Quantization of Fayet-Iliopoulos Parameters in Supergravity

In this short note we discuss quantization of the Fayet-Iliopoulos parameter in supergravity theories. We argue that in supergravity, the Fayet-Iliopoulos parameter determines a lift of the group action to a line bundle, and such lifts are quantized. Just as D-terms in rigid N=1 supersymmetry are interpreted in terms of moment maps and symplectic reductions, we argue that in supergravity the quantization of the Fayet-Iliopoulos parameter has a natural understanding in terms of linearizations in geometric invariant theory (GIT) quotients, the algebro-geometric version of symplectic quotients.Comment: 21 pages, utarticle class; v2: typos and tex issue fixe

Analogues of Discrete Torsion for the M-Theory Three-Form

In this article we shall outline a derivation of the analogue of discrete torsion for the M-theory three-form potential. We find that some of the differences between orbifold group actions on the C field are classified by H^3(G, U(1)). We also compute the phases that the low-energy effective action of a membrane on T^3 would see in the analogue of a twisted sector, and note that they are invariant under the obvious SL(3,Z) action.Comment: 27 pages, LaTeX, 4 figures; v2: typos fixe

Introducing First Year Medical Students to Personalized Medicine Concepts in a Small Group Activity

Presented as a Poster Presentation at 2020 IUSM Education Day.An individuals’ genetic profile is becomingly an increasingly important parameter in healthcare decisions. This small group activity was developed to introduce first year medical students in the Molecules to Cells and Tissues course to the concept and significance of Pharmacogenomics and personalized medicine. Additionally, this activity provided students with an opportunity to work with a large dataset and use the information to impact clinical decision making. This activity has two cases, takes student groups approximately 2 hours to complete, and requires internet access. Case materials are available through the learning management system Canvas, and include open-ended questions to guide students through the cases. In these cases students explore the functional significance of different alleles of a panel of cytochrome P450 genes. The group activity has the students examine a large data set of cytochrome P450 genes and cognate alleles to determine their prevalence in the local population and calculate the individuals’ gene scores. The students are then asked to explain the impact of the genotype (or gene score) on the resulting patient phenotype (i.e. the functional significance of the genotype). The first case involves a breast cancer survivor support group in which patients taking Taxol discuss lack of adequate pain relief from opioids and the potential impact of concomitant use of natural compounds/supplements on drug metabolism. The second case involves a patient presenting with recurrent stroke-like symptoms despite being on the anticoagulant medication clopidogrel. The patient is initially suspected to be non-compliant, but is later determined to be a poor metabolizer of the anticoagulant clopidogrelto its active form thus decreasing its efficacy. The expertise of the IUSM Medical Genetics research faculty was leveraged to provide a large data set of cytochrome P450 genes and cognate alleles. The selection of cytochrome P450 was based upon delivering content focused on the biochemistry of the enzyme system and provided an opportunity to highlight the drug interaction database available through IUSM Clinical Pharmacology (The FlockhartTable™ ; https://drug-interactions.medicine.iu.edu/). The addition of natural compounds was to draw students’ attention to the Natural Medicines database, which is the recommended source for evidence-based data on complementary and alternative medicine. Natural Medicines is available through the Ruth Lilly Medical Library and can be searched by substance or condition. It provides both a summary of the literature available on substances as well as the level of evidence or quality of studies done on the substance

Hadronic Electromagnetic Properties at Finite Lattice Spacing

Electromagnetic properties of the octet mesons as well as the octet and decuplet baryons are augmented in quenched and partially quenched chiral perturbation theory to include O(a) corrections due to lattice discretization. We present the results for the SU(3) flavor group in the isospin limit as well as the results for SU(2) flavor with non-degenerate quarks. These corrections will be useful for extrapolation of lattice calculations using Wilson valence and sea quarks, as well as calculations using Wilson sea quarks and Ginsparg-Wilson valence quarks.Comment: 19 pages, 0 figures, RevTeX

