# Blencowe ## A consistent interacting massless higher-spin field theory in D=2+1 \[Links: [IOP](https://iopscience.iop.org/article/10.1088/0264-9381/6/4/005/meta)\] \[Abstract: Using the approach of Fradkin and Vasiliev (1987), an action is constructed in $2+1$ spacetime dimensions describing interacting massless fields of all integer and half-integer spins $s\ge3/2$. The action is associated with an infinite-dimensional superalgebra, denoted $shs(1, 2)(+)shs(1,2)$. Truncation to the spin 3/2-spin 2 sector gives the (1,1) type anti-de Sitter (AdS) supergravity theory corresponding to $osp(1,2; R)(+)osp(1,2; R)$. Various properties of the $D=3$ [[0421 Higher-spin gravity|higher-spin theory]], and its relevance to the higher-spin problem in four dimensions, are discussed.\] # Cardy ## Boundary Conditions, Fusion Rules and the Verlinde Formula \[Links: [Inspire](https://inspirehep.net/literature/25279)\] \[Abstract: [[0548 Boundary CFT|Boundary]] operators in conformal field theory are considered as arising from the juxtaposition of different types of boundary conditions. From this point of view, the operator content of the theory in an annulus may be related to the fusion rules. By considering the partition function in such a geometry, we give a simple derivation of the Verlinde formula.\] # Elitzur, Moore, Schwimmer, Seiberg ## Remarks on the Canonical Quantization of the Chern-Simons-Witten Theory \[Links: [Inspire](https://inspirehep.net/literature/277426)\] \[Abstract: We comment on some aspects of the canonical quantization of the [[0089 Chern-Simons theory|Chern-Simons-Witten theory]]. We carry out explicitly the quantization on several interesting surfaces. The connection to the related two dimensional theory is illustrated from different points of view.\] # Greene, Shapere, Vafa, Yau ## Stringy cosmic strings and noncompact Calabi-Yau manifolds \[Links: [Inspire](https://inspirehep.net/literature/282564), [DOI](https://doi.org/10.1016/0550-3213(90)90248-C)\] \[Abstract: We describe string vacuum configurations for which the radii (moduli) of the internal compact space vary in four-dimensional space-time, focusing on configurations which have the interpretation of [[0577 Cosmic string|cosmic strings]]. We will show that some of them admit Ricci-flat Kähler metrics (i.e. they correspond to noncompact Calabi-Yau manifolds), thus providing new vacuum solutions to the full string theory. One novel feature of some of these solutions is that the internal space decompactifies near the core of the cosmic string, without producing any physical singularities.\] # Ishibashi ## The Boundary and Crosscap States in Conformal Field Theories \[Links: [Inspire](https://inspirehep.net/literature/262763)\] \[Abstract: A method to obtain the boundary states and the crosscap states explicitly in various conformal field theories, is presented. This makes it possible to construct and analyse open string theories in several closed string backgrounds. We discuss the construction of such theories in the case of the backgrounds corresponding to the conformal field theories with $SU(2)$ current algebra symmetry.\] # Moore, Seiberg ## Classical and Quantum Conformal Field Theory \[Links: [Inspire](https://inspirehep.net/literature/264529)\] \[Abstract: We define chiral vertex operators and duality matrices and review the fundamental identities they satisfy. In order to understand the meaning of these equations, and therefore of conformal field theory, we define the classical limit of a conformal field theory as a limit in which the conformal weights of all primary fields vanish. The classical limit of the equations for the duality matrices in rational field theory together with some results of category theory, suggest that (quantum) conformal field theory should be regarded as a generalization of group theory.\] ## Classical vs quantum CFT - classical: conformal weights of primary fields are all zero; nothing but group theory - quantum: can be considered as generalisations of group theory # Tseytlin ## Sigma model approach to string theory \[Links: [DOI](https://doi.org/10.1142/S0217751X8900056X)\] \[Abstract: A review of the $\sigma$-model approach to derivation of effective string equations of motion for the massless fields is presented. We limit our consideration to the case of the tree approximation in the closed Bose string theory.\] # Witten ## Quantum field theory and the Jones polynomial \[Links: [DOI](https://doi.org/10.1007/BF01217730), [Inspire](https://inspirehep.net/literature/264818)\] \[Abstract: It is shown that $2+1$ dimensional quantum Yang-Mills theory, with an action consisting purely of the [[0089 Chern-Simons theory|Chern-Simons]] term, is exactly soluble and gives a natural framework for understanding the Jones polynomial of knot theory in three dimensional terms. In this version, the Jones polynomial can be generalized from $S^3$ to arbitrary three manifolds, giving invariants of three manifolds that are computable from a surgery presentation. These results shed a surprising new light on conformal field theory in $1+1$ dimensions.\] # Zabrodin ## Non-archimedean strings and Bruhat-Tits trees \[Links: [DOI](https://doi.org/10.1007/BF01238811)\] \[Abstract: It is shown that the Bruhat-Tits tree for the $p$-adic linear group $GL(2)$ is a natural non-archimedean analog of the open string world sheet. The boundary of the tree can be identified with the field of $p$-adic numbers. We construct a “lattice” quantum field theory on the Bruhat-Tits tree with a simple local lagrangian and show that it leads to the Freund-Olson amplitudes for emission processes of the particle states from the boundary.\]