Lilly Endowment Annual Report 2020

While living through the challenges of two world wars and the Great Depression, Lilly Endowment founders, J.K. Lilly Sr. and his sons, Eli and J.K. Jr., dedicated themselves and their company to helping meet the immediate needs of their employees, community and country while they continued to plan and build for the future. During the past extraordinarily challenging year, the Endowment attempted to follow their example by working to help meet various urgent needs in our city, state and country arising from the COVID-19 pandemic while continuing to help build brighter futures for individuals, families, organizations and communities through our ongoing grantmaking in community development, education and religion, the areas of focus established by our founders when they created the Endowment in 1937.The Endowment's COVID-19-related grantmaking in 2020, which totaled nearly $208 million, supported the inspirational efforts of hundreds of organizations that worked diligently to help meet urgent needs in Indianapolis, throughout Indiana and across the nation. This grantmaking also included funding for several organizations to make pandemic-related adjustments needed to continue to operate their important programs safely.This annual report also highlights other grants the Endowment approved in 2020 that support promising endeavors to build brighter, more prosperous futures for young children and college students in Indiana and that enhance the future vitality of the community of Indianapolis and communities throughout the state, as well as congregations and seminaries around the country

I don’t want the money, I just want your time: how moral identity overcomes the aversion to giving time to pro-social causes

Four studies show that moral identity reduces people’s aversion to giving time—particularly as the psychological costs of doing so increase. In Study 1, we demonstrate that even when the cost of time and money are held equivalent, a moral cue enhances the expected self-expressivity of giving time—especially when it is given to a moral cause. We found that a moral cue reduces time aversion even when giving time was perceived to be unpleasant (Study 2), or when the time to be given was otherwise seen to be scarce (Study 3). Study 4 builds on these studies by examining actual giving while accounting for the real costs of time. In this study, we found that the chronic salience of moral identity serves as a buffer to time aversion, specifically as giving time becomes increasingly costly. These findings are discussed in terms of the time-versus-money literature and the identity literature. We also discuss policy implications for prosocial cause initiatives. (PsycINFO Database Record (c) 2015 APA, all rights reserved

The Low Energy Behavior of some Models with Dynamical Supersymmetry Breaking

We study supersymmetric SU(5) chiral gauge theories with 2 fields in the 10 representation, $2+N_F$ fields in the $\bar{5}$ representation and $N_F$ fields in the 5 representation, for $N_F=0,1,2$. With a suitable superpotential, supersymmetry is shown to be broken dynamically for each of these values of $N_F$. We analyze the calculable limit for the model with $N_F=0$ in detail, and determine the low energy effective sigma model in this case. For $N_F=1$ we find the quantum moduli space, and for $N_F=2$ we construct the s--confining potential.Comment: 16 page

CP, Charge Fractionalizations and Low Energy Effective Actions in the SU(2) Seiberg-Witten Theories with Quarks

Several dynamical aspects of the SU(2) Seiberg-Witten models with N_f quark hypermultiplets are explored. We first clarify the meaning of the number of the singularities of the space of vacua. CP invariance of the theories are then studied and periodicities of theories in \theta with and without bare quark masses are obtained ((4-N_f)\pi and \pi, respectively). CP noninvariance at a generic point of QMS manifests itself as the electric and quark-number charge fractionalizations for the dyons; we show that the exact Seiberg-Witten solution contains such effects correctly, in agreement with the semiclassical analysis recently made by F.Ferrari. Upon N=1 perturbation the low energy effective theories at the singularities display confinement, and in most cases chiral symmetry breaking as a consequence. In one of the vacua for N_f=3 confinement is not accompanied by chiral symmetry breaking: we interpret it as an example of oblique confinement of 't Hooft. We discuss further the consistency of the physical picture found here by studying the effects of soft supersymmetry breaking as well as the behavior of the theory in the N=1 limit.Comment: 38 pages, LaTex file with 3 PostScript figure

Application of the Large-N_c limit to a Chiral Lagrangian with Resonances

It is shown that the implementation of the Large--$N_c$ approximation helps to get insight into the structure of, in principle, any QCD-like theory. As an example, we will compute the NLO corrections to $L_{10}$ in the chiral limit with a Lagrangian with Resonances.Comment: 9 pages, 1 figure. Talk given at the International School of Subnuclear Physics (Erice 2002). To be published in the Proceeding

Super Yang-Mills on the lattice with domain wall fermions

The dynamical N=1, SU(2) Super Yang-Mills theory is studied on the lattice using a new lattice fermion regulator, domain wall fermions. This formulation even at non-zero lattice spacing does not require fine-tuning, has improved chiral properties and can produce topological zero-mode phenomena. Numerical simulations of the full theory on lattices with the topology of a torus indicate the formation of a gluino condensate which is sustained at the chiral limit. The condensate is non-zero even for small volume and small supersymmetry breaking mass where zero mode effects due to gauge fields with fractional topological charge appear to play a role.Comment: LaTeX, 35 pages, 11 eps figures. A few changes in sec. 5.3, figure 11 added. To appear in Phys. Rev.

