1. Lattice calculation of the gluino condensate in N=1 super Yang-Mills theory with overlap fermions
Jun Nishimura (KEK, SOKENDAI)
JLQCD Collaboration:
with Sang-Woo Kim, Hidenori Fukaya,
Shoji Hashimoto, Hideo Matsufuru, Tetsuya Onogi
Ref.) arXiv: [hep-lat] talk given by S.-W.Kim at LAT2011

2. Plan of the talk Introduction N=1 super Yang-Mills theory Results
Summary

3. 1. Introduction

4. Motivation for N=1 SUSY
Low energy effective theories of superstring theory that are phenomenologically viable
A natural solution to hierarchy problem is available if SUSY breaking occurs at O(TeV)
Natural candidates for the dark matter, Better unification of 3 forces at the GUT scale,…
(model dependent, though)

5. gluon (adjoint , vector boson)
QCD
gluon (adjoint , vector boson)
quark (fundamental, Dirac fermion)
N=1 SUSY
supersymmetric QCD (or SQCD)
superpartners
gluon gluino (adjoint Majorana fermion)
quark squark (fundamental, scalar boson)

6. SUSY on the lattice SUSY algebra includes translational symmetry
broken by the lattice regularization
And so is SUSY !
Restore SUSY in the continuum limit
by fine-tuning parameters in the lattice action
(# of param. to be fine-tuned)
= (# of SUSY breaking relevant ops.)

7. Developments in “lattice SUSY”
lattice actions with various symmetries,
which prohibit SUSY breaking relevant ops.
e.g.) preserving 1 supercharge using topological twist
# of parameters to be fine-tuned can be reduced
non-lattice simulations of SYM with 16 supercharges
1d gauge theory (gauge-fixed, momentum space sim.)
extension to higher dimensions
using the idea of large N reduction
In this work, we preserve chiral symmetry
by using overlap fermion
no fine-tuning

8. 2. N=1 super Yang-Mills theory

9. 4d N=1 super Yang-Mills theory
SUSY tr.

10. Known facts about 4d N=1 SYM
Witten index is nonzero
(anomalous)
Gluino condensate
SUSY is NOT spontaneously broken
SSB of
Rem.) no Nambu-Goldstone bosons !
may trigger SSB of SUSY in extended models with matters.

11. 4d N=1 SYM on the lattice SUSY can be restored in the continuum limit
by fine-tuning parameters in the lattice action
# of param. to be fine-tuned
= # of SUSY breaking relevant operators
In the case of 4d N=1 SYM,
the only SUSY breaking relevant operator
is the gluino mass term, which can be prohibited
by imposing chiral symmetry.
perturbative studies with Wilson fermions
(Curci-Veneziano ’87)

12. Previous studies The crucial problem : chiral extrapolation
difficult to do reliably
We use the overlap fermion for gluino,
for the first time !

13. 3. Results

14. How to calculate gluino condensate
The naïve defintion
Following previous works in QCD,
we use Banks-Casher relation (’80)
suffers from UV divergence,
which should be subtracted appropriately
(DeGrand-Schaefer ’05, Fukaya et al. (JLQCD) ’07)
free from UV divergence

15. Numerical setup Iwasaki gauge action with SU(2) gauge group
Restricted to zero topological charge sector
28 low-modes of Dirac op.
obtained by Lanczos method
BlueGene/L at KEK and SR16000 at YITP
Sommer scale

16. Low-lying spectrum of Dirac op.
non-zero
gluino condensate
suggested
(there are finite V effects, though)

17. A trick to get rid of finite V effects
Chiral Random Matrix Theory (Verbaarschot ’94)
Universal description of
the low-lying eigenvalue distribution of the Dirac op.
at finite V and m
corresponding to the symmetry of Dirac op. for adjoint fermions
chGSE (chiral Gaussian Symplectic Ensemble)

18. Lowest eigenvalue distribution in RMT
(Damgaard-Nishigaki ’01)
written in terms of dimensionless parameters
eigenvalue

19. Lowest eigenvalue distribution

20. Results for gluino condensate
Sommer scale

21. 4. Summary

22. Summary Lattice calculation of the gluino condensate overlap fermion
killed the problems of
chiral extrapolation
Banks-Casher rel.
killed the UV div.
RMT-based analysis
killed finite V effects
Comparison with
previous DWF study
(Giedt ’09)