Twisted lattice supersymmetry and applications to AdS/CFT

Abstract

I review recent approaches to constructing supersymmetric lattice theories focusing in particular on the concept of topological twisting. The latter technique is shown to expose a nilpotent, scalar supersymmetry which can be implemented exactly in the lattice theory. Using these ideas a lattice action for $\mathcal{N}=4$ super Yang-Mills in four dimensions can be written down which is gauge invariant, free of fermion doublers and respects one out of a total of 16 continuum supersymmetries. It is shown how these exact symmetries together with the large point group symmetry of the lattice strongly constrain the possible counterterms needed to renormalize the theory and hence determine how much residual fine tuning will be needed to restore all supersymmetries in the continuum limit. We report on progress to study these renormalization effects at one loop. We go on to give examples of applications of these supersymmetric lattice theories to explore the connections between gauge theories and gravity.

16 pages. Plenary talk at Lattice 2010

References in corpus (13)

• Monte Carlo studies of supersymmetric matrix quantum mechanics with sixteen supercharges at finite temperature
• Black hole thermodynamics from simulations of lattice Yang-Mills theory
• Higher derivative corrections to black hole thermodynamics from supersymmetric matrix quantum mechanics
• Schwarzschild radius from Monte Carlo calculation of the Wilson loop in supersymmetric matrix quantum mechanics
• Exact Extended Supersymmetry on a Lattice: Twisted N=4 Super Yang-Mills in Three Dimensions
• Thermal phases of D1-branes on a circle from lattice super Yang-Mills
• Lattice super-Yang-Mills using domain wall fermions in the chiral limit
• Simulation of 4d N=1 supersymmetric Yang-Mills theory with Symanzik improved gauge action and stout smearing
• Dynamical simulation of N=1 supersymmetric Yang-Mills theory with domain wall fermions
• Absence of sign problem in two-dimensional N=(2,2) super Yang-Mills on lattice
• A proposal of a fine tuning free formulation of 4d N=4 super Yang-Mills
• Lattice formulation of 2D $\mathcal{N}=(2,2)$ SQCD based on the B model twist
• Species Doublers as Super Multiplets in Lattice Supersymmetry: Exact Supersymmetry with Interactions for D=1 N=2

Cited by in corpus (3)

• Supersymmetric quantum mechanics on the lattice: I. Loop formulation
• Exact results for supersymmetric quantum mechanics on the lattice
• Lattice Gauge Theories at the Energy Frontier