Ñ�Q uc

ec

��dc

L

�� N

10�1 D � h � pD,D,H,Hq

Ñ�DH

��DH

�

12 S Ñ S


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.


THANK YOU !!!


YRM 2016 - JM ASHFAQUE

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