相关论文: Lattice W-algebras and logarithmic CFTs

I review motivations for the study of supersymmetric field theories by lattice techniques. In particular, some of the more interesting potential applications are described. These are models of quantum gravity, that rely on the AdS/CFT…

It is believed that any classical gauge symmetry gives rise to an L$_\infty$ algebra. Based on the recently realized relation between classical ${\cal W}$ algebras and L$_\infty$ algebras, we analyze how this generalizes to the quantum…

Warped conformal field theories (WCFTs) are two-dimensional non-relativistic systems, with a chiral scaling and shift symmetry. We present a detailed derivation of the near-extremal limit for their torus partition function. This limit…

We consider the continuum scaling limit of the infinite series of Yang-Baxter integrable logarithmic minimal models LM(p,p') as `rational' logarithmic conformal field theories with extended W symmetry. The representation content is found to…

We consider lattice analogues of some conformal theories, including WZW and Toda models. We describe discrete versions of Drinfeld-Sokolov reduction and Sugawara construction for the WZW model. We formulate perturbation theory in chiral…

Quadratic form reduction and lattice reduction are fundamental tools in computational number theory and in computer science, especially in cryptography. The celebrated Lenstra-Lenstra-Lov\'asz reduction algorithm (so-called LLL) has been…

We classify mobile Pauli stabilizer codes up to gapped interfaces and coarse-graining using the framework of algebraic $\mathrm{L}$-theory. We compare this classification with that of framed TQFTs, theories that arise naturally in the…

We investigate orbifolds of lattice conformal field theories with the goal of constructing theories with large gap. We consider Barnes-Wall lattices, which are a family of lattices with no short vectors, and orbifold by an extraspecial…

We study various aspects of warped conformal field theories (WCFTs) in two dimensions. We find new Lagrangian WCFTs, and show that all known Lagrangian WCFTs are local only after an infinite tuning. We deduce the anomalies of WCFTs and…

Two-dimensional critical percolation is the member LM(2,3) of the infinite series of Yang-Baxter integrable logarithmic minimal models LM(p,p'). We consider the continuum scaling limit of this lattice model as a `rational' logarithmic…

Recent work using a large-charge expansion for the $O(N)$ Wilson-Fisher conformal field theory has shown that the anomalous dimensions of large-charge operators can be expressed in terms of a few low-energy constants (LECs) of a…

We study W-algebras obtained by quantum Hamiltonian reduction of $sl(Mn)$ associated to the $sl(2)$ embedding of rectangular type. The algebra can be realized as the asymptotic symmetry of higher spin gravity with $M \times M$ matrix valued…

We study the scalar modes of linear perturbations in loop quantum cosmology. This is done on a lattice where each cell is taken to be homogeneous and isotropic and can be quantized via standard homogeneous loop quantum cosmology techniques.…

One major systematic uncertainty of lattice QCD results is due to the continuum extrapolation. For an asymptotically free theory like QCD one finds corrections of the form $a^{n_\mathrm{min}}[2b_0\bar{g}^2(1/a)]^{\hat{\Gamma}_i}$ with…

Logarithmic conformal field theories are based on vertex algebras with non-semisimple representation categories. While examples of such theories have been known for more than 25 years, some crucial aspects of local logarithmic CFTs have…

We show how to derive Catterall's supersymmetric lattice gauge theories directly from the general principle of orbifolding followed by a variant of the usual deconstruction. These theories are forced to be complexified due to a clash…

When a subgroup of the flavor symmetry group of a gauge theory is weakly coupled to additional gauge fields, the vacuum tends to align such that the gauged subgroup is unbroken. At the same time, the lattice discretization typically breaks…

Conformal interfaces separating two conformal field theories (CFTs) provide maps between different CFTs, and naturally exist in nature as domain walls between different phases. One particularly interesting construction of a conformal…

The major obstacle to a supersymmetric theory on the lattice is the failure of the Leibniz rule. We analyze this issue by using the Wess-Zumino model and a general Ginsparg-Wilson operator, which is local and free of species doublers. We…

We propose a general frame work for deriving the OPEs within a logarithmic conformal field theory (LCFT). This naturally leads to the emergence of a logarithmic partner of the energy momentum tensor within an LCFT, and implies that the…