arXiv subjects

Joel Giedt

Publications and source records attributed to Joel Giedt.

At least 73 records · Page 4Linked to original sources

arXiv2005

Symmetry and scaling in the Q-exact lattice (2,2) 2d Wess-Zumino model

As a nonperturbative check on the Q-exact lattice formulation, we demonstrate that the continuum R-symmetries are recovered. We locate the critical domain of the lattice theory. Aspects of the continuum nonrenormalization theorems are found to be respected at finite lattice spacing. Preliminary attempts to extract critical exponents--another nonperturbative check--are discussed. All of our results are obtained from Monte Carlo simulations with dynamical fermions.

hep-lat↗

arXiv2005

R-symmetry in the Q-exact (2,2) 2d lattice Wess-Zumino model

In this article we explore the R-symmetry of the (2,2) 2d Wess-Zumino model. We study whether or not this symmetry is approximately realized in the Q-exact lattice version of this theory. Our study is nonperturbative: it relies on Monte Carlo simulations with dynamical fermions. Irrelevant operators in the lattice action explicitly break the R-symmetry. In spite of this, it is found to be a symmetry of the effective potential. We find nonperturbative evidence that the nonrenormalization theorem of the continuum theory is recovered in the continuum limit; e.g., there is no additive mass renormalization. In our simulations we find that Fourier acceleration of the hybrid Monte Carlo algorithm allows us to avoid difficulties with critical slowing-down.

hep-lat↗

arXiv2005

Massive Neutrinos and (Heterotic) String Theory

String theories in principle address the origin and values of the quark and lepton masses. Perhaps the small values of neutrino masses could be explained generically in string theory even if it is more difficult to calculate individual values, or perhaps some string constructions could be favored by generating small neutrino masses. We examine this issue in the context of the well-known three-family standard-like Z_3 heterotic orbifolds, where the theory is well enough known to construct the corresponding operators allowed by string selection rules, and analyze the D- and F-flatness conditions. Surprisingly, we find that a simple see-saw mechanism does not arise. It is not clear whether this is a property of this construction, or of orbifolds more generally, or of string theory itself. Extended see-saw mechanisms may be allowed; more analysis will be needed to settle that issue. We briefly speculate on their form if allowed and on the possibility of alternatives, such as small Dirac masses and triplet see-saws. The smallness of neutrino masses may be a powerful probe of string constructions in general. We also find further evidence that there are only 20 inequivalent models in this class, which affects the counting of string vacua.

hep-th↗

arXiv2004

Less naive about supersymmetric lattice quantum mechanics

We explain why naive discretization results that have appeared in [hep-lat/0006013] do not appear to yield the desired continuum limit. The fermion propagator on the lattice inevitably yields a diagram with nonvanishing UV degree D=0 contribution in lattice perturbation theory, in contrast to what occurs in the continuum. This diagram gives a finite correction to the boson 2-point function that must be subtracted off in order to obtain the perturbation series of the continuum theory, in the limit where the lattice spacing $a$ vanishes. Using a transfer matrix approach, we provide a nonperturbative proof that this counterterm suffices to yield the desired continuum limit. This analysis also allows us to improve the action to O(a). We demonstrate by Monte Carlo simulation that the spectrum of the continuum theory is well-approximated at finite but small $a$, for both weak and strong coupling. We contrast the above situation for the naive lattice action to what occurs for the supersymmetric lattice action, which preserves a discrete version of half the supersymmetry. There, cancellations between D=0 diagrams occur, obviating the need for counterterms.

hep-lat↗

arXiv2004

Lattice supersymmetry, superfields and renormalization

We study Euclidean lattice formulations of non-gauge supersymmetric models with up to four supercharges in various dimensions. We formulate the conditions under which the interacting lattice theory can exactly preserve one or more nilpotent anticommuting supersymmetries. We introduce a superfield formalism, which allows the enumeration of all possible lattice supersymmetry invariants. We use it to discuss the formulation of Q-exact lattice actions and their renormalization in a general manner. In some examples, one exact supersymmetry guarantees finiteness of the continuum limit of the lattice theory. As a consequence, we show that the desired quantum continuum limit is obtained without fine tuning for these models. Finally, we discuss the implications and possible further applications of our results to the study of gauge and non-gauge models.

hep-th↗

arXiv2004

Modular Invariant Gaugino Condensation in the Presence of an Anomalous U(1)

