Lattice calculation of the gluino condensate in N=1 super Yang-Mills theory with overlap fermions

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:1111.2180 [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. 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 SUSY is NOT spontaneously broken • Witten index is nonzero • (anomalous) • Gluino condensate 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)