Related papers: Unified Einstein-Virasoro Master Equation in the G…
Following recent advances in the local theory of current-algebraic orbifolds, we study various geometric properties of the general WZW orbifold, the general coset orbifold and a large class of (non-linear) sigma model orbifolds. Phase-space…
Vertical density matrix algorithm (VDMA), a tensor product state formulation of the ``higher-dimensional'' density matrix renormalization group, is applied to the spin 1/2 antiferromagnetic XXZ model on the checkerboard lattice. The VDMA…
We construct the quantum versions of the monodromy matrices of KdV theory. The traces of these quantum monodromy matrices, which will be called as ``${\bf T}$-operators'', act in highest weight Virasoro modules. The ${\bf T}$-operators…
Let $A_n=\mathbb{C}[t_i^{\pm1},~1\leq i\leq n]$ be the algebra of Laurent polynomials in $n$-variables. Let $\mu=(\mu_1,\ldots,\mu_n)$ be a generic vector in $\mathbb{C}^n$ and $\Gamma_{\mu}=\{\mu\cdot\alpha,\alpha\in \mathbb{Z}^n\}$ where…
Generalized supergravity equations (GSEs) were originally proposed as a modification of the standard IIB supergravity equations to satisfy the background of $\eta$-deformed $AdS_5 \times S^5$ introduced by Arutyunov {\it et al}. In this…
This paper provides a unified framework resolving two long-standing problems: the intrinsic construction of global quantum gauge groups for braided tensor $C^*$-categories (the Doplicher-Roberts problem) and the direct proof of the…
We derive the generalized Gauss-Codazzi-Mainardi (GCM) equation for a general affine connection with torsion and non-metricity. Moreover, we show that the metric compatibility and torsionless condition of a connection on a manifold are…
We construct a centerless W-infinity type of algebra in terms of a generator of a centerless Virasoro algebra and an abelian spin-1 current. This algebra conventionally emerges in the study of pseudo-differential operators on a circle or…
We solve Virasoro constraints on the KP hierarchy in terms of minimal conformal models. The constraints we start with are implemented by the Virasoro generators depending on a background charge $Q$. Then the solutions to the constraints are…
The affine current algebra for Lie superalgebras is examined. The bilinear invariant forms of the Lie superalgebra can be either degenerate or non-degenerate. We give the conditions for a Virasoro construction, in which the currents are…
The approximate stress-energy tensor of the quantized massive scalar, spinor and vector fields in the spatially flat Friedman-Robertson-Walker universe is constructed. It is shown that for the scalar fields with arbitrary curvature…
We demonstrate that a supersymmetric theory twisted on a K\"ahler four manifold $M=\Sigma_1 \times \Sigma_2 ,$ where $\Sigma_{1,2}$ are 2D Riemann surfaces, possesses a "left-moving" conformal stress tensor on $\Sigma_1$ ($\Sigma_2$) in the…
Linear spinor fields are a generalization of the Dirac field that have direct correspondence with the known physics of fermions, inherent causality properties in their most fundamental constructions, and positive mass eigenvalues for all…
We prove a general mirror duality theorem for a subalgebra $U$ of a simple conformal vertex algebra $A$ and its commutant $V=\mathrm{Com}_A(U)$. Specifically, we assume that $A\cong\bigoplus_{i\in I} U_i\otimes V_i$ as a $U\otimes…
We find new duality transformations which allow us to construct the stress tensors of all the twisted sectors of any orbifold A(H)/H, where A(H) is the set of all current-algebraic conformal field theories with a finite symmetry group H…
We use the Kontsevich--Miwa transform to relate the Virasoro constraints on integrable hierarchies with the David-Distler-Kawai formalism of gravity-coupled conformal theories. The derivation relies on evaluating the energy-momentum tensor…
Within the framework of a local expansion of the logarithm of the O(N) sigma-model vacuum functional, valid for slowly varying fields, the modified Virasoro algebra is studied. The operator-like central charge term is given, up to second…
Random tensor models for a generic complex tensor generalize matrix models in arbitrary dimensions and yield a theory of random geometries. They support a 1/N expansion dominated by graphs of spherical topology. Their Schwinger Dyson…
We consider exceptional vertex operator algebras for which particular Casimir vectors constructed from the primary vectors of lowest conformal weight are Virasoro descendants of the vacuum. We discuss constraints on these theories that…
Entanglement entropy and entanglement spectrum have been widely used to characterize quantum entanglement in extended many-body systems. Given a pure state of the system and a division into regions $A$ and $B$, they can be obtained in terms…