Supersymmetry and conformal theories on the lattice from N = 1 super - PowerPoint PPT Presentation

Supersymmetry and conformal theories on the lattice from N = 1 super Yang-Mills towards super QCD Georg Bergner FSU Jena, WWU M¨ unster East Lansing: July 27, 2018

SQCD UMWT SQCD Supersymmetric Yang-Mills theory and SQCD on the lattice 1 Mixed representation composite Higgs model 2 Supersymmetric QCD 3 in collaboration with S. Ali, H. Gerber, P. Giudice, S. Kuberski, C. Lopez, G. M¨ unster, I. Montvay, S. Piemonte, P. Scior (DESY-M¨ unster-Regensburg-Jena) 2/17

SQCD UMWT SQCD Why study SUSY on the lattice? 1 BSM physics: Supersymmetric particle physics requires breaking terms based on an unknown non-perturbative mechanism. ⇒ need to understand non-perturbative SUSY 2 Supersymmetry is a general beautiful theoretical concept: (Extended) SUSY simplifies theoretical analysis and leads to new non-perturbative approaches. ⇒ need to bridge the gap between “beauty” and 3/17

SQCD UMWT SQCD Why study (near) conformal theories on the lattice? 1 BSM physics: Composite Higgs / walking Technicolour scenarios, walking behaviour allows large scale separation with light scalar bound state 2 Theoretical questions: What is the conformal window? What non-QCD-like behaviour of a strongly interacting theory is possible? What is the effective field theory description for a walking theory? 4/17

SQCD UMWT SQCD N = 1 super Yang-Mills theory Supersymmetric Yang-Mills theory: L = 1 4 F µν F µν + 1 ¯ λ ( / D + m g ) λ 2 supersymmetric counterpart of Yang-Mills theory; but in several respects similar to QCD λ Majorana fermion in the adjoint representation SUSY transformations: δ A µ = − 2 i ¯ λγ µ ε , δλ = − σ µν F µν ε 5/17

SQCD UMWT SQCD What has been investigated so far: SU(2) and SU(3): SUSY Ward-identities and particle spectrum ⇒ Talk by H. Gerber Indications for SUSY continuum limit and multiplet formation in SU(2) and SU(3) SYM. finite temperature SU(2) SYM ⇒ SU(3) SYM: talk by C.Lopez compacitfied SYM: Witten index and absence of any deconfinement transition (continuity) ⇒ nearly concluded studies of SYM for SU(2) and SU(3) 6/17

SQCD UMWT SQCD Conformal window: adjoint QCD with different N f near conformal behaviour with a constant mass ratios for N f > 1 / 2 range of N f completed with N f = 3 / 2 (Talk by P. Scior) γ ∗ small β γ ∗ larger β Theory scalar particle N f = 1 / 2 SYM part of multiplet – – N f = 1 adj QCD light 0.92(1) 0 . 75(4) ∗ N f = 3 / 2 adj QCD light 0 . 50(5) ∗ 0 . 38(2) ∗ N f = 2 adj QCD light 0.376(3) 0.274(10) ( ∗ preliminary) ⇒ Near conformal lattice data for a range of theories starting at smaller N f than expected from perturbative analysis. 7/17

SQCD UMWT SQCD Going beyond N = 1 SYM: SQCD add N c ⊕ ¯ N c chiral matter superfield SYM + quarks ψ and squarks Φ i with covariant derivatives, mass terms and √ λ a � � 2 g ¯ Φ † 1 T a P + + Φ 2 T a P − ψ i √ � � 2 g ¯ P − T a Φ 1 + P + T a Φ † λ a − i ψ 2 g 2 � 2 � Φ † 1 T a Φ 1 − Φ † 2 T a Φ 2 . 2 8/17

SQCD UMWT SQCD Why we consider SQCD natural extension of supersymmetric Yang-Mills theory relation to possible extensions of the standard model earlier studies of lattice formulation: perturbative [Costa, Panagopoulos], tuning [Giedt, Veneziano] SQCD analysis of Seiberg et al.: N f < N c No vacuum N f = N c confinement and chiral symmetry breaking 3 2 N c < N f < 3 N c infrared fixed point (duality) Like other SUSY theories beyond N = 1 SYM: conformal or near conformal behaviour 9/17

