RENSSELAER POLYTECHNIC INSTITUTE

__Background:__
Electroweak symmetry is one of the cornerstones of the Standard Model of
particle physics. However, we know that it is spontaneously broken.
All of the elementary particle masses that we
have observed in nature arise from this breaking of electroweak symmetry.
Restricting to four-dimensional theories,
there are two competing ideas for how electroweak symmetry is broken.
One is that there is a fundamental scalar
field, the Higgs field, that has a nonzero value in the ground state of the universe.
The alternative is that new particles, "technifermions",
form a condensate in the ground state. This phenomenon already is known to occur in quantum
chromodynamics (leading to spontaneous chiral symmetry breaking) and
superconductivity. This breaking of
electroweak symmetry due to dynamics of new fermions (and hence a new force in
nature) is called "technicolor".

__The challenge:__
We are involved in the study of technicolor theories from first principles.
This is challenging for a number of reasons. First, the technicolor
theory is strongly interacting, and so a nonperturbative
approach such as lattice gauge theory must be used in order to obtain
meaningful results. Second, the technicolor theories that we are interested have dynamics
that span a wide range of scales (walking technicolor).
One cannot directly simulate a system that
incorporates these scales all at once, and a renormalization group approach is
essential in order to circumvent this problem.
Third, the fermions in the technicolor theory
are massless, which makes them very expensive to study on a computer, because
the matrix problem becomes ill-conditioned.

__Goals:__ (1) Use Monte Carlo renormalization group to
identify the infrared fixed point in Minimal Walking Technicolor.
(2) Compute the anomalous mass dimension in
this theory. (3) Show that we are in the
basin of attraction of the Gaussian fixed point.
What do these things mean? For this, we turn to the:

__Method:__
We are using the two lattice matching method. This involves simulations
on a "fine" lattice which are matched to simulations on a "coarse" lattice,
using a number of "blocked" observables. Here blocking refers to an
intelligent sort of averaging. Evolution of the observables corresponds
to renormalization group flow. For more details click here.

__Fixed Point:__
In Minimal Walking Technicolor, it is now
believed that an infrared fixed point exists.
This means that under renormalization group flow, the gauge coupling approaches
a point in parameter space where it ceases to change.
This would be indicated by a zero of the bare
step scaling function (discrete beta function)
So far all that we have found is that the bare step scaling
function is small and could be zero once systematic uncertainties
are taken into account. We are currently
working to reduce these uncertainties by:
(1) going to larger lattices where more blocking steps can be taken, (2)
using O(a) improved actions (adding the clover
term). Both of these would reduce scaling
violations, which are the source of disagreement between different observables
as to the matching of the bare couplings on the fine and coarse lattices.

__Anomalous Mass Dimension:__
This quantity characterizes how the running
mass behaves with respect to the renormalization group.
It also dictates the quantum mass dimension of
the technifermion bilinear. According to a number
of methods, the anomalous mass dimension is about 0.4.
However, Monte Carlo renormalization group has been giving us confusing
results: about 0 if we assume that we
are near the fixed point where the couplings on the
two lattices should be equal, and somewhere between -0.6 and 0.6
if we take into account our uncertainties in the bare step
scaling function.
We are currently working to include fermionic
observables in the matching, in addition to reducing the scaling violations as
mentioned above. We are hopeful that
these improvements will lead to more definitive answers.

__Simulations and Measurements:__
These are demanding
computations, and we are currently using the CCNI and Department of Energy
computers at Fermi National Laboratory (as part of the
USQCD collaboration)
in order to do our work.

