Related papers: Universal Correlators and Novel Cosets in 2d RCFT

In this work, we present a comprehensive study of holographic stress tensor correlators on general Riemann surfaces, extending beyond the previously well-studied torus cases to explore higher genus conformal field theories (CFTs) within the…

The four point function of Conformal Field Theories (CFT's) with global symmetry gives rise to multiple crossing symmetry constraints. We explicitly study the correlator of four scalar operators transforming in the fundamental…

It is shown that Weyl spinors in 4D Minkowski space are composed of primary fields of half-integer conformal weights. This yields representations of fermionic 2-point functions in terms of correlators of primary fields with a factorized…

Three-dimensional conformal field theories (CFTs) with slightly broken higher spin symmetry provide an interesting laboratory to study general properties of CFTs and their roles in the AdS/CFT correspondence. In this work we compute the…

Quasi-characters are vector-valued modular functions having an integral, but not necessarily positive, q-expansion. Using modular differential equations, a complete classification has been provided in arXiv:1810.09472 for the case of two…

We consider the family of renormalizable scalar QFTs with self-interacting potentials of highest monomial $\phi^{m}$ below their upper critical dimensions $d_c=\frac{2m}{m-2}$, and study them using a combination of CFT constraints,…

We continue our study of multipoint correlators of scalar fields on the $1d$ defect CFT generated by inserting operators along the Maldacena-Wilson line in $\mathcal{N} = 4$ SYM. We present a weak-coupling recursion relation that captures…

A quadratic Lie conformal algebra corresponds to a Hamiltonian pair in \cite{GD}, which plays fundamental roles in completely integrable systems. Moreover, it also corresponds to certain compatible pairs of a Lie algebra and a Novikov…

We calculate six invariant terms of a gravitational field theory that nonlinearly realizes the Conformal/Poincar\'e quotient, and reduce to the known conformal Galileons in the limit when only the conformal mode is kept. Five of the six…

We consider all connected and simply connected 7-dimensional Lie groups whose Lie algebras have nilradical $\g_{5,2} = \s \{X_1, X_2, X_3, X_4, X_5 \colon [X_1, X_2] = X_4, [X_1, X_3] = X_5\}$ of Dixmier. First, we give a geometric…

Trialities of $\mathcal{W}$-algebras are isomorphisms between the affine cosets of three different $\mathcal{W}$-(super)algebras, and were first conjectured in the physics literature by Gaiotto and Rap\v{c}\'ak. In this paper we prove…

We study quantum aspects of the recently constructed doubly lambda-deformed sigma-models representing the effective action of two WZW models interacting via current bilinears. We show that although the exact beta-functions and current…

We define and study generalized nil-Coxeter algebras associated to Coxeter groups. Motivated by a question of Coxeter (1957), we construct the first examples of such finite-dimensional algebras that are not the 'usual' nil-Coxeter algebras:…

The relationship between the quasi-exactly solvable problems and W-algebras is revealed. This relationship enabled one to formulate a new general method for building multi-dimensional and multi-channel exactly and quasi-exactly solvable…

The author derives new family of series representations for the values of the Riemann Zeta function $\zeta(s)$ at positive odd integers. For $n\in\mathbb{N}$, each of these series representing $\zeta(2n+1)$ converges remarkably rapidly with…

Lines generated by marginal deformations of WZW models are considered. The Weyl symmetry at the WZW point implies the existence of a duality symmetry on such lines. The duality is interpreted as a broken gauge symmetry in string theory. It…

Starting with a gentle approach to the AGT correspondence from its 6d origin, these notes provide a wide (albeit shallow) survey of the literature on numerous extensions of the correspondence up to early 2020. This is an extended writeup of…

Relative self-linking and linking "numbers" for pairs of knots in oriented 3-manifolds are defined in terms of intersection invariants of immersed surfaces in 4-manifolds. The resulting concordance invariants generalize the usual…

We construct a generalization of the cyclic $\lambda$-deformed models of \cite{Georgiou:2017oly} by relaxing the requirement that all the WZW models should have the same level $k$. Our theories are integrable and flow from a single UV point…

We find that multiple vertex algebras can arise from a single 4d $\mathcal{N}=2$ superconformal field theory (SCFT). The connection is given by the BPS monodromy operator $M$, which is a wall-crossing invariant quantity that captures the…