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 OnogiRef.) arXiv:1111.2180 [hep-lat] talk given by S.-W.Kim at LAT2011

Plan of the talk

1. Introduction2. N=1 super Yang-Mills theory3. Results4. Summary

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)

supersymmetric QCD (or SQCD)

gluon gluino (adjoint Majorana fermion)

quark squark (fundamental, scalar boson)

QCD

gluon (adjoint , vector boson)

quark (fundamental, Dirac fermion)

N=1 SUSY

superpartners

SUSY algebra includes translational symmetry

broken by the lattice regularization

SUSY on the lattice

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.)

And so is SUSY !

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 symmetryby using overlap fermion

no fine-tuning

4d N=1 super Yang-Mills theory

SUSY tr.

•Witten index is nonzero

• (anomalous)

•Gluino condensate

Known facts about 4d N=1 SYM

SSB of

SUSY is NOT spontaneously broken

Rem.) no Nambu-Goldstone bosons !

may trigger SSB of SUSY in extended models with matters.

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.

(Curci-Veneziano ’87)perturbative studies with Wilson fermions

Previous studies

The crucial problem : chiral extrapolation difficult to do reliably

We use the overlap fermion for gluino, for the first time !

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

free from UV divergence

(DeGrand-Schaefer ’05, Fukaya et al. (JLQCD) ’07)

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

Low-lying spectrum of Dirac op.

non-zerogluino condensatesuggested

m = 0:2

(there are finite V effects, though)

A trick to get rid of finite V effects

•Chiral Random Matrix Theory (Verbaarschot ’94)

Universal description ofthe 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)

Lowest eigenvalue distribution in RMT

written in terms of dimensionless parameters

(Damgaard-Nishigaki ’01)

eigenvalue

Lowest eigenvalue distribution

Results for gluino condensate

Sommer scale

•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

Summary

•Comparison with previous DWF study (Giedt ’09)