Related papers: Diagonal Limit for Conformal Blocks in d Dimension…
We derive conformal blocks in an inverse spacetime dimension expansion. In this large D limit, the blocks are naturally written in terms of a new combination of conformal cross-ratios. We comment on the implications for the conformal…
We study the constraints of crossing symmetry and unitarity in general 3D Conformal Field Theories. In doing so we derive new results for conformal blocks appearing in four-point functions of scalars and present an efficient method for…
We show that conformal blocks simplify greatly when there is a large difference between two of the scaling dimensions for external operators. In particular the spacetime dimension only appears in an overall constant which we determine via…
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…
We derive expressions for conformal blocks involving operators with arbitrary spins in 3-dimensional CFTs. We use previous results on the action of the OPE in the embedding space to derive the conformal blocks. The blocks are given as…
In critical loop models, there exist diagonal fields with arbitrary conformal dimensions, whose $3$-point functions coincide with those of Liouville theory at $c\leq 1$. We study their $N$-point functions, which depend on the $2^{N-1}$…
We introduce a method for computing conformal blocks of operators in arbitrary Lorentz representations in any spacetime dimension, making it possible to apply bootstrap techniques to operators with spin. The key idea is to implement the…
The single-correlator conformal bootstrap is solved numerically for several values of dimension 4>d>2 using the available SDPB and Extremal Functional methods. Critical exponents and other conformal data of low-lying states are obtained…
We study the momentum-space 4-point correlation function of identical scalar operators in conformal field theory. Working specifically with null momenta, we show that its imaginary part admits an expansion in conformal blocks. The blocks…
We compute $M$-point conformal blocks with scalar external and exchange operators in the so-called comb configuration for any $M$ in any dimension $d$. Our computation involves repeated use of the operator product expansion to increase the…
We develop techniques useful for obtaining conformal blocks in embedding space. We construct a unique differential operator in embedding space and use it to construct a function that will be an important ingredient in assembling conformal…
The determinant method in the conformal bootstrap is applied for the critical phenomena of a single polymer in arbitrary $D$ dimensions. The scale dimensions (critical exponents) of the polymer ($2< D \le 4$) and the branched polymer ($3 <…
We continue the study of model-independent constraints on the unitary Conformal Field Theories in 4-Dimensions, initiated in arXiv:0807.0004. Our main result is an improved upper bound on the dimension \Delta of the leading scalar operator…
We consider the dimensional reduction of a CFT, breaking multiplets of the d-dimensional conformal group SO(d+1,1) up into multiplets of SO(d,1). This leads to an expansion of d-dimensional conformal blocks in terms of blocks in d-1…
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…
In critical loop models, we define diagonal boundaries as boundaries that couple to diagonal fields only. Using analytic bootstrap methods, we show that diagonal boundaries are characterised by one complex parameter, analogous to the…
We study conformal blocks (the space of correlation functions) over compact Riemann surfaces associated to vertex operator algebras which are the sum of highest weight modules for the underlying Virasoro algebra. Under the fairly general…
We study conformal blocks for thermal one-point-functions on the sphere in conformal field theories of general dimension. These thermal conformal blocks satisfy second order Casimir differential equations and have integral representations…
We apply numerical conformal bootstrap techniques to the four-point function of a Weyl spinor in 4d non-supersymmetric CFTs. We find universal bounds on operator dimensions and OPE coefficients, including bounds on operators in mixed…
The constraints of conformal bootstrap are applied to investigate a set of conformal field theories in various dimensions. The prescriptions can be applied to both unitary and non unitary theories allowing for the study of the spectrum of…