__Publications:__

- Simon Catterall (Syracuse U.), Luigi Del Debbio (Edinburgh U.), Joel Giedt and Liam Keegan (Edinburgh U.), "MCRG Minimal Walking Technicolor," LATTICE2010 (2010) 057 [arXiv:1010.5909].
- Simon Catterall (Syracuse U.), Luigi Del Debbio (Edinburgh U.), Joel Giedt and Liam Keegan (Edinburgh U.), "MCRG Minimal Walking Technicolor," submitted to Phys. Rev. D [arXiv:1108.3794].
- Simon Catterall (Syracuse U.), Luigi Del Debbio (Edinburgh U.), Joel Giedt and Liam Keegan (Edinburgh U.), "Systematic Errors of the MCRG Method," LATTICE2011 (2011) 068 [arXiv:1110.1660]

The MCRG project has its own webpage. Click here for more details

__Background:__
The Wess-Zumino model is the simplest interacting four-dimensional
supersymmetric theory. It consists of a Majorana fermion and a
complex scalar field, interacting through a Yukawa coupling.
Formulating theories with scalars on the lattice is especially challenging, since the
lattice regulator explicitly breaks supersymmetry and
hence there is no symmetry to protect the scalar mass from quantum corrections.
Because of the interest in supersymmetric theories with
scalars, such as super-QCD (used in phenomenology) and N=4 super-Yang-Mills
(used in gauge-gravity duality), it makes sense to first try out methods on the
relatively simple case of the Wess-Zumino model.

__Goal:__
Using a formulation based on Ginsparg-Wilson fermions, conduct the necessary fine-tuning
to achieve the supersymmetric continuum limit.

__Method:__
The Ginsparg-Wilson chiral symmetry reduces the number of
counterterms that must be adjusted nonperturbatively,
thus reducing the dimensionality of the parameter space that must be
searched. This is a significant savings. We are measuring the four-divergence of the
supercurrent as a probe of supersymmetry
violation. We are also measuring the
effective masses of bosons and fermions, as these must be equal when the
fine-tuning is successful.

__Simulations:__
We have written graphics processing unit
(GPU) code based on Nvidia's CUDA (a C interface) to perform our simulations.
The Wess-Zumino model is ideally suited to
this computing platform, because the memory requirements are not that
great. That is, we are able to fit the
problem onto a single GPU. We currently have four GPUs for these calculations.

__Publications:__

- Chen Chen, Eric Dzienkowski and Joel Giedt, "Lattice Wess-Zumino model with Ginsparg-Wilson fermions: One-loop results and GPU benchmarks," Phys. Rev. D82 (2010) 085001 [arXiv:1005.3276]
- Joel Giedt, Chen Chen and Eric Dzienkowski, "Lattice Wess-Zumino model simulation with GPUs," PoS LATTICE2010 (2010) 052.
- Chen Chen, Joel Giedt and Joseph Paki, "Supercurrent conservation in the lattice Wess-Zumino model with Ginsparg-Wilson fermions," Phys. Rev. D84 (2011) 025001 [arXiv:1104.1126].

__Definition:__
In theories with approximate scale invariance, where the coupling "walks"
instead of running over some range of scales, some workers have argued
that there will be a pseudo-Nambu-Goldstone
boson associated with the spontaneous breakdown of this symmetry.
This light scalar particle is called the dilaton.
To learn more about our studies of this scenario,
click here for more details.

In a project supported by the National Science Foundation, we are developing computer code to study scalar resonances in QCD-like theories, harvesting the significant computing power of GPUs. For further details, click here.

We have written code that integrates QUDA and CPS for clover fermions. For this, one should use a recent version of CPS and replace the file src/util/lattice/f_clover/f_clover.C with this file f_clover.C. The configure script needs some options, which are illustrated here do_configure.

__Goal:__ Study super-Yang-Mills using Domain Wall
Fermions, with large enough lattices and high enough statistics to extrapolate
to the continuum limit. Something that we are working on now is to obtain the
renormalized "gluino" condensate.

__Facilities:__ The Computational Center for Nanotechnology Innovations
(CCNI). We
are currently exploiting some of the 16 BlueGene/L racks that are available
to us at this facility, which was built as a partnership between Rensselaer,
IBM and New York State.

__Performance:__ Each rack provides 5.6 trillion floating point operations per second (TFlops),
and we use software built on a modification of the Columbia Physics System.
It has an approximate 10% sustained utilization.

__Other Project Members:__ Richard Brower (Boston
U.), Simon Catterall (Syracuse U.), George Fleming (Yale U.), Pavlos Vranas
(Lawrence Livermore Natl. Lab.)

__Publications:__