Gaugino condensation: 32,768 CPUs weigh inJoel Giedt

Physics, Applied Physics & AstronomyRensselaer Polytechnic Institute

JLab0901 – p.1/28

Outline

� SU(2) lattice gauge theory.� Chiral fermions (DWF) in adjoint

representation.� N = 1 super-Yang-Mills (pure super-glue).� Large-scale simulations on the Rensselaer

supercomputing facility (CCNI).

Tech trinity

JLab0901 – p.2/28

SUSY promo

Weak scale SUSY has a lot going for it:gauge coupl unif. / hierarchy prob. / CDMcandidate / logical spacetime symm. extension /flat dir.’s –> baryogensis / perturb. calculable TeVphysics. / natural consequence of string/M th. /custodial SU(2) / severely constrained by rareprocesses / elegant renormalization / light higgs

JLab0901 – p.3/28

Rubber meets the road

� Of course it has drawbacks too. SUSY has tobe broken somehow.

� This is encoded in the “soft Lagrangian”,introducing a vast parameter space, withgeneric points absolutely forbidden [EDM’s,FCNC’s].

� The search, for many years, has been formechanisms of SUSY-breaking that“naturally” lead to a “nice” soft Lagrangian.

� (This is getting progressively harder asexperiments nibble away at parameter spacein simpler scenarios.)

JLab0901 – p.4/28

Strong supersymmetric theories

� The models for SUSY breaking generallyinvolve nonperturbative behavior ofsupersymmetric gauge theories.

� Thus, to thoroughly study the relevantnonperturbative features ⇒ study strongSUSY.

� Obvious tool to include: LFT

JLab0901 – p.5/28

Lattice SUSY

� However, lattice SUSY has problems.� Lattice breaks SUSY: discretization errors.� Divergences in quantum field theories ⇒

errors can be dangerously amplified:

ε ×∞ = ∞. (1)

� For example:

QS = a2OS, 〈OSOX〉 = O(1/a2) (2)

⇒ O(ln a) violation of SUSY.

JLab0901 – p.6/28

Various tacks

� For a few years now, I have studied ways thatexact lattice symmetries might be used toovercome this problem, with manyencouraging results.

� We are making steady progress towardfull-scale simulation of realistic models.

� Today I’ll tell you about a supersymmetricmodel that we can study w/o fear, due tolattice chiral symmetries.

� Some emerging results of very-large-scalesimulations will be presented.

JLab0901 – p.7/28

N = 1 4d SYM w/ chiral fermions

� From [Curci, Veneziano 86] we know thatN = 1 4d SYM with Ginsparg-Wilsonfermions require no counterterms.

� Overlap-Dirac was proposed [Narayanan,Neuberger 95] and sketched [Maru,Nishimura 97].

� But LO simulation studies, such as glueballspectra, have yet to be attempted.

JLab0901 – p.8/28

N = 1 4d SYM w/ chiral fermions

Another type of GW fermion is:� Domain Wall Fermions (DWF) [Kaplan 92] +

improvements [Shamir 93].� Proposed for LSYM [Nishimura 97]

[Neuberger 98] [Kaplan, Schmaltz 99]� Briefly studied [Fleming, Kogut, Vranas 00].

L R

Ls

JLab0901 – p.9/28

Gluino condensation

� They studied the condensate vs. Ls

� NB: all the good ideas for spontaneousSUSY-breaking (that I know of) involve gluinocondensation:

〈λ̄λ〉 6= 0 (3)

JLab0901 – p.10/28

Gluino condensation

Essentially, 4 types of evidence from continuumtechniques:1. VY/chiral ring

[Veneziano, Yankielowicz 82;Cachazo, Douglas, Seiberg, Witten 02]

2. strong instanton (discredited)[Novikov, Shifman, Vainshtein, Zakharov 83; Rossi,Veneziano 84]

3. weak instanton[Affleck, Dine, Seiberg 83]

4. R3 × S1 [Davies, Hollowood, Khoze, Mattis 99]

JLab0901 – p.11/28

A 5th pathway?

The above approaches are rather indirect.� Lattice: direct, brute force.� Simulate at various a, extrapolate to

continuum.� Extrapolation to chiral limit mλ = 0.� Nonperturbative renormalization.

Besides, finding the linear regime

〈λ̄λ〉 ∼ mres (4)

tells us where to study SUSY dynamics.

