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1. Universal thermalization dynamics in (1+1)d QFTs

   https://doi.org/10.21468/SciPostPhys.18.6.177  

   Davison, Richard; Delacrétaz, Luca V (January 2025, SciPost Physics)

   We identify the universal mechanism behind the thermalization of (1+1)d QFTs at high and low temperatures. Viewing these theories as CFTs perturbed by relevant or irrelevant deformations, we show that conformal perturbation theory in the thermal state breaks down at late times allowing for the emergence of hydrodynamics. This breakdown occurs universally due to the unsuppressed exchange of stress tensors near the lightcone. Furthermore, for theories with central chargec→∞ $c\to \infty$we solve for the emergent hydrodynamic theory to all orders in the gradient expansion by arguing that all transport parameters appearing in two-point functions have universal expressions in terms of the scaling dimension\Delta $\Delta$of the perturbation. The radius of convergence of the hydrodynamic dispersion relations provides an early time cutoff for hydrodynamics, which agrees with the time scale at which conformal perturbation theory breaks down. 

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2. A $$d^{1/2+o(1)}$$ Monotonicity Tester for Boolean Functions on $$d$$-Dimensional Hypergrids

   Hadley Black, Deeparnab Chakrabarty (November 2023, Annual Symposium on Foundations of Computer Science)

   Monotonicity testing of Boolean functions on the hypergrid, $$f:[n]^d \to \{0,1\}$$, is a classic topic in property testing. Determining the non-adaptive complexity of this problem is an important open question. For arbitrary $$n$$, [Black-Chakrabarty-Seshadhri, SODA 2020] describe a tester with query complexity $$\widetilde{O}(\varepsilon^{-4/3}d^{5/6})$$. This complexity is independent of $$n$$, but has a suboptimal dependence on $$d$$. Recently, [Braverman-Khot-Kindler-Minzer, ITCS 2023] and [Black-Chakrabarty-Seshadhri, STOC 2023] describe $$\widetilde{O}(\varepsilon^{-2} n^3\sqrt{d})$$ and $$\widetilde{O}(\varepsilon^{-2} n\sqrt{d})$$-query testers, respectively. These testers have an almost optimal dependence on $$d$$, but a suboptimal polynomial dependence on $$n$$. \smallskip In this paper, we describe a non-adaptive, one-sided monotonicity tester with query complexity $$O(\varepsilon^{-2} d^{1/2 + o(1)})$$, \emph{independent} of $$n$$. Up to the $$d^{o(1)}$$-factors, our result resolves the non-adaptive complexity of monotonicity testing for Boolean functions on hypergrids. The independence of $$n$$ yields a non-adaptive, one-sided $$O(\varepsilon^{-2} d^{1/2 + o(1)})$$-query monotonicity tester for Boolean functions $$f:\mathbb{R}^d \to \{0,1\}$$ associated with an arbitrary product measure. 

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3. A d^(1/2+o(1)) Monotonicity Tester for Boolean Functions on d-Dimensional Hypergrids

   https://doi.org/10.1109/FOCS57990.2023.00110  

   Black, Hadley; Chakrabarty, Deeparnab; Seshadhri, C. (November 2023, Annual Symposium on Foundations of Computer Science)
4. Absolute anomalies in (2+1)D symmetry-enriched topological states and exact (3+1)D constructions

   https://doi.org/10.1103/PhysRevResearch.2.043033  

   Bulmash, Daniel; Barkeshli, Maissam (October 2020, Physical Review Research)

   null (Ed.)
5. Gauging U(1) symmetry in (2+1)d topological phases

   https://doi.org/10.21468/SciPostPhys.12.6.202  

   Cheng, Meng; Jian, Chao-Ming (January 2022, SciPost Physics)

   We study the gauging of a global U(1) symmetry in a gapped system in(2+1)d. The gauging procedure has been well-understood for a finiteglobal symmetry group, which leads to a new gapped phase with emergentgauge structure and can be described algebraically using themathematical framework of modular tensor category (MTC). We develop acategorical description of U(1) gauging in a MTC, taking into accountthe dynamics of U(1) gauge field absent in the finite group case. Whenthe ungauged system has a non-zero Hall conductance, the gauged theoryremains gapped and we determine the complete set of anyon data for thegauged theory. On the other hand, when the Hall conductance vanishes, weargue that gauging has the same effect of condensing a special Abeliananyon nucleated by inserting 2\pi 2 π U(1) flux. We apply our procedure to theSU(2) _k k MTCs and derive the full MTC data for the \mathbb{Z}_k ℤ k parafermion MTCs. We also discuss a dual U(1) symmetry that emergesafter the original U(1) symmetry of an MTC is gauged. 

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