Starting from the previously constructed effective supergravity theory below the scale of U(1) breaking in orbifold compactifications of the weakly coupled heterotic string, we study the effective theory below the scale of supersymmetry breaking by gaugino and matter condensation in a hidden sector. Issues we address include vacuum stability, soft supersymmetry-breaking masses in the observable sector, and the masses of the various moduli fields, including those associated with flat directions at the U(1)-breaking scale, and of their fermionic superpartners. The consistent treatment of U(1) breaking together with condensation yields qualitatively new results.

hep-th↗

arXiv2004

Deconstruction, 2d lattice super-Yang-Mills, and the dynamical lattice spacing

We study expectation values related to the dynamical lattice spacing that occurs in the recent 2d lattice super-Yang-Mills constructions of Cohen et al. [hep-lat/0307012]. The corresponding observable in the fully-quenched ensemble would appear to indicate a difficulty with the proposed continuum limit. However, we find that the same observable in the phase-quenched ensemble takes a very different, perhaps encouraging, average value. Unfortunately, we are not able to obtain results for the full theory, due to the nearly flat distribution of the complex phase of the fermion determinant in the phase-quenched ensemble.

hep-lat↗

arXiv2004

Instanton effects and linear-chiral duality

We discuss duality between the linear and chiral dilaton formulations, in the presence of super-Yang-Mills instanton corrections to the effective action. In contrast to previous work on the subject, our approach appeals directly to explicit instanton calculations and does not rely on the introduction of an auxiliary Veneziano-Yankielowicz superfield. We discuss duality in the case of an axion that has a periodic scalar potential, and find that the bosonic fields of the dual linear multiplet have a modified interpretation. We note that symmetries of the axion potential manifest themselves as symmetries of the equations of motion for the linear multiplet. We also make some brief remarks regarding dilaton stabilization. We point out that corrections recently studied by Dijkgraaf and Vafa can be used to stabilize the axion in the case of a single super-Yang-Mills condensate.

hep-th↗

arXiv2004

Lack of trinification in Z_3 orbifolds of the SO(32) heterotic string

We report results relating to the trinification scenario in some explicit string constructions that contain SU(3)^3 as a gauge symmetry. These models are obtained from symmetric Z_3 orbifolds of the SO(32) heterotic string with one discrete Wilson line. We highlight the obstacles that were encountered: the absence of the usual Higgs sector that would break SU(3)^3 \to SU(3)_c \times SU(2)_L \times U(1)_Y; the presence of exotics that would generically befoul gauge coupling unification and lead to fractionally-charged states in the low energy spectrum.

hep-ph↗

arXiv2003

Deconstruction, 2d lattice Yang-Mills, and the dynamical lattice spacing

We study expectation values related to the dynamical lattice spacing that occurs in the recent supersymmetric 2d lattice Yang-Mills constructions of Cohen et al. [hep-lat/0307012]. For the purposes of this preliminary analysis, we restrict our attention to the bosonic part of that theory. That is, we compute observables in the fully quenched ensemble, equivalent to non-supersymmetric 2d lattice Yang-Mills with a dynamical lattice spacing and adjoint scalars. Our numerical simulations indicate difficulties with the proposed continuum limit. We find that expectation values tend to those of the undeformed ``daughter theory,'' in spite of the deformation suggested by Cohen et al. In an effort to understand these results, we examine the zero action configurations, with and without the deformation. Based on these considerations, we are able to interpret the simulation results in terms of entropic effects.

hep-lat↗

arXiv2003

Lattice supersymmetry and string phenomenology

I discuss the usefulness of lattice supersymmetry in relation to string phenomenology. I suggest how lattice results might be incorporated into string phenomenology. I outline difficulties and describe some constructions that contain an exact lattice version of supersymmetry, thereby reducing fine-tuning of the regulator. I mention some problems that occur for these lattices.

hep-ph↗

arXiv2003

The fermion determinant in (4,4) 2d lattice super-Yang-Mills

We find that the fermion determinant is not generally positive in a class of lattice actions recently constructed by Cohen et al. [hep-lat/0307012]; these are actions that contain an exact lattice supersymmetry and have as their target (continuum) theory (4,4) 2-dimensional super-Yang-Mills. We discuss the implications of this finding for lattice simulations and give some preliminary results for the phase of the determinant in the phase-quenched ensemble.

