A bstract We derive explicit formulae to compute the a and c central charges of four dimensional $$ \mathcal{N} $$ N = 2 superconformal field theories (SCFTs) directly from Coulomb branch related quantities. The formulae apply at arbitrary rank. We also discover general properties of the low-energy limit behavior of the flavor symmetry of $$ \mathcal{N} $$ N = 2 SCFTs which culminate with our $$ \mathcal{N} $$ N = 2 UV-IR simple flavor condition . This is done by determining precisely the relation between the integrand of the partition function of the topologically twisted version of the 4d $$ \mathcal{N} $$ N = 2 SCFTs and the singular locus of their Coulomb branches. The techniques developed here are extensively applied to many rank-2 SCFTs, including new ones, in a companion paper. This manuscript is dedicated to the memory of Rayshard Brooks, George Floyd, Breonna Taylor and the countless black lives taken by US police forces and still awaiting justice. Our hearts are with our colleagues of color who suffer daily the consequences of this racist world.
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Towards a classification of rank r $$ \mathcal{N} $$ = 2 SCFTs. Part II. Special Kahler stratification of the Coulomb branch
A bstract We study the stratification of the singular locus of four dimensional $$ \mathcal{N} $$ N = 2 Coulomb branches. We present a set of self-consistency conditions on this stratification which can be used to extend the classification of scale-invariant rank 1 Coulomb branch geometries to two complex dimensions, and beyond. The calculational simplicity of the arguments presented here stems from the fact that the main ingredients needed — the rank 1 deformation patterns and the pattern of inclusions of rank 2 strata — are discrete topological data which satisfy strong self-consistency conditions through their relationship to the central charges of the SCFT. This relationship of the stratification data to the central charges is used here, but is derived and explained in a companion paper [1] by one of the authors. We illustrate the use of these conditions by re-analyzing many previously-known examples of rank 2 SCFTs, and also by finding examples of new theories. The power of these conditions stems from the fact that for Coulomb branch stratifications a conjecturally complete list of physically allowed “elementary slices” is known. By contrast, constraining the possible elementary slices of symplectic singularities relevant for Higgs branch stratifications remains an open problem.
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- Award ID(s):
- 1914679
- NSF-PAR ID:
- 10339021
- Date Published:
- Journal Name:
- Journal of High Energy Physics
- Volume:
- 2020
- Issue:
- 12
- ISSN:
- 1029-8479
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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A bstract There is a well-known map from 4d $$ \mathcal{N} $$ N = 2 superconformal field theories (SCFTs) to 2d vertex operator algebras (VOAs). The 4d Schur index corresponds to the VOA vacuum character, and must be a solution with integral coefficients of a modular differential equation. This suggests a classification program for 4d $$ \mathcal{N} $$ N = 2 SCFTs that starts with modular differential equations and proceeds by imposing all known constraints that follow from the 4d → 2d map. This program becomes fully algorithmic once one specifies the order of the modular differential equation and the rank (complex dimension of the Coulomb branch) of the $$ \mathcal{N} $$ N = 2 theory. As a proof of concept, we apply the algorithm to the study of rank-two $$ \mathcal{N} $$ N = 2 SCFTs whose Schur indices satisfy a fourth-order untwisted modular differential equation. Scanning over a large number of putative cases, only 15 satisfy all of the constraints imposed by our algorithm, six of which correspond to known 4d SCFTs. More sophisticated constraints can be used to argue against the existence of the remaining nine cases. Altogether, this indicates that our knowledge of such rank-two SCFTs is surprisingly complete.more » « less
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Abstract The $p$-tensor Ising model is a one-parameter discrete exponential family for modeling dependent binary data, where the sufficient statistic is a multi-linear form of degree $p \geqslant 2$. This is a natural generalization of the matrix Ising model that provides a convenient mathematical framework for capturing, not just pairwise, but higher-order dependencies in complex relational data. In this paper, we consider the problem of estimating the natural parameter of the $p$-tensor Ising model given a single sample from the distribution on $N$ nodes. Our estimate is based on the maximum pseudolikelihood (MPL) method, which provides a computationally efficient algorithm for estimating the parameter that avoids computing the intractable partition function. We derive general conditions under which the MPL estimate is $\sqrt N$-consistent, that is, it converges to the true parameter at rate $1/\sqrt N$. Our conditions are robust enough to handle a variety of commonly used tensor Ising models, including spin glass models with random interactions and models where the rate of estimation undergoes a phase transition. In particular, this includes results on $\sqrt N$-consistency of the MPL estimate in the well-known $p$-spin Sherrington–Kirkpatrick model, spin systems on general $p$-uniform hypergraphs and Ising models on the hypergraph stochastic block model (HSBM). In fact, for the HSBM we pin down the exact location of the phase transition threshold, which is determined by the positivity of a certain mean-field variational problem, such that above this threshold the MPL estimate is $\sqrt N$-consistent, whereas below the threshold no estimator is consistent. Finally, we derive the precise fluctuations of the MPL estimate in the special case of the $p$-tensor Curie–Weiss model, which is the Ising model on the complete $p$-uniform hypergraph. An interesting consequence of our results is that the MPL estimate in the Curie–Weiss model saturates the Cramer–Rao lower bound at all points above the estimation threshold, that is, the MPL estimate incurs no loss in asymptotic statistical efficiency in the estimability regime, even though it is obtained by minimizing only an approximation of the true likelihood function for computational tractability.more » « less
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The Study on U.S. Parents’ Divisions of Labor During COVID-19 (SPDLC) collects longitudinal survey data from partnered U.S. parents that can be used to assess changes in parents’ divisions of domestic labor, divisions of paid labor, and well-being throughout and after the COVID-19 pandemic. The goal of SPDLC is to understand both the short- and long-term impacts of the pandemic for the gendered division of labor, work-family issues, and broader patterns of gender inequality.