SQCD UMWT SQCD Why we should better not consider SQCD large space of tuning parameters [Giedt] ( O (10) parameters) just test the mismatch might need formulation with Ginsparg-Wilson fermions still test it with Wilson fermions complex Pfaffian related to bosonic symmetry transforming Pf → Pf ∗ not well behaved chiral limit: either near conformal test near conformal scenario in a related theory or unstable vacuum test with N f = 1 SQCD 10/17

SQCD UMWT SQCD Why we should better not consider SQCD large space of tuning parameters [Giedt] ( O (10) parameters) just test the mismatch might need formulation with Ginsparg-Wilson fermions still test it with Wilson fermions complex Pfaffian related to bosonic symmetry transforming Pf → Pf ∗ not well behaved chiral limit: either near conformal test near conformal scenario in a related theory or unstable vacuum test with N f = 1 SQCD 10/17

SQCD UMWT SQCD Ultra Minimal Walking Technicolour suggested composite Higgs model [Ryttov,Sannino]: N f = 1 in adjoint + N f = 2 in fundamental representation of SU(2) lattice studies indicate near conformal behaviour at lower N f for the adjoint representation N f = 1 / 2 adjoint + N f = 2 in fundamental expectations: close to conformal, but still walking ideal candidate for a check of effective theories SQCD without scalars 11/17

SQCD UMWT SQCD Cross check in pure N f = 2 SU(2) fundamental theory 3 . 5 reference 3 2 . 5 w 0 m v 2 1 . 5 1 0 . 5 0 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 ( am 2 π ) reasonable agreement with recent (continuum extrapolated) results [Arthur,Drach,Hansen,Hietanen,Pica,Sannino] larger β to avoid possible bulk transition (SU(2) N f = 1 adjoint) 12/17

SQCD UMWT SQCD First investigations in mixed representation setup: tuning 0 . 7 fund adj 0 . 6 0 . 5 m 2 π 0 . 4 0 . 3 0 . 2 0 . 1 6 . 16 6 . 18 6 . 2 6 . 22 6 . 24 6 . 26 6 . 28 6 . 3 6 . 32 6 . 34 1 /κ adj one-loop improved Wilson clover fermions: tuning of fundamental and adjoint not independent 13/17

SQCD UMWT SQCD First investigations in mixed representation setup 1 . 9 κ a = 0 κ a = 0 . 1600 1 . 8 κ a = 0 . 1620 1 . 7 1 . 6 1 . 5 m v /m π 1 . 4 1 . 3 1 . 2 1 . 1 1 0 . 9 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 0 . 9 am π adjoint flavour drives theory towards near conformal behaviour 14/17

SQCD UMWT SQCD N f = 1 SU(2) SQCD vacuum 20 18 16 14 12 Φ d ag Φ 10 8 6 4 2 0 20 40 60 80 100 120 140 160 180 HMC the expected instability when going chiral 15/17

SQCD UMWT SQCD N f = 1 SU(2) SQCD vacuum 0 . 2 0 . 18 0 . 16 0 . 14 0 . 12 κ fund 0 . 1 0 . 08 0 . 06 0 . 04 0 . 02 0 0 0 . 02 0 . 04 0 . 06 0 . 08 0 . 1 0 . 12 0 . 14 0 . 16 0 . 18 0 . 2 κ adj constraint phase diagram for the parameter tuning simulations with an O ( g 0 ) SUSY action 16/17

SQCD UMWT SQCD Conclusions SYM finished, new challenge theories with scalars like SQCD challenging tuning problem other challenges: conformal behaviour, vacuum structure two approaches for our investigations: study of related mixed representation theory simulations of N f = 1 SQCD and search for non-perturbative tuning conditions Requires analysis in a regime where SUSY is restored in SYM (at least 24 3 × 48 lattice with unimproved action) 17/17