Related papers: A note on defect Mellin amplitudes
Celestial amplitudes are multiple Mellin transforms w.r.t. conformal dimensions. For arbitrary multiplicity $n$ of massless states in sufficiently high space--time dimension $D$ we perform all Mellin integrations and find an associahedron…
The generalized Verlinde formulae expressing traces of mapping classes corresponding to automorphisms of certain Riemann surfaces, and the congruence relations on allowed modular representations following from them are presented. The…
Differential equations are powerful tools in the study of correlation functions in conformal field theories (CFTs). Carrollian amplitudes behave as correlation functions of Carrollian CFT that holographically describes asymptotically flat…
To a finite quadratic module, that is, a finite abelian group D together with a non-singular quadratic form Q:D --> Q/Z, it is possible to associate a representation of either the modular group, SL(2,Z), or its metaplectic cover, Mp(2,Z),…
A closed-form expression for the amplitudes of source waves in 2D discrete lattice with local and linear (waveguides) defects is derived. The numerical implementation of this analytic expression is demonstrated by several examples.
In this paper, we create a Mellin space method for boundary correlation functions in de Sitter (dS) and anti-de Sitter (AdS) spaces. We demonstrate that the analytic continuation between AdS${}_{d+1}$ and dS${}_{d+1}$ is encoded in a set of…
We revisit the so-called "Geodesic Witten Diagrams" (GWDs) \cite{ScalarGWD}, proposed to be the holographic dual configuration of scalar conformal partial waves, from the perspectives of CFT operator product expansions. To this end, we…
Studies of modular linear differential equations (MLDE) for the classification of rational CFT characters have been limited to the case where the coefficient functions (in monic form) have no poles, or poles at special points of moduli…
We investigate a deformation of $w_{1+\infty}$ algebra recently introduced in arxiv:2111.11356 in the context of Celestial CFT that we denote by $\widetilde{W}_{1+\infty}$ algebra. We obtain the operator product expansions of the generating…
Holographic correlators on the celestial sphere of Minkowski space were recently defined in arXiv:2301.01810 as the extrapolation of bulk time-ordered correlation functions to the celestial sphere. In this work we explore the Mellin…
In this paper we generalize Drinfeld's twisted quantum affine algebras to construct twisted quantum algebras for all simply-laced generalized Cartan matrices and present their vertex representation realizations.
We extend the investigation of the Generalized Parton Distribution for a charged pion within a fully covariant constituent quark model, in two respects: (i) calculating the tensor distribution and (ii) adding the treatment of the evolution,…
We describe in more detail our approach to the conformal bootstrap which uses the Mellin representation of $CFT_d$ four point functions and expands them in terms of crossing symmetric combinations of $AdS_{d+1}$ Witten exchange functions.…
Cosmological correlators encode statistical properties of the initial conditions of our universe. Mathematically, they can often be written as Mellin integrals of a certain rational function associated to graphs, namely the flat space…
Both celestial and momentum space amplitudes in four dimensions are beset by divergences resulting from spacetime translation and sometimes scale invariance. In this paper we consider a (linearized) marginal deformation of the celestial CFT…
We give a systematic procedure to evaluate conformal partial waves involving symmetric tensors for an arbitrary CFT$_d$ using geodesic Witten diagrams in AdS$_{d+1}$. Using this procedure we discuss how to draw a line between the tensor…
Carrollian Conformal Field Theories (CFTs) have been proposed as co-dimension one holographic duals to asymptotically flat spacetimes as opposed to Celestial CFTs which are co-dimension two. In this paper, drawing inspiration from Celestial…
A brief survey of the theory of soliton perturbations is presented. The focus is on the usefulness of the so-called Generalised Fourier Transform (GFT). This is a method that involves expansions over the complete basis of `squared olutions`…
These notes offer an introduction to the functorial and algebraic description of 2-dimensional topological quantum field theories `with defects', assuming only superficial familiarity with closed TQFTs in terms of commutative Frobenius…
We use the recently developed framework of the Mellin bootstrap to study perturbatively free scalar CFTs in arbitrary dimensions. This approach uses the crossing-symmetric Mellin space formulation of correlation functions to generate…