arXiv subjects
Publications and source records attributed to Joel Giedt.
We present a Monte Carlo renormalisation group study of the SU(2) gauge theory with two Dirac fermions in the adjoint representation. Using the two lattice matching technique recently advocated and exploited in [arXiv:0907.0919], we measure the running of the coupling and the anomalous mass dimension.
We numerically evaluate the one-loop counterterms for the four-dimensional Wess-Zumino model formulated on the lattice using Ginsparg-Wilson fermions of the overlap (Neuberger) variety, together with an auxiliary fermion (plus superpartners), such that a lattice version of $U(1)_R$ symmetry is exactly preserved in the limit of vanishing bare mass. We confirm previous findings by other authors that at one loop there is no renormalization of the superpotential in the lattice theory, but that there is a mismatch in the wavefunction renormalization of the auxiliary field. We study the range of the Dirac operator that results when the auxiliary fermion is integrated out, and show that localization does occur, but that it is less pronounced than the exponential localization of the overlap operator. We also present preliminary simulation results for this model, and outline a strategy for nonperturbative improvement of the lattice supercurrent through measurements of supersymmetry Ward identities. Related to this, some benchmarks for our graphics processing unit code are provided. Our simulation results find a nearly vanishing vacuum expectation value for the auxiliary field, consistent with approximate supersymmetry at weak coupling.
We present results from high precision, large volume simulations of the lattice gauge theory corresponding to minimal walking technicolor. We find evidence that the pion decay constant vanishes in the infinite volume limit and that the dependence of the chiral condensate on quark mass m_q is inconsistent with spontaneous symmetry breaking. These findings are consistent with the all-orders beta function prediction as well as the Schroedinger functional studies that indicate the existence of a nontrivial infrared fixed point.
Recent lattice measurements have given accurate estimates of the light and strange quark condensates in the proton. We use these new results to significantly improve the dark matter predictions in a set of benchmark models that represent different scenarios in the constrained minimal supersymmetric standard model (CMSSM). Because the predicted cross sections are at least an order of magnitude smaller than previously suggested, our results have significant consequences for dark matter searches.
We are entering an era where a number of large-scale lattice simulations of four-dimensional supersymmetric theories are under way. Moreover, proposals for how to approach such studies continue to progress. One particular line of research in this direction is described here. General actions for super-QCD, including counterterms required on the lattice, are given. We obtain the number of fine-tunings that is required, once gauge and flavor symmetries are accounted for, provided Ginsparg-Wilson fermions are used for the gauginos. We also review and extend our recent work on lattice formulations of N=4 super-Yang-Mills and N=1 super-Yang-Mills that exploit Ginsparg-Wilson fermions.
Lattice N=1 super-Yang-Mills theory formulated using Ginsparg-Wilson fermions provides a rigorous non-perturbative definition of the continuum theory that requires no fine-tuning as the lattice spacing is reduced to zero. Domain wall fermions are one explicit scheme for achieving this and using them we have performed large-scale Monte Carlo simulations of the theory for gauge group SU(2). We have measured the gaugino condensate, static potential, Creutz ratios and residual mass for several values of the domain wall separation L_s, four-dimensional lattice volume, and two values of the gauge coupling. With this data we are able to extrapolate the gaugino condensate to the chiral limit, to express it in physical units, and to establish important benchmarks for future studies of super-Yang-Mills on the lattice.
We report on numerical simulations of SU(2) lattice gauge theory with two flavors of light dynamical quarks in the adjoint of the gauge group. The dynamics of this theory is thought to be very different from QCD -- the theory exhibiting conformal or near conformal behavior in the infrared. We make a high resolution survey of the phase diagram of this model in the plane of the bare coupling and quark mass on lattices of size 8^3 \times 16. Our simulations reveal a line of first order phase transitions extending from beta=0 to beta=beta_c \sim 2.0. For beta > beta_c the phase boundary is no longer first order but continues as the locus of minimum meson mass. For beta > 2.0 we observe the pion and rho masses along the phase boundary to be light, independent of bare coupling and approximately degenerate. We discuss possible interpretations of these observations and corresponding continuum limits.
We report preliminary results of lattice super-Yang-Mills computations using domain wall fermions, performed at an actual rate of 1000 Gflop/s, over the course of six months, using two BlueGene/L racks at Rensselaer's CCNI supercomputing center. This has allowed us to compute the gluino condensate and string tension over a wide range of lattice parameters, setting the stage for continuum, chiral extrapolations.
We examine the possible extension of the parameter space of the minimal supersymmetric extension of the Standard Model (MSSM), as expressed via the renormalization-group equations in terms of universal soft supersymmetry-breaking terms at the unification scale, to include tachyonic input scalar masses. Many models with negative masses-squared for scalars at the unification scale may be viable because the small sizes of the masses-squared allow them to change signs during the renormalization-group evolution to the electroweak scale. However, in many cases, there is, in addition to the electroweak vacuum, a much deeper high-scale vacuum located along some F- and D-flat direction in the effective potential for the MSSM. We perform a numerical search for such vacua in both the CMSSM and the NUHM. We discuss the circumstances under which the existence of such a deep charge- and color-breaking vacuum is consistent with standard cosmology. A crucial role is played by the inflation--induced scalar masses, whereas thermal effects are often irrelevant.
