Related papers: Parafermionizing the Monster
We consider toy models of holography arising from 3d Chern-Simons theory. In this context a duality to an ensemble average over 2d CFTs has been recently proposed. We put forward an alternative approach in which, rather than summing over…
Let $p>0$ be a prime, $G$ be a finite $p$-group and $\Bbbk$ be an algebraically closed field of characteristic $p$. Dave Benson has conjectured that if $p=2$ and $V$ is an odd-dimensional indecomposable representation of $G$ then all…
We propose an elegant formulation of parafermionic algebra and parasupersymmetry of arbitrary order in quantum many-body systems without recourse to any specific matrix representation of parafermionic operators and any kind of deformed…
Non-abelian Chern-Simons theories coupled to fermions are known to provide an interesting class of non-supersymmetric conformal fixed points \cite{Giombi:2011kc}. These theories, particularly those based on bifundamental matter, are…
Let $\mathfrak g$ be a finite-dimensional Lie algebra. The symmetric algebra $\mathcal S(\mathfrak g)$ is equipped with the standard Lie-Poisson bracket. In this paper, we elaborate on a surprising observation that one naturally associates…
Discrete spacetime symmetries of parity P or reflection R, and time-reversal T, act naively as $\mathbb{Z}_2$-involutions in the passive transformation on the spacetime coordinates; but together with a charge conjugation C, the total…
We show that the single-mode parafermionic type systems possess supersymmetry, which is based on the symmetry of characteristic functions of the parafermions related to the generalized deformed oscillator of Daskaloyannis et al. The…
Generalized global symmetries, in particular non-invertible and categorical symmetries, have become a focal point in the recent study of quantum field theory (QFT). In this paper, we investigate aspects of symmetry topological field…
We hypothesize a new and more complete set of anomalies of certain quantum field theories (QFTs) and then give an eclectic verification. First, we propose a set of 't Hooft higher anomalies of 4d time-reversal symmetric pure…
In this paper we discuss gauging noninvertible zero-form symmetries in two dimensions. We specialize to certain gaugeable cases, specifically, fusion categories of the form Rep(H) for H a suitable Hopf algebra (which includes the special…
Let $p$ be a prime and $\mathcal{K}$ be an imaginary quadratic field. In this paper we generalize a recent construction of a new type of $p$-adic $L$-function and $p$-adic Waldspurger formula by Andreatta-Iovita for $p$ non-split in…
Let $V$ be a rational, selfdual, $C_2$-cofinite vertex operator algebra of CFT type, and $G$ a finite automorphism group of $V.$ It is proved that the kernel of the representation of the modular group on twisted conformal blocks associated…
Some solutions to the strong CP problem assume that CP symmetry is a gauge symmetry, which is then spontaneously broken. For this scenario to be possible, the CP symmetry should not have any nonperturbative (global) anomalies. In this…
In previous work [Rosenbaum M. et al., J. Phys. A: Math. Theor. 40 (2007), 10367-10382, hep-th/0611160] we have shown how for canonical parametrized field theories, where space-time is placed on the same footing as the other fields in the…
It is known that the 't Hooft anomalies of invertible global symmetries can be characterized by an invertible TQFT in one higher dimension. The analogous statement remains to be understood for non-invertible symmetries. In this note we…
Many six-dimensional $(1,0)$ SCFTs are known to fall into families labelled by nilpotent orbits of certain simple Lie algebras. For each of the three infinite series of such families, we show that the anomalies for the continuous zero-form…
We present a family of conformal field theories (or candidates for CFTs) that is build on extremal partition functions. Spectra of these theories can be decomposed into the irreducible representations of the Fischer-Griess Monster sporadic…
We investigate orbifold constructions of conformal field theories from lattices by no-fixed-point automorphisms (NFPA's) $Z_p$ for $p$ prime, $p>2$, concentrating on the case $p=3$. Explicit expressions are given for most of the relevant…
What comprises a global symmetry of a Quantum Field Theory (QFT) has been vastly expanded in the past 10 years to include not only symmetries acting on higher-dimensional defects, but also most recently symmetries which do not have an…
Classifying endotrivial kG-modules, i.e., elements of the Picard group of the stable module category for an arbitrary finite group G, has been a long-running quest. By deep work of Dade, Alperin, Carlson, Thevenaz, and others, it has been…