Higgsless gauge symmetry breaking with a large mass hierarchy

1
Higgsless gauge symmetry breaking with a large
mass hierarchy
Tomoaki Nagasawa (Kobe Univ.)
Prog. Theor. Phys. 112(2004)629, hep-ph/0406024
with M. Sakamoto (Kobe Univ.)
Key Words
Higher dimensional gauge theory
A large mass hierarchy
Supersymmetry (in QM)
Non-trivial bounray consitions
2
?Introduction
Our aim is to get the following hierarchical
mass spectrum
Heavy KK modes
scale of extra dimensions
or
massless modes can be obtained by gaugy sym.
chiral sym. susy, etc
The problem is how to get hierarchical small
masses without a fine tuning
3
?A toy model
( )
gauge invariant theory with a weight function
The weight function comes from
metric ansatz
We take
a dilaton background
as a concrete
4
?Mode expansion
expansion by complete sets
questions?
Which complete sets?
BCs
Criterion for allowed BCs?
Consistent with gauge theory?
5
?Mode expansion2
How to expand of
?
diagonalization of 4d mass terms of
How to expand of
?
5d gauge transf.
6
?Supersymmetry
Supersymmetry is always hidden in higher
dimensional gauge theory
C.S. Lim, T. Nagasawa, M. Sakamoto, H. Sonoda,
hep-th/0502022
SUSY structure
E. Witten, NPB188(1981)513
BCs
We cannot specify independent BCs for

7
?Boundary conditions (BCs)
We require the boundary conditions to preserve
the supersymmetry
There are only two types of BCs at each boundary
very restrictive!
T. Nagasawa, M. Sakamoto, K. Takenaga, PLB562(2003
)358, PLB583(2004)357
N Type

at
D Type

4 type BCs sets
(N,N)
(D,N)
(N,D)
(D,D)
4 types spectrums
y0 L
0 L
0 L
0 L
8
?KK spectrum
(D,N)
(N,D)
(N,N)
(D,D)
y0 L
0 L
0 L
0 L
9
?SUSY point of view
SUSY ensures the degeneracy between

for
10
?SUSY point of view
SUSY ensures that the vacuum state is massless
11
?SUSY point of view
Massless modes are special in SUSY, because they
do not form a supermultiplet
12
?SUSY point of view
If susy is broken, vacuum state has non zero mass
Broken SUSY
13
?SUSY point of view
If susy is broken, vacuum state has non zero mass
typical scale GUT scale or Planck
scale
SUSY is broken
at
weight
Broken SUSY
14
?SUSY point of view
If susy is broken, vacuum state has non zero mass
SUSY is broken
We get a hierarchical small mass without a fine
tuning
at
weight
Broken SUSY
15
Realistic model
Localized at boundary
16
?Summary
We get hierarchical mass spectrum without a fine
tuning
A weight function
Supersymmetry
Key points
Non-trivial bounday conditions
?Outlook
A hierarchy problem
(quadratic divergence problem)
(There are two scenarios)
supersymmetry
Solution to the problem
close relation?
higher dimensional gauge theory