An official website of the United States government
A<sc>bstract</sc> In this paper, we discuss how gauging one-form symmetries in Chern-Simons theories is implemented in an A-twisted topological open string theory. For example, the contribution from a fixed H/Z bundle on a three-manifold M, arising in a BZ gauging of H Chern-Simons, for Z a finite subgroup of the center of H, is described by an open string worldsheet theory whose bulk is a sigma model with target a Z-gerbe (a bundle of one-form symmetries) over T∗M, of characteristic class determined by the H/Z bundle. We give a worldsheet picture of the decomposition of one-form-symmetry-gauged Chern-Simons in three dimensions, and we describe how a target-space constraint on bundles arising in the gauged Chern-Simons theory has a natural worldsheet realization. Our proposal provides examples of the expected correspondence between worldsheet global higher-form symmetries, and target-space gauged higher-form symmetries.
more »
« less
MONOPOLES AND LANDAU-GINZBURG MODELS I
The end point of this series of papers is to construct the monopole Floer ho- mology for 3-manifolds with torus boundary. In the first paper, we explain the idea from the standpoint of gauged Landau-Ginzburg models and address a few model problems related to the compactness of moduli spaces, using a Bochner-type formula associated to the gauged Witten equations.
more »
« less
- Award ID(s):
- 1808794
- PAR ID:
- 10168548
- Date Published:
- Journal Name:
- ArXivorg
- ISSN:
- 2331-8422
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Abstract Streamflow prediction is a long‐standing hydrologic problem. Development of models for streamflow prediction often requires incorporation of catchment physical descriptors to characterize the associated complex hydrological processes. Across different scales of catchments, these physical descriptors also allow models to extrapolate hydrologic information from one catchment to others, a process referred to as “regionalization”. Recently, in gauged basin scenarios, deep learning models have been shown to achieve state of the art regionalization performance by building a global hydrologic model. These models predict streamflow given catchment physical descriptors and weather forcing data. However, these physical descriptors are by their nature uncertain, sometimes incomplete, or even unavailable in certain cases, which limits the applicability of this approach. In this paper, we show that by assigning a vector of random values as a surrogate for catchment physical descriptors, we can achieve robust regionalization performance under a gauged prediction scenario. Our results show that the deep learning model using our proposed random vector approach achieves a predictive performance comparable to that of the model using actual physical descriptors. The random vector approach yields robust performance under different data sparsity scenarios and deep learning model selections. Furthermore, based on the use of random vectors, high‐dimensional characterization improves regionalization performance in gauged basin scenario when physical descriptors are uncertain, or insufficient.more » « less
-
A bstract Non-topological solitons such as Q-balls and Q-shells have been studied for scalar fields invariant under global and gauged U(1) symmetries. We generalize this frame-work to include a Proca mass for the gauge boson, which can arise either from spontaneous symmetry breaking or via the Stückelberg mechanism. A heavy (light) gauge boson leads to solitons reminiscent of the global (gauged) case, but for intermediate values these Proca solitons exhibit completely novel features such as disconnected regions of viable parameter space and Q-shells with unbounded radius. We provide numerical solutions and excellent analytic approximations for both Proca Q-balls and Q-shells. These allow us to not only demonstrate the novel features numerically, but also understand and predict their origin analytically.more » « less
-
A<sc>bstract</sc> In this paper we discuss gauging noninvertible zero-form symmetries in two dimensions, extending our previous work. Specifically, in this work we discuss more general gauged noninvertible symmetries in which the noninvertible symmetry is not multiplicity free, and discuss the case of Rep(A4) in detail. We realize Rep(A4) gaugings for thec= 1 CFT at the exceptional point in the moduli space and find new self-duality under gauging a certain non-group algebra object, leading to a larger noninvertible symmetry Rep(SL(2, ℤ3)). We also discuss more general examples of decomposition in two-dimensional gauge theories with trivially-acting gauged noninvertible symmetries.more » « less
-
We extend recent work on hydrodynamics with global multipolarsymmetries — known as “fracton hydrodynamics” — to systems in which themultipolar symmetries are gauged. We refer to the latter as “fractonmagnetohydrodynamics”, in analogy to conventional magnetohydrodynamics(MHD), which governs systems with gauged charge conservation. We showthat fracton MHD arises naturally from higher-rank Maxwell’s equationsand in systems with one-form symmetries obeying certain constraints;while we focus on “minimal” higher-rank generalizations of MHD thatrealize diffusion, our methods may also be used to identify other, moreexotic hydrodynamic theories (e.g., with magnetic subdiffusion). Incontrast to semi-microscopic derivations of MHD, our approach elucidatesthe origin of the hydrodynamic modes by identifying the correspondinghigher-form symmetries. Being rooted in symmetries, the hydrodynamicmodes may persist even when the semi-microscopic equations no longerprovide an accurate description of the system.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- The DOI is not currently available.
