Three-dimensional super-Yang--Mills theory on the lattice and dual black branes
This HDF5 file collects data and analysis results for non-perturbative lattice field theory calculations investigating three-dimensional maximally supersymmetric SU(N) Yang--Mills theory on a skewed euclidean torus, and its holographic connection to dual D2-brane solutions in supergravity.
Each group in the HDF5 file 3dSYM_data.h5 corresponds to a Markov chain (or 'ensemble') generated by the rational hybrid Monte Carlo (RHMC) algorithm and defined by the following features:
* The gauge group SU(N) with N=4, 6 or (mostly) 8
* The temporal extent of the lattice, Nt=8, 12 or 16
* The linear spatial extent of the lattice, L, where the spatial lattice size is L^2 --- currently L=Nt for all ensembles
* The dimensionless temporal extent of the lattice, rt
* The deformation parameter zeta
Each group has the following attributes:
* The dimensionless 'generalized' temperature t (determined by rt)
* The dimensionless lattice 't Hooft coupling lambda_lat (determined by rt and Nt)
* The two deformation parameters mu and kappa (determined by rt, Nt and zeta)
* The total number of RHMC trajectories
* The thermalization cut
* The block size
* The resulting total number of thermalized blocks used in jackknife analyses
* The overall acceptance rate
* The autocorrelation time of the (complexified) 'Maldacena' loop magnitude
* The autocorrelation times of the lowest fermion operator eigenvalue and of the violation of a Q-supersymmetry Ward identity involving a fermion bilinear, for reference
For each group, there are datasets containing the following information:
* The plaquette normalized by N, measured after every RHMC trajectory (which reveals whether the new configuration was accepted or rejected)
* The bosonic action density SB normalized by 9N^2/2, measured after every RHMC trajectory
* The link trace normalized by N, Tr[U.Ubar] / N, measured after every RHMC trajectory
* The exponential of the negative change in energy, exp(-Delta H), after each RHMC trajectory
* The real part, imaginary part and magnitude of the (complexified) Maldacena loop, measured after every RHMC trajectory
* The real part, imaginary part and magnitude of the (unitarized) Polyakov loop defined through polar decomposition, measured after every RHMC trajectory
* The magnitudes of the complexified Wilson lines in the two spatial directions, measured after every RHMC trajectory
* The magnitudes of the unitarized (polar-projected) Wilson lines in the two spatial directions, measured after every RHMC trajectory
* The violation of a Q-supersymmetry Ward identity involving a fermion bilinear, measured on every saved configuration
* The subset of trajectories after a configuration was saved for these measurements (typically every tenth RHMC trajectory)
* The minimum and maximum eigenvalues of the fermion operator, along with the log of the resulting condition number, measured on every saved configuration and compared with the spectral range of the RHMC rational approximation (which can change during thermalization but not after the thermalization cut)
* The phases of the N eigenvalues of the unitarized Wilson line in one spatial direction, measured on the saved configurations that follow the thermalization cut
The average plaquette, link trace, exp(-Delta H), and magnitudes of the Maldacena loop, Polyakov loop, complexified and unitarized Wilson lines are recorded as attributes of the corresponding dataset, along with the statistical uncertainty.
For reference, we also include a few python scripts used in the workflow:
* parse_SYM.py illustrates how the raw data are extracted from output files, to enable automated time-series plotting using the dygraphs library
* average_SYM.py illustrates how these time-series data are blocked and run through jackknife analyses to compute basic observables
* 3dQ16_package.py illustrates how this HDF5 file is compiled from the data and results set up by the scripts listed above