Survey data for this study is collected using Prolifc (www.prolific.co), an opt-in online platform designed to facilitate scientific research. The sample is comprised U.S. adults who were residing with a romantic partner and at least one biological child (at the time of entry into the study). In each survey, parents answer questions about both themselves and their partners. Wave 1 of SPDLC was conducted in April 2020, and parents who participated in Wave 1 were asked about their division of labor both prior to (i.e., early March 2020) and one month after the pandemic began. Wave 2 of SPDLC was collected in November 2020. Parents who participated in Wave 1 were invited to participate again in Wave 2, and a new cohort of parents was also recruited to participate in the Wave 2 survey. Wave 3 of SPDLC was collected in October 2021. Parents who participated in either of the first two waves were invited to participate again in Wave 3, and another new cohort of parents was also recruited to participate in the Wave 3 survey. This research design (follow-up survey of panelists and new cross-section of parents at each wave) will continue through 2024, culminating in six waves of data spanning the period from March 2020 through October 2024. An estimated total of approximately 6,500 parents will be surveyed at least once throughout the duration of the study.
SPDLC data will be released to the public two years after data is collected; Waves 1 and 2 are currently publicly available. Wave 3 will be publicly available in October 2023, with subsequent waves becoming available yearly. Data will be available to download in both SPSS (.sav) and Stata (.dta) formats, and the following data files will be available: (1) a data file for each individual wave, which contains responses from all participants in that wave of data collection, (2) a longitudinal panel data file, which contains longitudinal follow-up data from all available waves, and (3) a repeated cross-section data file, which contains the repeated cross-section data (from new respondents at each wave) from all available waves. Codebooks for each survey wave and a detailed user guide describing the data are also available. Response Rates: Of the 1,157 parents who participated in Wave 1, 828 (72%) also participated in the Wave 2 study. Presence of Common Scales: The following established scales are included in the survey:- Self-Efficacy, adapted from Pearlin's mastery scale (Pearlin et al., 1981) and the Rosenberg self-esteem scale (Rosenberg, 2015) and taken from the American Changing Lives Survey
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To help provide estimates that are more representative of U.S. partnered parents, the SPDLC includes sampling weights. Weights can be included in statistical analyses to make estimates from the SPDLC sample representative of U.S. parents who reside with a romantic partner (married or cohabiting) and a child aged 18 or younger based on age, race/ethnicity, and gender. National estimates for the age, racial/ethnic, and gender profile of U.S. partnered parents were obtained using data from the 2020 Current Population Survey (CPS). Weights were calculated using an iterative raking method, such that the full sample in each data file matches the nationally representative CPS data in regard to the gender, age, and racial/ethnic distributions within the data. This variable is labeled CPSweightW2 in the Wave 2 dataset, and CPSweightLW2 in the longitudinal dataset (which includes Waves 1 and 2). There is not a weight variable included in the W1-W2 repeated cross-section data file.
Carlson, Daniel L. and Richard J. Petts. 2022. Study on U.S. Parents’ Divisions of Labor During COVID-19 User Guide: Waves 1-2.
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A bstract We develop an approach to the study of Coulomb branch operators in 3D $$ \mathcal{N} $$ N = 4 gauge theories and the associated quantization structure of their Coulomb branches. This structure is encoded in a one-dimensional TQFT subsector of the full 3D theory, which we describe by combining several techniques and ideas. The answer takes the form of an associative and noncommutative star product algebra on the Coulomb branch. For “good” and “ugly” theories (according to the Gaiotto-Witten classification), we also exhibit a trace map on this algebra, which allows for the computation of correlation functions and, in particular, guarantees that the star product satisfies a truncation condition. This work extends previous work on abelian theories to the non-abelian case by quantifying the monopole bubbling that describes screening of GNO boundary conditions. In our approach, monopole bubbling is determined from the algebraic consistency of the OPE. This also yields a physical proof of the Bullimore-Dimofte-Gaiotto abelianization description of the Coulomb branch.more » « less
- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1007/JHEP12(2020)022
