Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userState-Operator Correspondence in Celestial Conformal Field Theory
72
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
The bulk-to-boundary dictionary for 4D celestial holography is given a new entry defining 2D boundary states living on oriented circles on the celestial sphere. The states are constructed using the 2D CFT state-operator correspondence from operator insertions corresponding to either incoming or outgoing particles which cross the celestial sphere inside the circle. The BPZ construction is applied to give an inner product on such states whose associated bulk adjoints are shown to involve a shadow transform. Scattering amplitudes are then given by BPZ inner products between states living on the same circle but with opposite orientations. 2D boundary states are found to encode the same information as their 4D bulk counterparts, but organized in a radically different manner.
rate research
Read More
The 4D 4-point scattering amplitude of massless scalars via a massive exchange is expressed in a basis of conformal primary particle wavefunctions. This celestial amplitude is expanded in a basis of 2D conformal partial waves on the unitary principal series, and then rewritten as a sum over 2D conformal blocks via contour deformation. The conformal blocks include intermediate exchanges of spinning light-ray states, as well as scalar states with positive integer conformal weights. The conformal block prefactors are found as expected to be quadratic in the celestial OPE coefficients.
We review recent progress in operator algebraic approach to conformal quantum field theory. Our emphasis is on use of representation theory in classification theory. This is based on a series of joint works with R. Longo.
We discuss consequences of the breaking of conformal symmetry by a flat or spherical extended operator. We adapt the embedding formalism to the study of correlation functions of symmetric traceless tensors in the presence of the defect. Two-point functions of a bulk and a defect primary are fixed by conformal invariance up to a set of OPE coefficients, and we identify the allowed tensor structures. A correlator of two bulk primaries depends on two cross-ratios, and we study its conformal block decomposition in the case of external scalars. The Casimir equation in the defect channel reduces to a hypergeometric equation, while the bulk channel blocks are recursively determined in the light-cone limit. In the special case of a defect of codimension two, we map the Casimir equation in the bulk channel to the one of a four-point function without defect. Finally, we analyze the contact terms of the stress-tensor with the extended operator, and we deduce constraints on the CFT data. In two dimensions, we relate the displacement operator, which appears among the contact terms, to the reflection coefficient of a conformal interface, and we find unitarity bounds for the latter.
We extend the work of Hellerman (arxiv:0902.2790) to derive an upper bound on the conformal dimension $Delta_2$ of the next-to-lowest nontrival primary operator in unitary two-dimensional conformal field theories without chiral primary operators. The bound we find is of the same form as found for $Delta_1$: $Delta_2 leq c_{tot}/12 + O(1)$. We find a similar bound on the conformal dimension $Delta_3$, and present a method for deriving bounds on $Delta_n$ for any $n$, under slightly modified assumptions. For asymptotically large $c_{tot}$ and fixed $n$, we show that $Delta_n leq frac{c_{tot}}{12}+O(1)$. We conclude with a brief discussion of the gravitational implications of these results.
Krylov complexity, or K-complexity for short, has recently emerged as a new probe of chaos in quantum systems. It is a measure of operator growth in Krylov space, which conjecturally bounds the operator growth measured by the out of time ordered correlator (OTOC). We study Krylov complexity in conformal field theories by considering arbitrary 2d CFTs, free field, and holographic models. We find that the bound on OTOC provided by Krylov complexity reduces to bound on chaos of Maldacena, Shenker, and Stanford. In all considered examples including free and rational CFTs Krylov complexity grows exponentially, in stark violation of the expectation that exponential growth signifies chaos.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
