We apply analytic conformal bootstrap ideas in Mellin space to conformal field theories with O(N ) symmetry and cubic anisotropy. We write down the conditions arising from the consistency between the operator product expansion and crossing symmetry in Mellin space. We solve the constraint equations to compute the anomalous dimension and the OPE coefficients of all operators quadratic in the fields in the epsilon expansion. We reproduce known results and derive new results up to O( 3 ). For the O(N ) case, we also study the large N limit in general dimensions and reproduce known results at the leading order in 1/N .

We set up the conventional conformal bootstrap equations in Mellin space and analyse the anomalous dimensions and OPE coefficients of large spin double trace operators. By decomposing the equations in terms of continuous Hahn polynomials, we derive explicit expressions as an asymptotic expansion in inverse conformal spin to any order, reproducing the contribution of any primary operator and its descendants in the crossed channel. The expressions are in terms of known mathematical functions and involve generalized Bernoulli (Nørlund) polynomials and the Mack polynomials and enable us to derive certain universal properties. Comparing with the recently introduced reformulated equations in terms of crossing symmetric tree level exchange Witten diagrams, we show that to leading order in anomalous dimension but to all orders in inverse conformal spin, the equations are the same as in the conventional formulation. At the next order, the polynomial ambiguity in the Witten diagram basis is needed for the equivalence and we derive the necessary constraints for the same.

We construct 1/4 BPS, threshold F-Dp bound states (with 0 ≤ p ≤ 5) of type II string theories by applying S-and T-dualities to the D1-D5 system of type IIB string theory. These are different from the known 1/2 BPS, non-threshold F-Dp bound states. The near horizon limits of these solutions yield Lifshitz-like spacetimes with varying dynamical critical exponent z = 2(5 − p)/(4 − p), for p = 4, along with the hyperscaling violation exponent θ = p − (p − 2)/(4 − p), showing how Lifshitz-like space-time can be obtained from string theory. The dilatons are in general non-constant (except for p = 1). We discuss the holographic RG flows and the phase structures of these solutions. For p = 4, we do not get a Lifshitz-like space-time, but the near horizon limit in this case leads to an AdS 2 space.

We present a dispersion relation in conformal field theory which expresses the four point function as an integral over its single discontinuity. Exploiting the analytic properties of the OPE and crossing symmetry of the correlator, we show that in perturbative settings the correlator depends only on the spectrum of the theory, as well as the OPE coefficients of certain low twist operators, and can be reconstructed unambiguously. In contrast to the Lorentzian inversion formula, the validity of the dispersion relation does not assume Regge behavior and is not restricted to the exchange of spinning operators. As an application, the correlator φφφφ in φ 4 theory at the Wilson-Fisher fixed point is computed in closed form to order 2 in the expansion. arXiv:1910.04661v1 [hep-th]

We show that in boundary CFTs, there exists a one-to-one correspondence between the boundary operator expansion of the two-point correlation function and a power series expansion of the layer susceptibility. This general property allows the direct identification of the boundary spectrum and expansion coefficients from the layer susceptibility and opens a new way for efficient calculations of two-point correlators in BCFTs. To show how it works we derive an explicit expression for the correlation function 〈ϕiϕi〉 of the O(N) model at the extraordinary transition in 4 − ϵ dimensional semi-infinite space to order O(ϵ). The bulk operator product expansion of the two-point function gives access to the spectrum of the bulk CFT. In our example, we obtain the averaged anomalous dimensions of scalar composite operators of the O(N) model to order O(ϵ2). These agree with the known results both in ϵ and large-N expansions.