The infrared regime of SU(2) with one adjoint Dirac Fermion Ed Bennett with Andreas Athenodorou, Georg Bergner, and Biagio Lucini
Outline Introduction Motivation and background Chiral symmetry breaking Aims and predictions Results Phase diagram Spectrum Mass anomalous dimension Conclusions and outlook
Motivation window • Can we pin down the end of the conformal window? • Look at SU 1 adjoint Dirac flavour • SU (2)+ 2 adjoint Dirac flavours known to be in the conformal
Motivation window • Can we pin down the end of the conformal window? • Look at SU 1 adjoint Dirac flavour • SU (2)+ 2 adjoint Dirac flavours known to be in the conformal
Motivation window • Can we pin down the end of the conformal window? • SU (2)+ 2 adjoint Dirac flavours known to be in the conformal • Look at SU (2)+ 1 adjoint Dirac flavour
Analytic prediction Model is widely predicted to be confining. Why? • Large- N volume reduction: 1 adjoint flavour is confining – IR behaviour unclear – N dependence uncertain • SYM is confining; take large scalar mass limit – But confinement requires SUSY, which requires massless scalars. – Fate of confinement when SUSY is broken is unclear Strong assertions of confinement are not justified.
Analytic prediction Model is widely predicted to be confining. Why? • Large- N volume reduction: 1 adjoint flavour is confining – IR behaviour unclear – N dependence uncertain • SYM is confining; take large scalar mass limit – But confinement requires SUSY, which requires massless scalars. – Fate of confinement when SUSY is broken is unclear Strong assertions of confinement are not justified.
Analytic prediction Model is widely predicted to be confining. Why? • Large- N volume reduction: 1 adjoint flavour is confining – IR behaviour unclear – N dependence uncertain • SYM is confining; take large scalar mass limit – But confinement requires SUSY, which requires massless scalars. – Fate of confinement when SUSY is broken is unclear Strong assertions of confinement are not justified.
Analytic prediction Model is widely predicted to be confining. Why? • Large- N volume reduction: 1 adjoint flavour is confining – IR behaviour unclear – N dependence uncertain – But confinement requires SUSY, which requires massless scalars. – Fate of confinement when SUSY is broken is unclear Strong assertions of confinement are not justified. • N = 2 SYM is confining; take large scalar mass limit
Analytic prediction Model is widely predicted to be confining. Why? • Large- N volume reduction: 1 adjoint flavour is confining – IR behaviour unclear – N dependence uncertain – But confinement requires SUSY, which requires massless scalars. – Fate of confinement when SUSY is broken is unclear Strong assertions of confinement are not justified. • N = 2 SYM is confining; take large scalar mass limit
Analytic prediction Model is widely predicted to be confining. Why? • Large- N volume reduction: 1 adjoint flavour is confining – IR behaviour unclear – N dependence uncertain – But confinement requires SUSY, which requires massless scalars. – Fate of confinement when SUSY is broken is unclear Strong assertions of confinement are not justified. • N = 2 SYM is confining; take large scalar mass limit
Analytic prediction Model is widely predicted to be confining. Why? • Large- N volume reduction: 1 adjoint flavour is confining – IR behaviour unclear – N dependence uncertain – But confinement requires SUSY, which requires massless scalars. – Fate of confinement when SUSY is broken is unclear Strong assertions of confinement are not justified. • N = 2 SYM is confining; take large scalar mass limit
Chiral symmetry breaking • One flavour—surely no chiral structure? • 1 Dirac flavour = 2 Majorana/Weyl d.o.f. • SU(2) symmetry between two chiral flavours • Breaks to SO(2): 2 Goldstones • Insufficient for EWSB; not a WT candidate
Chiral symmetry breaking • One flavour—surely no chiral structure? • 1 Dirac flavour = 2 Majorana/Weyl d.o.f. • SU(2) symmetry between two chiral flavours • Breaks to SO(2): 2 Goldstones • Insufficient for EWSB; not a WT candidate
Chiral symmetry breaking • One flavour—surely no chiral structure? • 1 Dirac flavour = 2 Majorana/Weyl d.o.f. • SU(2) symmetry between two chiral flavours • Breaks to SO(2): 2 Goldstones • Insufficient for EWSB; not a WT candidate
Chiral symmetry breaking • One flavour—surely no chiral structure? • 1 Dirac flavour = 2 Majorana/Weyl d.o.f. • SU(2) symmetry between two chiral flavours • Breaks to SO(2): 2 Goldstones • Insufficient for EWSB; not a WT candidate
Chiral symmetry breaking • One flavour—surely no chiral structure? • 1 Dirac flavour = 2 Majorana/Weyl d.o.f. • SU(2) symmetry between two chiral flavours • Breaks to SO(2): 2 Goldstones • Insufficient for EWSB; not a WT candidate
Aims • First-principles confirmation of IR conformality/confinement • Spectroscopy • Anomalous dimension • Topological charge, susceptibility • Static potential
Aims • First-principles confirmation of IR conformality/confinement • Spectroscopy • Anomalous dimension • Topological charge, susceptibility • Static potential
Aims • First-principles confirmation of IR conformality/confinement • Spectroscopy • Anomalous dimension • Topological charge, susceptibility • Static potential
Aims • First-principles confirmation of IR conformality/confinement • Spectroscopy • Anomalous dimension • Topological charge, susceptibility • Static potential
Aims • First-principles confirmation of IR conformality/confinement • Spectroscopy • Anomalous dimension • Topological charge, susceptibility • Static potential
– Ratios of spectral quantities in this regime constant . Predictions • Conformal: Locking at scale m lock : – m PCAC m lock m state m . • Near-conformal: Intermediary conformal-like region, IR confining region – Not clearly identifiable, for limited range of masses • Confinement: m PS → 0 , m V ̸→ 0 as m PCAC → 0 .
