Related papers: Verlinde lines, anyon permutations and commutant p…
We study the electronic properties of a novel topological defect structure for graphene interspersed with C558-line defects along the Armchair boundary. This system has the topological property of being topologically three-periodic and the…
We initiate a systematic investigation of endomorphisms of graph C*-algebras C*(E), extending several known results on endomorphisms of the Cuntz algebras O_n. Most but not all of this study is focused on endomorphisms which permute the…
$T\bar{T}$ deformed conformal field theories can be reformulated as worldsheet theories of non-critical strings. We use this correspondence to compute and study the $T\bar{T}$ deformed partition sum of a symmetric product CFT. We find that…
Topological defects are ubiquitous, they manifest in a wide variety of systems such as liquid crystals, magnets or superconductors. The recent quest for nonabelian anyons in condensed matter physics stimulates the interest for topological…
We study fermionic non-invertible symmetries in (1+1)d, which are generalized global symmetries that mix fermion parity symmetry with other invertible and non-invertible internal symmetries. Such symmetries are described by fermionic fusion…
The study of critical quantum many-body systems through conformal field theory (CFT) is one of the pillars of modern quantum physics. Certain CFTs are also understood to be dual to higher-dimensional theories of gravity via the anti-de…
We identify Narain conformal field theories (CFTs) that correspond to code lattices for quantum error-correcting codes (QECC) over integers of cyclotomic fields $Q(\zeta_p)$ $(\zeta_p=e^{\frac{2\pi i}p})$ for general prime $p\geq 3$. This…
Verlinde's formula for rational vertex operator algebras computes the fusion rules from the modular transformations of characters. In the non semisimple and non finite case, a logarithmic Verlinde formula has been proposed together with…
We study ${\mathcal N}=(1,0)$ six-dimensional theories living on defects of non-geometric backgrounds of the $E_8\times E_8$ and the $\text{Spin}(32)/{\mathbb Z}_2$ heterotic strings. Such configurations can be analyzed by dualizing to…
The topological part of the M-theory partition function was shown by Witten to be encoded in the index of an E8 bundle in eleven dimensions. This partition function is, however, not automatically anomaly-free. We observe here that the…
We resolve a puzzle in the theory of strings propagating on locally flat spacetimes with nontrivial Wilson lines for stringy Z_N gauge symmetries. We find that strings probing such backgrounds are described by consistent worldsheet CFTs.…
Yang-Baxter integrable dense $A_1^{(1)}$ and dilute $A_2^{(2)}$ loop models are considered on the torus in their simplest physical regimes. A combination of boundary conditions $(h,v)$ is applied in the horizontal and vertical directions…
We propose a reformulation of the conformal perturbation theory of the correlation functions in $J\bar{J}$-deformed CFTs as a dressing on the deformed operators, that matches both bare and renormalized perturbation theory. The key is to use…
We study the superconformal index of five-dimensional SCFTs and the sphere partition function of four-dimensional gauge theories with eight supercharges in the presence of co-dimension two half-BPS defects. We derive a prescription which is…
Modular invariance imposes rigid constrains on the partition functions of two-dimensional conformal field theories. Many fundamental results follow strictly from modular invariance, giving rise to the numerical modular bootstrap program.…
We show how to construct correlators for the $CFT_1$ which is dual to non-commutative $AdS_2$ ($ncAdS_2$). We do it explicitly for the example of the massless scalar field on Euclidean $ncAdS_2$. $ncAdS_2$ is the quantization of $AdS_2$…
We use the numerical bootstrap to study conformal line defects with $O(2)$ global symmetry. Our results are very general and capture in particular conformal line defects originating from bulk CFTs with a continuous global symmetry, which…
We review recent progress in the study of line defects in three-dimensional Chern-Simons-matter superconformal field theories, notably the ABJM theory. The first part is focused on kinematical defects supporting a topological sector of the…
Recently, a special type of non-conformal line defect, known as thin-shell operator, has played a key role in demonstrating the chaotic nature of the high energy sector in AdS$_3$/CFT$_2$. The chaotic nature was revealed concretely through…
We propose a general formalism to characterize orientational frustration of smectic liquid crystals in confinement by interpreting the emerging networks of grain boundaries as objects with a topological charge. In a formal idealization,…