We show that nonperturbative lattice studies of four-dimensional N=4 Super-Yang-Mills are within reach. We use Ginsparg-Wilson fermions to avoid gluino masses and an exact implementation of the (chiral) $R$-symmetry, which greatly limits the number of counterterms that must be fine-tuned. Only bosonic operators require fine tuning, so all tunings can be done ``offline'' by a Ferrenberg-Swendsen type reweighting. We show what measurables can be used to perform the tuning.
The Yukawa-Higgs/Ginsparg-Wilson-fermion construction of chiral lattice gauge theories described in hep-lat/0605003 uses exact lattice chirality to decouple the massless chiral fermions from a mirror sector, whose strong dynamics is conjectured to give cutoff-scale mass to the mirror fermions without breaking the chiral gauge symmetry. In this paper, we study the mirror sector dynamics of a two-dimensional chiral gauge theory in the limitof strong Yukawa and vanishing gauge couplings, in which case it reduces to an XY model coupled to Ginsparg-Wilson fermions. For the mirror fermions to acquire cutoff-scale mass it is believed to be important that the XY model remain in its "high temperature" phase, where there is no algebraic ordering--a conjecture supported by the results of our work. We use analytic and Monte-Carlo methods with dynamical fermions to study the scalar and fermion susceptibilities, and the mirror fermion spectrum. Our results provide convincing evidence that the strong dynamics does not "break" the chiral symmetry (more precisely, that the mirror fermions do not induce algebraic ordering in two-dimensions), and that the mirror fermions decouple from the infrared physics.
We propose a gravitational dual of ``single-sector'' models of supersymmetry breaking which contain no messenger sector and naturally explain the scale of supersymmetry breaking and the fermion mass hierarchy. In five dimensions these models can be given a simple interpretation. Inspired by flux-background solutions of type IIB supergravity, a metric background that deviates from AdS_5 in the IR breaks supersymmetry, while the fermion mass hierarchy results from the wavefunction overlap of bulk fermions with a UV-confined Higgs field. The first and second generation squarks and sleptons, which are localized near the IR brane, directly feel the supersymmetry breaking and obtain masses of order 10 TeV. These are interpreted as composite states of the dual 4D theory. The gauginos and third generation squarks and sleptons are elementary states that obtain soft masses of order 1 TeV at the loop level via direct gauge mediation. This particle spectrum leads to distinctive signatures at the LHC, similar to the usual gauge mediation with a neutralino NLSP that decays promptly to a gravitino LSP, but with lower event rates. Nevertheless we show that with 1-10 fb^{-1} of LHC data "single-sector" models can easily be detected above background and distinguished from conventional gravity and gauge mediation.
I review motivations for the study of supersymmetric field theories by lattice techniques. In particular, some of the more interesting potential applications are described. These are models of quantum gravity, that rely on the AdS/CFT correspondence. The dual gauge theory is an ideal place for lattice studies to make a contribution. I also survey some of the recent advances in lattice formulations of supersymmetric theories.
We relate bulk fields in Randall-Sundrum AdS_5 phenomenological models to the world-volume fields of probe D7 branes in the Klebanov-Witten background of type IIB string theory. The string constructions are described by AdS_5 X T^{1,1} in their near-horizon geometry, with T^{1,1} a 5d compact internal manifold that yields N=1 supersymmetry in the dual 4d gauge theory. The effective 5d Lagrangian description derived from the explicit string construction leads to additional features that are not usually encountered in phenomenological model building.
In this article, I generalize the deconstruction lattice formulation of Endres and Kaplan [hep-lat/0604012] to two-dimensional super-QCD with eight supercharges, denoted (4,4), and bifundamental matter. I specialize to a particularly interesting (4,4) gauge theory, with gauge group U(N_c) \times U(N_f), and U(N_f) weakly gauged. It describes the infrared limit of the D1/D5 brane system, which has been studied extensively as an example of the AdS_3/CFT_2 correspondence. The construction here preserves two supercharges exactly, and has a lattice structure quite similar to that which has previously appeared in the deconstruction approach; i.e., site, link and diagonal fields with both Bose and Fermi statistics. I remark on possible applications of the lattice theory that would test the AdS_3/CFT_2 correspondence, particularly one that would exploit the recent worldsheet instanton analysis of Chen and Tong [hep-th/0604090].
Lattice power-counting is extended to QCD with staggered fermions. As preparation, the difficulties encountered by Reisz's original formulation of the lattice power-counting theorem are illustrated. One of the assumptions that is used in his proof does not hold for staggered fermions, as was pointed out long ago by Luscher. Finally, I generalize the power-counting theorem, and the methods of Reisz's proof, such that the difficulties posed by staggered fermions are overcome.
This report contains both a review of recent approaches to supersymmetric lattice field theories and some new results on the deconstruction approach. The essential reason for the complex phase problem of the fermion determinant is shown to be derivative interactions that are not present in the continuum. These irrelevant operators violate the self-conjugacy of the fermion action that is present in the continuum. It is explained why this complex phase problem does not disappear in the continuum limit. The fermion determinant suppression of various branches of the classical moduli space is explored, and found to be supportive of previous claims regarding the continuum limit.
In this note I briefly discuss ideas related to the so-called fourth-root trick. A decomposition of the ``rooted'' fermion effective action into Wilson fermions and a nonlocal, lattice spacing suppressed functional is presented, complete with link interactions. Some proposals are given for analytical, nonperturbative studies of the fourth-root trick.