Parallel software for lattice N=4 supersymmetric Yang-Mills theory

We present new parallel software, SUSY LATTICE, for lattice studies of four-dimensional N=4N=4 supersymmetric Yang–Mills theory with gauge group SU(NN). The lattice action is constructed to exactly preserve a single supersymmetry charge at non-zero lattice spacing, up to additional potential terms included to stabilize numerical simulations. The software evolved from the MILC code for lattice QCD, and retains a similar large-scale framework despite the different target theory. Many routines are adapted from an existing serial code (Catterall and Joseph, 2012), which SUSY LATTICE  supersedes. This paper provides an overview of the new parallel software, summarizing the lattice system, describing the applications that are currently provided and explaining their basic workflow for non-experts in lattice gauge theory. We discuss the parallel performance of the code, and highlight some notable aspects of the documentation for those interested in contributing to its future development. Program summary Program title: SUSY LATTICE Catalogue identifier: AELS_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AELS_v2_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 72821 No. of bytes in distributed program, including test data, etc.: 1294754 Distribution format: tar.gz Programming language: C. Operating system: Any, tested on Linux workstations and MPI clusters with InfiniBand. Has the code been vectorized or parallelized?: Code is parallelized Classification: 11.5. Catalogue identifier of previous version: AELS_v1_0 Journal reference of previous version: Comput. Phys. Comm. 183 (2012) 1336. External routines: Lapack, Blas, Primme (optional) Does the new version supersede the previous version?: Yes Nature of problem: To carry out non-perturbative Monte Carlo importance sampling for maximally supersymmetric Yang–Mills theories in two and four dimensions, and thereby compute observables including Wilson loops, fermion bilinears, eigenvalues of D†DD†D and the Pfaffian of the sparse fermion operator DD. Solution method: The central application is a rational hybrid Monte Carlo algorithm with a two-level Omelyan molecular dynamics integrator. Gauge field configurations generated by this application may be saved to disk for subsequent measurements of additional observables. Input parameters for either configuration generation or analysis may be entered manually or read from a file. Reasons for new version: The code is parallelized to improve performance and scalability. In addition, several new features and measurements are provided. Summary of revisions: The program is completely rewritten on the basis of the MILC code for lattice QCD, and several new features and measurements are added. Restrictions: The code is currently restricted to two-dimensional N=(2,2)N=(2,2) and four-dimensional N=4N=4 supersymmetric Yang–Mills theories. The process of topological twisting on which it is based can also be applied to a few other systems, as discussed in Sections  1 ;  5. Additional comments: Further documentation is provided in the distribution file, including a set of test runs with reference output in the testsuite directory. Running time: From seconds to hours depending on the computational task, lattice volume, gauge group, and desired statistics, as well as on the computing platform and number of cores used. For example, rational hybrid Monte Carlo generation of 50 molecular dynamics time units for a 163×32 lattice volume with gauge group U(2) takes approximately 16 hours on 512 cores of the USQCD bc cluster at Fermilab, while standard measurements on a saved 83×24 U(2) configuration require only 8 seconds on one eight-core workstation.

[1]  S. Catterall.  From Twisted Supersymmetry to Orbifold Lattices , 2007, 0712.2532.

[2]  J. Nishimura,et al.  Testing a novel large-N reduction for Script N = 4 super Yang-Mills theory on R × S3 , 2009, 0907.1488.

[3]  A. Kennedy,et al.  Hybrid Monte Carlo , 1988 .

[4]  I. Montvay,et al.  Towards the spectrum of low-lying particles in supersymmetric Yang-Mills theory , 2013, 1304.2168.

[5]  Phase structure of lattice $\mathcal{N}=4$ super Yang-Mills , 2012, 1209.5285.

[6]  Andreas Stathopoulos,et al.  PRIMME: preconditioned iterative multimethod eigensolver—methods and software description , 2010, TOMS.

[7]  Michael G. Endres.  Dynamical simulation of N=1 supersymmetric Yang-Mills theory with domain wall fermions , 2009, 0902.4267.

[8]  B. Jegerlehner.  Krylov space solvers for shifted linear systems , 1996, hep-lat/9612014.

