Gauging the bulk: generalized gauging maps and holographic codes

Gauging is a general procedure for mapping a quantum many-body system with a global symmetry to one with a local gauge symmetry. We consider a generalized gauging map that does not enforce gauge symmetry at all lattice sites, and show that it is an isometry on the full input space including all charged sectors. We apply this generalized gauging map to convert global-symmetric bulk systems of holographic codes to gauge-symmetric bulk systems, and vice versa, while preserving duality with a global-symmetric boundary. We separately construct holographic codes with gauge-symmetric bulk systems by directly imposing gauge-invariance constraints onto existing holographic codes, and show that the resulting bulk gauge symmetries are dual to boundary global symmetries. Combining these ideas produces a toy model that captures several interesting features of holography - it exhibits a rudimentary sort of dynamical duality, can be modified to demonstrate the relationship between metric fluctuations and approximate error-correction, and serves as an illustration for certain no-go theorems concerning symmetries in holography. Finally, we apply the generalized gauging map to construct codes with arbitrary transversal gate sets - for any compact Lie group, we use a symmetry-preserving truncation scheme to construct covariant finite-dimensional approximate holographic codes.Comment: 69 pages, 13 figure

The Efficiency-Equity Trade-off, Self-Interest, and Moral Principles in Health and Safety Valuation

Policy makers try to take account of public preferences when making trade-offs between policy options. Yet most estimates of the value of health and safety reflect only individuals’ self-interested preferences, neglecting their preferences over the distribution of public resources. We conduct an experiment in which participants choose between policy options that differ in their efficiency (expected number of fatalities or cases of ill health they would prevent) and their equity (defined in terms of the balance of risk reductions for different sections of the population). The policy options were framed as interventions to improve a hypothetical city’s water supply that would reduce the risk of death or ill health for people in different areas of the city to varying degrees. In order to examine whether self-interest would affect the trade-offs, we asked half of the sample about scenarios where they would personally benefit from some options. Our results suggest that efficiency is the most important single factor determining preferences between policy options, but decisions were influenced almost as much by equity as by efficiency. The effect of self-interest was smaller than that of the general concern for efficiency. We also elicited participants’ stated moral principles regarding trade-offs between equity, efficiency and self-interest, and found that their expressed principles were well-aligned with their choices. Our findings contribute to the growing evidence that distributional concerns matter when evaluating health interventions