We consider the non-local operator ${\mathcal T}$ defined in 2-dimensional CFTs by the path integral over a torus with two punctures. Using the AdS/CFT correspondence, we study the spectrum and ground state of this operator in holographic such CFTs in the limit of large central charge $c$. In one region of moduli space, we argue that the operator retains a finite gap and has a ground state that differs from the CFT vacuum only by order one corrections. In this region the torus operator is much like the cylinder operator. But in another region of moduli space we find a puzzle. Although our ${\mathcal T}$ is of the manifestly positive form $A^\dagger A$, studying the most tractable phases of $\text{Tr}( {\mathcal T}^n)$ suggests that ${\mathcal T}$ has negative eigenvalues. It seems clear that additional phases must become relevant at large $n$, perhaps leading to novel behavior associated with a radically different ground state or a much higher density of states. By studying the action of two such torus operators on the CFT ground state, we also provide evidence that, even at large $n$, the relevant bulk saddles have $t=0$ surfaces with small genus.
Yukawa Institute for Theoretical Physics, Kyoto University（京都大学汤川理论物理研究所）；Universitat de Barcelona（巴塞罗那大学）；Inamori Research Institute for Science（稻盛科学研究所）
Background geometry of DLCQ M theory on a p-torus and holography
通过超引力，我们论证了沿着M理论圆a la Seiberg到在p-环面（p<5）上紧化的DLCQ M理论的无限洛伦兹推进意味着微观理论的全息描述。这一论证让我们确定了DLCQ $M$理论在p-环面上的背景几何;当p=0（p=1）时，背景几何分别是11维（10维）平坦闵可夫斯基时空。在这些情况下，全息术是由光锥动量的局部化引起的。当p = 2，3，4时，背景几何是Anti de Sitter空间和球面的张量积，根据AdS/CFT对应，它们具有全息共形场论描述.这些全息描述与Seiberg基于$\tilde{M}$理论的空间圆上的微观理论兼容，重新缩放普朗克长度，从而理解AdS/CFT对应的有效性。
We construct two-dimensional quantum states associated to four-dimensional linearized rotating self-dual black holes in $(2,2)$ signature Klein space. The states are comprised of global conformal primaries circulating on the celestial torus, the Kleinian analog of the celestial sphere. By introducing a generalized tower of Goldstone operators we identify the states as coherent exponentiations carrying an infinite tower of ${\rm w}_{1+\infty}$ charges or soft hair. We relate our results to recent approaches to black hole scattering, including a connection to Wilson lines, $\mathcal{S}$-matrix r…
Two-dimensional diffeomorphism symmetry can be described by an operator algebra extension of the well-known Virasoro algebra description of conformal symmetry. Utilizing this extension, this note explains why the conformal symmetry that appears in celestial holography should not be extended to diffeomorphism symmetry, a possibility that several authors have proposed. The description of the two-dimensional diffeomorphism algebra presented here might be useful for other purposes.
Holography can provide a microscopic interpretation of a gravitational solution as corresponding to a particular CFT state: the asymptotic expansion in gravity encodes the expectation values of operators in the dual CFT state. Such a correspondence is particularly valuable in black hole physics. We study supersymmetric D1-D5-P black holes, for which recently constructed microstate solutions known as "superstrata" provide strong motivation to derive the explicit D1-D5 holographic dictionary for CFT operators of total dimension two. In this work we derive the explicit map between one-point funct…
Starting from gravity in asymptotically flat spacetime, the BMS momentum fluxes are constructed. These are non-local expressions of the solution space living on the celestial Riemann surface. They transform in the coadjoint representation of the extended BMS group and correspond to Virasoro primaries under the action of bulk superrotations. The relation between the BMS momentum fluxes and celestial CFT operators is then established: the supermomentum flux is related to the supertranslation operator and the super angular momentum flux is linked to the stress-energy tensor of the celestial CFT. …
Asymptotically AdS wormhole solutions are considered in the context of holography. Correlation functions of local operators on distinct boundaries are studied. It is found that such correlators are finite at short distances. Correlation functions of non-local operators (Wilson loops) on distinct boundaries are also studied, with similar conclusions. Deformations of the theory with multi-trace operators on distinct boundaries are considered and studied. As a consequence of these results, the dual theory is expected to factorize in the UV, and the two sectors to be coupled by a soft non-local in…
We compute one-loop corrections to the OPE of gluons in the celestial conformal field theory corresponding to Yang-Mills coupled to arbitrary matter. We exploit universal hard/soft factorization to derive an IR finite OPE for the hard gluon operators. This OPE involves logarithms and operators that resemble logarithmic partners of primary operators. We derive an exact all-loop OPE in a limit of the Higgs-regulated planar $\mathcal{N}=4$ super Yang-Mills theory.
Given an asymptotically Anti-de Sitter supergravity solution, one can obtain a microscopic interpretation by identifying the corresponding state in the holographically dual conformal field theory. This is of particular importance for heavy pure states that are candidate black hole microstates. Expectation values of light operators in such heavy CFT states are encoded in the asymptotic expansion of the dual bulk configuration. In the D1-D5 system, large families of heavy pure CFT states have been proposed to be holographically dual to smooth horizonless supergravity solutions. We derive the pre…
In the twisted M-theory setting, various types of fusion of M2 and M5 branes induce coproducts between the algebra of operators on M2 branes and the algebra of operators on M5 branes. By doing a perturbative computation in the gravity side, which is captured by the 5d topological holomorphic $U(1)$ Chern-Simons theory, we reproduce the non-perturbative coproducts.
We explore the celestial holography proposal for non-trivial asymptotically flat backgrounds including the Coulomb field of a static and spinning point charge, their gravitational counterparts described by the Schwarzschild and Kerr metrics, as well as the Aichelburg-Sexl shockwave and spinning shockwave geometries and their electromagnetic cousins. We compute celestial two-point amplitudes on these Kerr-Schild type backgrounds which have the desirable feature, due to the presence of an external source, that they are non-vanishing for general operator positions and are not constrained by the k…
By using the approach introduced in arXiv:2107.09677 we construct non-BPS solutions of 6D $(1,0)$ supergravity coupled to two tensor multiplets as a perturbation of AdS$_3\times S^3$. These solutions are both regular and asymptotically AdS$_3\times S^3$, so according to the standard holographic framework they must have a dual CFT interpretation as non-supersymmetric heavy operators of the D1-D5 CFT. We provide quantitative evidence that such heavy CFT operators are bound states of a large number of light BPS operators that are mutually non-BPS.
