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.

In a previous paper [1] we have shown how Lifshitz-like space-times (space-times having Lifshitz scaling with hyperscaling violation) arise from 1/4 BPS, threshold FDp bound state solutions of type II string theories in the near horizon limit. In this paper we show that similar structures also arise from the near horizon limit of 1/4 BPS, threshold intersecting D-brane solutions of type II string theories. Some of these solutions are standard (Dp-D(p + 4) for p = 0, 2) and some are non-standard (Dp-D(p + 2) for p = 1, 2, 3) including D2-D2 ′ , D3-D3 ′ and D4-D4 ′ solutions. The dilatons of these solutions in general run (except in D2-D4 and D3-D3 ′ cases) and produce RG flows. We discuss the phase structures of these solutions. D2-D4 and D3-D3 ′ in the near horizon limit do not produce Lifshitz-like space-time, but give AdS 3 spaces.

This note is an extension of a recent work on the analytical bootstrapping of O(N ) models. An additonal feature of the O(N ) model is that the OPE contains trace and antisymmetric operators apart from the symmetric-traceless objects appearing in the OPE of the singlet sector. This in addition to the stress tensor (T µν ) and the φ i φ i scalar, we also have other minimal twist operators as the spin-1 current J µ and the symmetric-traceless scalar in the case of O(N ). We determine the effect of these additional objects on the anomalous dimensions of the corresponding trace, symmetric-traceless and antisymmetric operators in the large spin sector of the O(N ) model, in the limit when the spin is much larger than the twist. As an observation, we also verified that the leading order results for the large spin sector from the −expansion are an exact match with our n = 0 case. A plausible holographic setup for the special case when N = 2 is also mentioned which mimics the calculation in the CFT.

A class of (2+1)-dimensional quantum many body system characterized by an anisotropic scaling symmetry (Lifshitz symmetry) near their quantum critical point can be described by a (3+1)-dimensional dual gravity theory with negative cosmological constant along with a massive vector field, where the scaling symmetry is realized by the metric as an isometry. We calculate the entanglement entropy of an excited state of such a system holographically, i.e., from the asymptotic perturbation of the gravity dual using the prescription of Ryu and Takayanagi, when the subsystem is sufficiently small. With suitable identifications, we show that this entanglement entropy satisfies an energy conservation relation analogous to the first law of thermodynamics. The non-trivial massive vector field here plays a crucial role and contributes to an additional term in the energy relation.