Significance When we grasp an object, thousands of tactile nerve fibers become activated and inform us about its physical properties (e.g., shape, size, texture). Although the individual have been described, our understanding how object information is encoded in populations remains primitive. To fill this gap, developed a simulation that incorporates much what known skin mechanics fibers. We show simulated match biological ones across wide range conditions sampled from literature. then can...

The authors provide a comprehensive study of the role boundary conditions in presence generalized non-invertible symmetries, beginning with question when are symmetric under those symmetries. They find different categories (which would be identical normal symmetries) and discuss their relation to 't Hooft anomalies, gauging, RG flows.

Subsystem symmetry has emerged as a powerful organizing principle for unconventional quantum phases of matter, most prominently fracton topological orders. Here, we focus on special subclass such symmetries, known higher-form subsystem which allow us to adapt tools from the study conventional setting. We demonstrate that certain transitions out familiar phases, including X-cube model, can be understood in terms spontaneous breaking symmetries. find simple pictures these seemingly complicated...

A (1 + 1)D unitary bosonic rational conformal field theory (RCFT) may be organized according to its genus, a tuple (c,C) consisting of central charge c and modular tensor category C which describes the (2 topological quantum for maximally extended chiral algebra forms holomorphic boundary condition. We establish number results pertaining RCFTs in “small” genera, by we informally mean genera with primary operators rank(C) both not too large. start completely solving bootstrap problem theories...

Kitaev's quantum double models in 2D provide some of the most commonly studied examples topological order. In particular, ground space is thought to yield a error-correcting code. We offer an explicit proof that this case for arbitrary finite groups. Actually stronger claim shown: any two states with zero energy density contractible region must have same reduced state region. Alternatively, local properties gauge-invariant are fully determined by specifying its holonomies trivial. contrast...

We describe a relationship between the representation theory of Thompson sporadic group and weakly holomorphic modular form weight one-half that appears in work Borcherds Zagier on products traces singular moduli. conjecture existence an infinite dimensional graded module for provide evidence our by constructing McKay--Thompson series each conjugacy class coincide with forms higher level. also observe discriminant property this moonshine is closely related to conjectured exist Umbral Moonshine.

We derive a refined version of the Affleck-Ludwig-Cardy formula for <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mn>1</a:mn><a:mo>+</a:mo><a:mn>1</a:mn><a:mi mathvariant="normal">D</a:mi></a:mrow></a:math> conformal field theory, which controls asymptotic density high energy states on an interval transforming under given representation noninvertible global symmetry. use this to determine universal leading and subleading contributions symmetry-resolved...

By leveraging the physics of Higgs branch, we argue that conformal central charges <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>a</a:mi></a:math> and <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>c</c:mi></c:math> an arbitrary 4D <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi mathvariant="script">N</e:mi><e:mo>=</e:mo><e:mn>2</e:mn></e:math> superconformal field theory (SCFT) are rational numbers. Our...

What does it mean for a boundary condition to be symmetric with respect non-invertible global symmetry? We discuss two possible definitions in 1+1d. On the one hand, we call weakly if symmetry defects can terminate topologically on it, leading conserved operators Hamiltonian an interval (in open string channel). other strongly corresponding state is eigenstate of closed These notions boundaries are equivalent invertible symmetries, but bifurcate symmetries. relation anomalies, where observe...

Abstract The emerging study of fractons, a new type quasi‐particle with restricted mobility, has motivated the construction several classes interesting continuum quantum field theories novel properties. One such class consists foliated which, roughly, are built by coupling together fields supported on leaves foliations spacetime. Another approach, which we refer to as exotic theory , focuses constructing Lagrangians consistent special symmetries (like subsystem symmetries) that adjacent...

We show that certain BPS counting functions for both fundamental strings and arising from fivebranes wrapping divisors in Calabi--Yau threefolds naturally give rise to skew-holomorphic Jacobi forms at rational attractor points the moduli space of string compactifications. For M5-branes these are weight negative one, case multiple mock arise. further find simple examples related (mock) two play starring roles moonshine. discuss involving on complex projective plane, del Pezzo surfaces degree...

A (1+1)D unitary bosonic rational conformal field theory (RCFT) may be organized according to its genus, a tuple $(c,\mathscr{C})$ consisting of central charge $c$ and modular tensor category $\mathscr{C}$ which describes the (2+1)D topological quantum (TQFT) for maximally extended chiral algebra forms holomorphic boundary condition. We establish number results pertaining RCFTs in "small" genera, by we informally mean genera with primary operators $\mathrm{rank}(\mathscr{C})$ both not too...

In this first of a series two papers, we investigate different equivalence relations obtained by generalizing the notion genus even lattices to setting vertex operator algebras (or two-dimensional chiral algebras). The bulk relation was defined in arXiv:math/0209333 and groups (suitably regular) according their modular tensor category central charge. Hyperbolic arXiv:2004.01441 tests isomorphy after tensoring with hyperbolic plane algebra. Physically, rational are said belong same if they...

We introduce a class of generalized tube algebras which describe how finite, non-invertible global symmetries bosonic 1+1d QFTs act on operators sit at the intersection point collection boundaries and interfaces. develop 2+1d symmetry topological field theory (SymTFT) picture interfaces which, among other things, allows us to deduce representation these algebras. In particular, we initiate study character theory, echoing that finite groups, demonstrate many representation-theoretic...

We derive a refined version of the Affleck-Ludwig-Cardy formula for 1+1d conformal field theory, which controls asymptotic density high energy states on an interval transforming under given representation non-invertible global symmetry. use this to determine universal leading and sub-leading contributions symmetry-resolved entanglement entropy single interval. As concrete example, we show that ground state Hamiltonian in critical double Ising model enjoys Kac-Paljutkin $H_8$ Hopf algebra...

When can two strongly rational vertex operator algebras or 1+1d conformal field theories (RCFTs) be related by topological manipulations? For algebras, the term "topological manipulations" refers to operations like passing a extension restricting subalgebra; for RCFTs, manipulations include gauging (or orbifolding) finite subpart of generalized global symmetry interpolating new theory via line interface quantum dimension. Inspired results in even lattices, and also tensor categories, we say...

Subsystem symmetry has emerged as a powerful organizing principle for unconventional quantum phases of matter, most prominently fracton topological orders. Here, we focus on special subclass such symmetries, known higher-form subsystem which allow us to adapt tools from the study conventional setting. We demonstrate that certain transitions out familiar phases, including X-cube model, can be understood in terms spontaneous breaking symmetries. find simple pictures these seemingly complicated...

As Mathieu moonshine is a special case of umbral moonshine, Thompson (in half-integral weight) family similar relationships between finite groups and vector-valued modular forms certain kind. We call this penumbral moonshine. introduce explain some features phenomenon in work.

By leveraging the physics of Higgs branch, we argue that conformal central charges $a$ and $c$ an arbitrary 4d $N=2$ superconformal field theory (SCFT) are rational numbers. Our proof rationality is conditioned on a well-supported conjecture about how branch SCFT encoded in its protected chiral algebra. To establish $a$, further rely widely-believed technical assumption high-temperature limit index.