Joel Giedt

Associate Professor

Department of Physics, Applied Physics & Astronomy


Curriculum Vitae

Lattice N=4 super-Yang-Mills

Gauge-gravity duality N=4 super-Yang-Mills is the unique four-dimensional renormalizable field theory with maximal supersymmetry, meaning that it has the maximum number of conserved supercharges. These are four Majorana spinor charges, hence N=4. In the late 90s it was discovered by Maldacena (and elaborated by others) that this theory with gauge group U(Nc) is dual to Type IIB string theory with Nc coincident D3 branes compactified on the space AdS(5) × S(5). Since the latter is a gravitational theory, and the former is a gauge theory, this is an example of a gauge-gravity duality. Subsequently, many other gauge-gravity duals have been discovered, all of which are supersymmetric.

construction dimensions supersymmetry string background conformal/confining
Maldacena 1+3 N=4 AdS(5) × S(5) conformal
Klebanov-Witten 1+3 N=1 AdS(5) × T(1,1) conformal
Klebanov-Strassler 1+3 N=1 resolved AdS(5) × T(1,1) confining

Examples of the gauge-gravity duality

Monte Carlo Renormalization Group for Minimal Walking Technicolor

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.


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

Lattice Wess-Zumino Model

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.


A dilaton near the conformal window?

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.

Scalar resonances from the lattice, using GPUs

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.

Integrating CPS and QUDA for clover fermions

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.

Lattice N=1 super-Yang-Mills


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.)


Flavor physics in M theory

We are exploring how the physics of flavor is predicted based on the geometry of the compact space, which is a seven-dimensional manifold with G(2) holonomy. For further details, click here.


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