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The requirements of conformal invariance for two and three point functions for general dimension $d$ on flat space are investigated. A compact group theoretic construction of the three point function for arbitrary spin fields is presented…
Unitarity cuts diverge in the channel of a single massive external fermion. We propose an off-shell continuation of the momentum that allows a finite evaluation of the unitarity cuts. If the cut is taken with complete amplitudes on each…
The calculation of both spinor and tensor Green's functions in four-dimensional conformally invariant field theories can be greatly simplified by six-dimensional methods. For this purpose, four-dimensional fields are constructed as…
We compute conformal correlation functions with spinor, tensor, and spinor-tensor primary fields in general dimensions with Euclidean and Lorentzian metrics. The spinors are taken to be Dirac spinors, which exist for any dimensions. For…
This work deals with the conformal transformations in six-dimensional spinorial formalism. Several conformally invariant equations are obtained and their geometrical interpretation are worked out. Finally, the integrability conditions for…
We consider the evaluation of D-dimensional conformal invariant integrals which involve spin one-half and spin-one particles. The star-triangle relation for the massless Yukawa theory is derived, and the longitudinal part of the three-point…
In this paper we develop further the relation between conformal four-point blocks involving external spinning fields and Calogero-Sutherland quantum mechanics with matrix-valued potentials. To this end, the analysis of…
We exploit a gauge invariant approach for the analysis of the equations governing the dynamics of active scalar fluctuations coupled to the fluctuations of the metric along holographic RG flows. In the present approach, a second order ODE…
We extend previous work on conformally covariant differential operators to consider the case of second order operators acting on symmetric traceless tensor fields. The corresponding flat space Green function is explicitly constructed and…
We present a calculation of the spectral properties of a single charge doped at a Cu($3d$) site of the Cu-F plane in KCuF$_{3}$. The problem is treated by generating the equations of motion for the Green's function by means of subsequent…
Given a relativistic two-point Green's function for a spinor system with spherical symmetry we show how to obtain another in the same class by extended point canonical transformations (XPCT).
In this paper, we study the conformally invariant field equations for vector-spinor field in de Sitter space-time. The solutions are also obtained in terms of the de Sitter-Dirac plane waves. The related two-point functions are calculated…
At variance with fully inclusive quantities, which have been computed already at the two- or three-loop level, most exclusive observables are still known only at one-loop, as further progress was hampered so far by the greater computational…
The AGT conjecture identifying conformal blocks with the Nekrasov functions is investigated for the spherical conformal blocks with more than 4 external legs. The diagram technique which arises in conformal block calculation involves…
We exactly solve the ferromagnetic spin-1/2 Ising model on the Bethe lattice in the presence of an external magnetic field by means of the equations of motion method within the Green's function formalism. In particular, such an approach is…
For conformal field theories in arbitrary dimensions, we introduce a method to derive the conformal blocks corresponding to the exchange of a traceless symmetric tensor appearing in four point functions of operators with spin. Using the…
Conformal blocks for four point functions for fields with arbitrary spins in two dimensions are obtained by evaluating an appropriate integral. The results are just products of hypergeometric functions of the conformally invariant cross…
In two-dimensional models of critical non-intersecting loops, there are $\ell$-leg fields that insert $\ell\in\mathbb{N}^*$ open loop segments, and diagonal fields that change the weights of closed loops. We conjecture an exact formula for…
We construct the three point function involving an axial vector current and two energy-momentum tensors for four dimensional conformal field theories. Conformal symmetry determines the form of this three point function uniquely up to a…
In this note we present a simple method of constructing general conformally invariant three point functions of operators of various spins in three dimensions. Upon further imposing current conservation conditions, we find new parity…