Lattice field theory beyond QCD Liam Keegan November 2013 CERN - - PowerPoint PPT Presentation

Lattice field theory beyond QCD

Liam Keegan November 2013 CERN Theory Group Retreat, Les Houches.

Introduction

Fundamental Antisymmetric Symmetric Adjoint

MWTC

[arXiv:hep-ph/0611341]

I Perturbative phase

diagram of SU(N) gauge theories with Nf fermions

I Shaded region shows

conformal window

I Can be very different

to QCD

RG flows in mass-deformed CFT

m g IRFP UVFP

I Flow from UV to IR I Finite mass drives us away

from FP in the IR

I Interested in intermediate

blue region

I 1 L ⌧ m ⌧ blue ⌧ 1 a

Large N Twisted Volume Reduction

Lattice field theory:

I ˆ

L4 points, lattice spacing a

I Physical volume

L4 = (ˆ La)4

I UV cut–off: 1/a I IR cut–off: 1/L

Twisted reduction: ˆ L ! p N

I Single site lattice, lattice

spacing a

I Physical volume

L4 = ( p Na)4

I UV cut–off: 1/a I IR cut–off: 1/

p N

Mass Anomalous Dimension at IRFP γ⇤

0.2 0.4 0.6 0.8 1 0.1 0.2 0.3 0.4 0.5 γ (aΩIR)2 γ vs (aΩIR)2, N=289,b=0.35,0.36,κ=0.16 N=289, b=0.35 N=289, b=0.36 SU(2) Patella [1204.4432]

[Margarita Garc´ ıa Per´ ez, Antonio Gonz´ alez-Arroyo, Masanori Okawa]

I SU(N) + 2 adjoint

Dirac fermions

I γ∗ determined from

fit to the Dirac mode number

I data points:

SU(N) with N=289 (single site)

I dotted line:

SU(2) (324 lattice) [Patella 1204.4432]