[10]  M. Sakamoto,et al.  Taming the Leibniz rule on the lattice , 2008, 0803.3121.

[11]  P. Damgaard,et al.  Geometry of orbifolded supersymmetric lattice gauge theories , 2008, 0801.2936.

[12]  The Other topological twisting of N=4 Yang-Mills , 1995, hep-th/9506002.

[13]  S. Karamov,et al.  Lattice study of the two-dimensional Wess-Zumino model , 2003, hep-lat/0305002.

[14]  J. Terning.  Modern Supersymmetry: Dynamics and Duality , 2006 .

[15]  Absence of sign problem in two-dimensional $ \mathcal{N} = \left( {2,2} \right) $ super Yang-Mills on lattice , 2010, 1010.2948.

[16]  J. Nishimura,et al.  Lattice study of 4d {\cal N}=1 super Yang-Mills theory with dynamical overlap gluino , 2011, 1111.2180.

[17]  N = 4 super Yang-Mills theory from the plane wave matrix model , 2008, 0807.2352.

[18]  H. Nicolai,et al.  Lattice supersymmetry , 1977 .

[19]  Greg van Anders,et al.  Accelerating the solution of families of shifted linear systems with CUDA , 2011 .

[20]  A euclidean lattice construction of supersymmetric Yang-Mills theories with sixteen supercharges , 2005, hep-lat/0503039.

[21]  Twisted Supersymmetric Gauge Theories and Orbifold Lattices , 2006, hep-th/0603046.

[22]  J. Nishimura,et al.  Holographic description of a quantum black hole on a computer , 2013, Science.

[23]  Igor P. Omelyan,et al.  Symplectic analytically integrable decomposition algorithms: classification, derivation, and application to molecular dynamics, quantum and celestial mechanics simulations , 2003 .

[24]  J. Nishimura,et al.  Direct test of the AdS/CFT correspondence by Monte Carlo studies of $ \mathcal{N}=4 $ super Yang-Mills theory , 2013, 1308.3525.

[25]  T. DeGrand,et al.  N=4 supersymmetry on a space-time lattice , 2014, 1405.0644.

[26]  Karl Jansen,et al.  HMC algorithm with multiple time scale integration and mass preconditioning , 2006, Comput. Phys. Commun..

[27]  Simon Catterall,et al.  An object oriented code for simulating supersymmetric Yang-Mills theories , 2011, Comput. Phys. Commun..

[28]  Fumihiko Sugino,et al.  Lattice formulation for 2d $ \mathcal{N} $ = (2, 2), (4, 4) super Yang-Mills theories without admissibility conditions , 2014, 1402.0952.

[29]  J. Giedt,et al.  Real space renormalization group for twisted lattice N$$ \mathcal{N} $$ =4 super Yang-Mills , 2014, 1408.7067.

[30]  Michael Wimmer,et al.  Algorithm 923: Efficient Numerical Computation of the Pfaffian for Dense and Banded Skew-Symmetric Matrices , 2011, TOMS.

[31]  Anosh Joseph.  Two-dimensional N$$ \mathcal{N} $$ = (2, 2) lattice gauge theories with matter in higher representations , 2014, 1403.4390.

[32]  J. Nishimura,et al.  Deconfinement phase transition in N=4 super Yang-Mills theory on R x S3 from supersymmetric matrix quantum mechanics. , 2008, Physical review letters.

[33]  Ulli Wolff,et al.  A factorization algorithm to compute Pfaffians , 2011, Comput. Phys. Commun..

[34]  R Folk,et al.  Optimized Verlet-like algorithms for molecular dynamics simulations. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[35]  R. Brower,et al.  Lattice super-Yang-Mills using domain wall fermions in the chiral limit , 2008, 0810.5746.

[36]  M A Clark,et al.  Accelerating dynamical-fermion computations using the rational hybrid Monte Carlo algorithm with multiple pseudofermion fields. , 2007, Physical review letters.

[37]  Electric-Magnetic Duality And The Geometric Langlands Program , 2006, hep-th/0604151.