Baryon Decuplet to Octet Electromagnetic Transitions in Quenched and Partially Quenched Chiral Perturbation Theory

We calculate baryon decuplet to octet electromagnetic transition form factors in quenched and partially quenched chiral perturbation theory. We work in the isospin limit of SU(3) flavor, up to next-to-leading order in the chiral expansion, and to leading order in the heavy baryon expansion. Our results are necessary for proper extrapolation of lattice calculations of these transitions. We also derive expressions for the case of SU(2) flavor away from the isospin limit.Comment: 16 pages, 3 figures, revtex

Partial Flavor Symmetry Restoration for Chiral Staggered Fermions

We study the leading discretization errors for staggered fermions by first constructing the continuum effective Lagrangian including terms of O(a^2), and then constructing the corresponding effective chiral Lagrangian. The terms of O(a^2) in the continuum effective Lagrangian completely break the SU(4) flavor symmetry down to the discrete subgroup respected by the lattice theory. We find, however, that the O(a^2) terms in the potential of the chiral Lagrangian maintain an SO(4) subgroup of SU(4). It follows that the leading discretization errors in the pion masses are SO(4) symmetric, implying three degeneracies within the seven lattice irreducible representations. These predictions hold also for perturbatively improved versions of the action. These degeneracies are observed, to a surprising degree of accuracy, in existing data. We argue that the SO(4) symmetry does not extend to the masses and interactions of other hadrons (vector mesons, baryons, etc), nor to higher order in a^2. We show how it is possible that, for physical quark masses of O(a^2), the new SO(4) symmetry can be spontaneously broken, leading to a staggered analogue of the Aoki-phase of Wilson fermions. This does not, however, appear to happen for presently studied versions of the staggered action.Comment: 26 pages, 2 figures (using psfig). Version to appear in PRD (clarifications added to introduction and section 6; typos corrected; references updated

Decomposition, Condensation Defects, and Fusion

In this paper we outline the application of decomposition to condensation defects and their fusion rules. Briefly, a condensation defect is obtained by gauging a higher-form symmetry along a submanifold, and so there is a natural interplay with notions of decomposition, the statement that d-dimensional quantum field theories with global (Formula presented.) -form symmetries are equivalent to disjoint unions of other quantum field theories. We will also construct new (sometimes non-invertible) defects, and compute their fusion products, again utilizing decomposition. An important role will be played in all these analyses by theta angles for gauged higher-form symmetries, which can be used to select individual universes in a decomposition

Chiral Perturbation Theory for the Quenched Approximation of QCD

[This version is a minor revision of a previously submitted preprint. Only references have been changed.] We describe a technique for constructing the effective chiral theory for quenched QCD. The effective theory which results is a lagrangian one, with a graded symmetry group which mixes Goldstone bosons and fermions, and with a definite (though slightly peculiar) set of Feynman rules. The straightforward application of these rules gives automatic cancellation of diagrams which would arise from virtual quark loops. The techniques are used to calculate chiral logarithms in $f_K/f_\pi$, $m_\pi$, $m_K$, and the ratio of $\langle{\bar s}s\rangle$ to $\langle{\bar u}u\rangle$. The leading finite-volume corrections to these quantities are also computed. Problems for future study are described.Comment: 14 page

Nucleons Properties at Finite Lattice Spacing in Chiral Perturbation Theory

Properties of the proton and neutron are studied in partially-quenched chiral perturbation theory at finite lattice spacing. Masses, magnetic moments, the matrix elements of isovector twist-2 operators and axial-vector currents are examined at the one-loop level in a double expansion in the light-quark masses and the lattice spacing. This work will be useful in extrapolating the results of simulations using Wilson valence and sea quarks, as well as simulations using Wilson sea quarks and Ginsparg-Wilson valence quarks, to the continuum.Comment: 16 pages LaTe