This webpage calculates the fluxes and Higgs vevs felt by the different matter representations around a point of E8 enhancement in a local F-theory model. It also outputs the induced local chirality by the flux assuming that the wavefunctions are sufficiently localised for this to be trustable in a local patch. It is associated to a publication ArXiv:1202.xxxx to which we refer for conventions.

U(1)_1U(1)_2U(1)_3U(1)_4U(1)_5U(1)_YTraceless?


m1 +i +i +i +i +i
m2 +i +i +i +i +i
M11 +i +i +i +i +i +i
M12 +i +i +i +i +i +i
M21 +i +i +i +i +i +i
M22 -M11 +i -M11 +i -M11 +i -M11 +i -M11 +i -M11 +i

The local chirality induced on the point of E8:

Curve (3,2)1/6 (3,1)-2/3 (1,1)1 (3,1)-1/3 (1,2)1/2
t1
t2
t3
t4
t5
-t1-t2
-t1-t3
-t1-t4
-t1-t5
-t2-t3
-t2-t4
-t2-t5
-t3-t4
-t3-t5
-t4-t5
Singlet Curve(1,1)0
t1-t2
t1-t3
t1-t4
t1-t5
t2-t3
t2-t4
t2-t5
t3-t4
t3-t5
t4-t5

Click on cell to view induced Higgs and Flux for that representation:

m1
m2
M11
M12
M21
M22

These can be used in the associated Mathematica worksheet to calculate the wavefunction overlaps.