hep-lat↗

arXiv2003

Non-positive fermion determinants in lattice supersymmetry

We find that fermion determinants are not generally positive in a recent class of constructions with explicit lattice supersymmetry. These involve an orbifold of supersymmetric matrix models, and have as their target (continuum) theory (2,2) 2-dimensional super-Yang-Mills. The fermion determinant is shown to be identically zero for all boson configurations due to the existence of a zeromode fermion inherited from the "mother theory." Once this eigenvalue is factored out, the fermion determinant generically has arbitrary complex phase. We discuss the implications of this result for simulation of the models.

hep-lat↗

arXiv2003

Full Component Lagrangian in the Linear Multiplet Formulation of String-inspired Effective Supergravity

We compute the component field 4-dimensional N=1 supergravity Lagrangian that is obtained from a superfield Lagrangian in the U(1)_K formalism with a linear dilaton multiplet. All fermionic terms are presented. In a variety of important ways, our results generalize those that have been reported previously, and are flexible enough to accomodate many situations of phenomenological interest in string-inspired effective supergravity, especially models based on orbifold compactifications of the weakly-coupled heterotic string. We provide for an effective theory of hidden gaugino and matter condensation. We include supersymmetric Green-Schwarz counterterms associated with the cancellation of U(1) and modular duality anomalies; the modular duality counterterm is of a rather general form. Our assumed form for the dilaton Kahler potential is quite general and can accomodate Kahler stabilization methods. We note possible applications of our results. We also discuss the usefulness of the linear dilaton formulation as a complement to the chiral dilaton approach.

hep-th↗

arXiv2003

Z_3 orbifolds of the SO(32) heterotic string: 1 Wilson line embeddings

We consider compactification of the SO(32) heterotic string on a 6-dimensional Z_3 orbifold with one discrete Wilson line. A complete set of all possible embeddings is given, 159 in all. The unbroken subgroups of SO(32) are tabulated. The extended gauge symmetry SU(3)^3, recently discussed by J. E. Kim [hep-th/0301177] for semi-realistic E_8 x E_8 heterotic string models, occurs for several embeddings, as well as other groups that may be of interest in unified string models. The extent to which extra gauge group factors can be hidden is discussed and compared to the E_8 x E_8 case. Along flat directions where an effective hidden sector exists, the embeddings described here provide for hidden gauge groups that are not possible in the E_8 x E_8 heterotic string.

hep-th↗

arXiv2003

Deconstruction, Lattice Supersymmetry, Anomalies and Branes

We study the realization of anomalous Ward identities in deconstructed (latticized) supersymmetric theories. In a deconstructed four-dimensional theory with N=2 supersymmetry, we show that the chiral symmetries only appear in the infrared and that the anomaly is reproduced in the usual framework of lattice perturbation theory with Wilson fermions. We then realize the theory on the world-volume of fractional D-branes on an orbifold. In this brane realization, we show how deconstructed theory anomalies can be computed via classical supergravity. Our methods and observations are more generally applicable to deconstructed/latticized supersymmetric theories in various dimensions.

hep-th↗

arXiv2002

D-Moduli Stabilization

The matter sector of four-dimensional effective supergravity models obtained from the weakly coupled heterotic string contains many moduli. In particular, flat directions of the D-term part of the scalar potential in the presence of an anomalous U(1) give rise to massless chiral multiplets which have been referred to elsewhere as D-moduli. The stabilization of these moduli is necessary for the determination of the large vacuum expectation values of complex scalar fields induced by the corresponding Fayet-Illiopoulos term. This stabilization is of phenomenological importance since these background values determine the effective theory below the scale of the anomalous U(1) symmetry breaking. In some simple models we illustrate the stabilization of these moduli due to the nonperturbative dynamics associated with gaugino condensation in a hidden sector. We find that background field configurations which are stable above the condensation scale no longer represent global minima once dynamical supersymmetry breaking occurs. The implications for low energy models based on promising ``flat'' directions are discussed.

hep-ph↗

arXiv2002

Optical Unification

We discuss string scale unification facilitated by exotic matter with masses at intermediate scales, between the observable sector supersymmetry breaking scale and the string scale. We point out a mechanism by which string scale unification may occur while producing a (lower) virtual unification scale independent of the location of the intermediate scale and the value of the string coupling. The apparent unification obtained by extrapolating low energy gauge couplings is not accidental when this mechanism is invoked; virtual unification is robust.

hep-ph↗