ADHM Construction of Instantons on the Torus

We apply the ADHM instanton construction to SU(2) gauge theory on T^n x R^(4-n)for n=1,2,3,4. To do this we regard instantons on T^n x R^(4-n) as periodic (modulo gauge transformations) instantons on R^4. Since the R^4 topological charge of such instantons is infinite the ADHM algebra takes place on an infinite dimensional linear space. The ADHM matrix M is related to a Weyl operator (with a self-dual background) on the dual torus tilde T^n. We construct the Weyl operator corresponding to the one-instantons on T^n x R^(4-n). In order to derive the self-dual potential on T^n x R^(4-n) it is necessary to solve a specific Weyl equation. This is a variant of the Nahm transformation. In the case n=2 (i.e. T^2 x R^2) we essentially have an Aharonov Bohm problem on tilde T^2. In the one-instanton sector we find that the scale parameter, lambda, is bounded above, (lambda)^2 tv<4 pi, tv being the volume of the dual torus tilde T^2.Comment: 35 pages, LATeX. New section on Nahm transform included, presentation improved, reference added, to appear in Nuclear Physics

String scale unification in an SU(6)xSU(2) GUT

We construct and analyze an $SU(6)\times SU(2)$ GUT. The model is k=1 string embedable in the sense that we employ only chiral representations allowed at the k=1 level of the associated Ka\v{c}-Moody Algebra. Both cases $SU(6)\times SU(2)_{L}$ and $SU(6)\times SU(2)_{R}$ are realized. The model is characterized by the $SU(6)\times SU(2) \to SU(4)\times SU(2)\times SU(2)$ breaking scale $M_X$, and the $SU(4)\times SU(2)\times SU(2) \to SU(3)_{C}\times SU(2)_{L}\times U(1)_{Y}$ breaking scale $M_{R}$ . The spectrum bellow $M_R$ includes an extra pair of charge-1/3 colour-triplets of mass $M_{I}\leq M_{R}$ that does not couple to matter fields and, possibly, an extra pair of isodoublets. Above $M_{X}$ the SU(6) and SU(2) gauge couplings always unify at a scale which can be taken to be the string unification scale $M_{s}\sim 5\times 10^{17} GeV$. The model has Yukawa coupling unification since quarks and leptons obtain their masses from a single Yukawa coupling. Neutrinos obtain acceptably small masses through a see-saw mechanism. Coloured triplets that couple to matter fields are naturally split from the coexisting isodoublets without the need of any numerical fine tuning.Comment: 15 pages, Latex2e, three figures included, comments added, published versio

Which “we” should I be? Conflict between social identities in consumer choice

Prior research has found that when a social identity is salient, consumers choose products consistent with that identity. However, consumers possess multiple social identities (e.g., family identity, professional identity) (Brewer 2008), which may sometimes conflict during decision-making. Little is known about how consumers respond when forced to choose between two salient, conflicting identities. The present dissertation fills this gap, proposing an important consequence of identity conflict in choice: mixed emotions (Williams and Aaker 2002). While consumers feel good about choosing in line with one identity, they simultaneously feel bad about choosing against another. Studies 1 and 2 of this dissertation document these mixed emotions, showing they are greater among consumers for whom the conflicting identities are important. Study 3 shows that these mixed emotions carry over, making consumers feel more distant from individuals who are associated with the identities and who benefited from the choice (e.g., friends, relatives). Consumers may worry that these individuals take the difficult choice for granted. The final three studies examine how consumers cope with (try to reduce) these consequences of social identity conflict. Since the identities are social, consumers may cope through support from individuals who are associated with the identities and who benefited from the choice. Study 4 reveals that support acknowledging the mixed emotions—compared to support focusing only on the positive—reduces mixed emotions, particularly when the identities are important to consumers. Such support may convey to consumers that the individuals are grateful for the choice and do not take it for granted. Study 5 shows this effect and finds that acknowledgement is most effective at reducing mixed emotions when it includes an expression of gratitude. Study 6 explores whether some forms of support fail to reduce mixed emotions yet still prevent relationship distancing. In sum, this research examines (1) how consumers react when forced to choose between salient, conflicting social identities and (2) how social support helps consumers cope with the resultant mixed emotions (rather than negative emotion, as in prior work) and relationship distancing. These contributions are important for helping consumers feel comfortable with their choices when social identities conflict