JLab0901 – p.12/28

Chiral critical point

� Anomaly, no pions (good! bad!). Z2Nc

remains.� mλ = 0, spontaneous breaking of Z2Nc

symmetry occurs.� Nc vacua: theory picks one.� Old-fashioned lattice fermions (Wilson) broke

this symmetry to avoid fermion doublers.� Due to additive renormalization

mλ,R =√

Zmλ,0 − δmλ (5)

it was impossible to say a priori wheremλ,R = 0 really was.

JLab0901 – p.13/28

Wilson fermion approach

� Perturbation theory won’t tell us√

Z, δmλ.� The old simulations (Munster-DESY-Roma)

tried various masses mλ,0.� Very costly (scan, renorm., op. mixing,

coding).� Did not generate enough data to do a → 0

extrapolations. Only 1 lattice spacing.� Also: sign problem/exceptional configs. near

critical point.

JLab0901 – p.14/28

First foray into 5th dimension

� The old DWF simulations [Fleming, Kogut,Vranas 00] avoided fine-tuning. But sim.’scostly ==> small lattices.

� Did not generate enough data to do a → 0extrapolations. Only 1 lattice spacing.

� Small lattice ==> far from continuum. SUSY?

L R

Ls

JLab0901 – p.15/28

DWF-LSYM @ CCNI

� With collab.’s: Rich Brower (Boston U), SimonCatterall (Syracuse U), George Fleming (YaleU), Pavlos Vranas (LLNL).

� DWF simulations using� excellent modern code (CPS) and� one of the world’s fastest computers

(CCNI).

L R

Ls

JLab0901 – p.16/28

A marriage made in heaven: CPS + CCNI

SciDAC Layers and CCNI BlueGene/L’ssoftware module arch.

( USQCD, esp. ( RPI, NYS, IBM )Columbia’s CPS )

JLab0901 – p.17/28

DWF-LSYM @ CCNI

� Minor hack of CPS code: modify 15 files outof 1800. (CPS = 5MB of C++ code.)

� Currently using 1 to 2 racks: each 5.6 Tflop/s.9% efficiency ==> 0.75 Tflop/s actualcompute rate.

� We had hoped to nail the condensate,extrapolate to the continuum, within the year(2008).

� Turns out mres is kind of big (==>Mobius/Gap/DBW2/...topo. sampling...?).

JLab0901 – p.18/28

Early results & comparison

Ls 〈λ̄λ〉(here) 〈λ̄λ〉(FKV) notes16 0.00700(6) 0.00694(7)24 0.00507(8) 0.00516(6)48 0.003134(20) —∞ — 0.00432(22) method III∞ 0.0012(2) — method IV

Ls cases simulated for spacetime volume 84. Also shown:Ls → ∞ extrapolations of FKV (Ls = 12, 16, 20, 24).Take-away: very large Ls important to Ls → ∞extrapolation.

JLab0901 – p.19/28

Chiral limit

Figure 1: Condensate vs. mres.JLab0901 – p.20/28

Chiral limit, β = 2.3

Figure 2: Condensate vs. mres.JLab0901 – p.21/28

Chiral limit, β = 2.3

� It is moving around a lot when we drop theLs = 24 point.

� The mres is worrisome.� Need to suppress topology changing

dislocations.� Mobius tests well.� Could also use improved glue.� Problem: sampling topological sectors

adequately if we suppress the tunneling.

JLab0901 – p.22/28

Chiral limit, β = 2.4

Figure 3: Condensate vs. mres.JLab0901 – p.23/28

Chiral limit, β = 2.4

� The results stretch over factor 3 interval.� Chiral extrapolation looks robust. Much

smaller mres. (Slower simul.)� Noticeable finite size effects due to smaller a;

need systematic study.

JLab0901 – p.24/28

Running coupling

� Define β = 4/g2. Then 2-loop SUSY RGE’s==>

aΛSY M ∼(

3

2π2β

)−1/3

exp

(

−π2β

3

)

(6)

JLab0901 – p.25/28

Correct scaling

Creutz ratios for 163 × 32 × 16 lattice. The dashed lineindicates the 2-loop prediction for the dependence a2(β),obtained from (6). JLab0901 – p.26/28

LSYM Conclusions

� Will (eventually) obtain first evercontinuum/chiral extrapolation of 〈λ̄λ〉 forSYM.

� If we show 〈λ̄λ〉 nonzero (RI’ scheme), it willprovide strong evidence by the lattice method.

� Complimentary to VY & Cachazo et al.,Affleck-Dine-Seiberg, and the Hollowood etal. instanton results.

JLab0901 – p.27/28

LSYM Conclusions

� Benchmarks for DWF-LSYM simulation.

JLab0901 – p.28/28