We study the conformal bootstrap for systems of correlators involving non-identical operators. The constraints of crossing symmetry and unitarity for such mixed correlators can be phrased in the language of semidefinite programming. We apply this formalism to the simplest system of mixed correlators in 3D CFTs with a Z2 global symmetry. For the leading Z2-odd operator σ and Z2-even operator ǫ, we obtain numerical constraints on the allowed dimensions (�σ,�ǫ) assuming that σ and ǫ are the only relevant scalars in the theory. These constraints yield a small closed region in (�σ,�ǫ) space compatible with the known values in the 3D Ising CFT.

/pdf/bootstrapping-mixed-correlators-in-the-3d-ising-model-10pe41fwvh.pdf

Bootstrapping mixed correlators in the 3D Ising model

Further results for conformal partial waves for four point functions for conformal primary scalar fields in conformally invariant theories are obtained. They are de- fined as eigenfunctions of the differential Casimir operators for the conformal group acting on two variable functions subject to appropriate boundary conditions. As well as the scale dimensionand spin l the conformal partial waves depend on two parameters a,b related to the dimensions of the operators in the four point function. Expressions for the Mellin transform of conformal partial waves are ob- tained in terms of polynomials of the Mellin transform variables given in terms of finite sums. Differential operators which change a,b by ±1, shift the dimension d by ±2 and also change �,l are found. Previous results for d = 2,4,6 are recovered. The trivial case of d = 1 and also d = 3 are also discussed. For d = 3 formulae for the conformal partial waves in some restricted cases as a single variable integral representation based on the Bateman transform are found.

Conformal Partial Waves: Further Mathematical Results

We describe a new correspondence between four-dimensional conformal field theories with extended supersymmetry and two-dimensional chiral algebras. The meromorphic correlators of the chiral algebra compute correlators in a protected sector of the four-dimensional theory. Infinite chiral symmetry has far-reaching consequences for the spectral data, correlation functions, and central charges of any four-dimensional theory with ${\mathcal N}=2$ superconformal symmetry.

/pdf/infinite-chiral-symmetry-in-four-dimensions-1c5kj7h41k.pdf

Infinite Chiral Symmetry in Four Dimensions

We revisit the calculation of holographic correlation functions in type-IIB supergravity on ${\text{AdS}}_{5}\ifmmode\times\else\texttimes\fi{}{\mathrm{S}}^{5}$. Results for four-point functions simplify drastically when expressed in Mellin space. We conjecture a compact formula for the four-point functions of one-half Bogomol'nyi-Prasad-Sommerfield single-trace operators of arbitrary weight. Our methods rely on general consistency conditions and eschew detailed knowledge of the supergravity effective action.

Mellin Amplitudes for Supergravity on AdS_{5}×S^{5}.

Using conformal field theory (CFT) arguments we derive an infinite number of constraints on the large spin expansion of the anomalous dimensions and structure constants of higher spin operators. These arguments rely only on analiticity, unitarity, crossing-symmetry and the structure of the conformal partial wave expansion. We obtain results for both, perturbative CFT to all order in the perturbation parameter, as well as non-perturbatively. For the case of conformal gauge theories this provides a proof of the reciprocity principle to all orders in perturbation theory and provides a new "reciprocity" principle for structure constants. We argue that these results extend also to non-conformal theories.

Large spin systematics in CFT

Superconformal Ward identities and their solution

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Superconformal Ward identities and their solution