– Ratios of spectral quantities in this regime constant . Predictions • Conformal: Locking at scale m lock : – m PCAC m lock m state m . • Near-conformal: Intermediary conformal-like region, IR confining region – Not clearly identifiable, for limited range of masses • Confinement: m PS → 0 , m V ̸→ 0 as m PCAC → 0 .
– Ratios of spectral quantities in this regime constant . Predictions • Conformal: Locking at scale m lock : • Near-conformal: Intermediary conformal-like region, IR confining region – Not clearly identifiable, for limited range of masses • Confinement: m PS → 0 , m V ̸→ 0 as m PCAC → 0 . – m PCAC < m lock ⇒ m state ∼ m 1/(1+ γ ∗ ) → 0 .
Predictions • Conformal: Locking at scale m lock : • Near-conformal: Intermediary conformal-like region, IR confining region – Not clearly identifiable, for limited range of masses • Confinement: m PS → 0 , m V ̸→ 0 as m PCAC → 0 . – m PCAC < m lock ⇒ m state ∼ m 1/(1+ γ ∗ ) → 0 . – Ratios of spectral quantities in this regime constant .
Predictions • Conformal: Locking at scale m lock : • Near-conformal: Intermediary conformal-like region, IR confining region – Not clearly identifiable, for limited range of masses • Confinement: m PS → 0 , m V ̸→ 0 as m PCAC → 0 . – m PCAC < m lock ⇒ m state ∼ m 1/(1+ γ ∗ ) → 0 . – Ratios of spectral quantities in this regime constant .
Predictions • Conformal: Locking at scale m lock : • Near-conformal: Intermediary conformal-like region, IR confining region – Not clearly identifiable, for limited range of masses • Confinement: m PS → 0 , m V ̸→ 0 as m PCAC → 0 . – m PCAC < m lock ⇒ m state ∼ m 1/(1+ γ ∗ ) → 0 . – Ratios of spectral quantities in this regime constant .
Lattice results Spin- • Center unbroken torelon • Wilson loop • Spectral ratios roughly constant—consistent with conformality L , L L • V Anomalous dimension (mode number) gluion-glue) state mass ( Mesonic spectoscopy Gluonic spectroscopy (glueballs and torelon mass) only: – Topological charge Static potential Baryon spectroscopy, : and – • Full set of simulations at two values of • Good sampling of topological sectors • Phase diagram: plaquette on 4 4 lattice; 1 . 4 ≤ β ≤ 2 . 8 , − 1 . 7 ≤ am ≤ − 0 . 1
Phase diagram 0.75 1.4 1.5 0.7 1.6 1.7 1.8 0.65 1.85 1.9 0.6 1.95 Plaquette 2.0 0.55 2.05 2.1 2.15 0.5 2.2 2.3 0.45 2.4 2.5 0.4 2.6 2.7 2.8 0.35 -1.6 -1.4 -1.2 -1 -0.8 -0.6 -0.4 -0.2 a m
Lattice results Spin- • Center unbroken torelon • Wilson loop • Spectral ratios roughly constant—consistent with conformality L , L L • V Anomalous dimension (mode number) gluion-glue) state mass ( Mesonic spectoscopy Gluonic spectroscopy (glueballs and torelon mass) only: – Topological charge Static potential Baryon spectroscopy, : and – • Good sampling of topological sectors • Phase diagram: plaquette on 4 4 lattice; 1 . 4 ≤ β ≤ 2 . 8 , − 1 . 7 ≤ am ≤ − 0 . 1 • Full set of simulations at two values of β
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