Related papers: Dimensional Uplift in Conformal Field Theories
The critical $O(N)$ CFT in spacetime dimensions $2 < d < 4$ is one of the most important examples of a conformal field theory, with the Ising CFT at $N=1$, $2 \leq d < 4$, as a notable special case. Apart from numerous physical…
We introduce the analytic superspace formalism for six-dimensional $(N,0)$ superconformal field theories. Concentrating on the $(2,0)$ theory we write down the Ward identities for correlation functions in the theory and show how to solve…
In this note we demonstrate that, as we conjectured earlier in [1], the a-charge in the conformal anomaly in dimension $d=2n$ manifests in a $n$-point correlation function of energy momentum tensor of a CFT considered in flat spacetime with…
In this work, we study the supersymmetric warped conformal field theory in two dimensions. We show that the Hofman-Strominger theorem on symmetry enhancement could be generalized to the supersymmetric case. More precisely, we find that…
We study the conformal bootstrap constraints for 3D conformal field theories with a $\mathbb{Z}_2$ or parity symmetry, assuming a single relevant scalar operator $\epsilon$ that is invariant under the symmetry. When there is additionally a…
The D1-D5 system is believed to have an `orbifold point' in its moduli space where its low energy theory is a N=4 supersymmetric sigma model with target space M^N/S^N, where M is T^4 or K3. We study correlation functions of chiral operators…
We study four-point correlation functions of half-BPS operators of arbitrary weight for all dimensions d=3,4,5,6 where superconformal theories exist. Using harmonic superspace techniques, we derive the superconformal Ward identities for…
We present a comprehensive discussion of renormalisation of 3-point functions of scalar operators in conformal field theories in general dimension. We have previously shown that conformal symmetry uniquely determines the momentum-space…
We discuss specific hypergeometric solutions of the conformal Ward identities (CWI's) of scalar 4-point functions of primary fields in momentum space, in $d$ spacetime dimensions. We determine such solutions using various dual conformal…
Recent programs on conformal bootstrap suggest an empirical relationship between the existence of non-trivial conformal field theories and non-trivial features such as a kink in the unitarity bound of conformal dimensions in the conformal…
We study the finite part of the sphere partition function of d-dimensional Conformal Field Theories (CFTs) as a function of exactly marginal couplings. In odd dimensions, this quantity is physical and independent of the exactly marginal…
Scalar-fermion models, such as the Gross-Neveu-Yukawa model, admit natural $1d$ defects given by the exponential of a scalar field integrated along a straight line. In $4-\varepsilon$ dimensions the defect coupling is weakly relevant and…
Three-dimensional conformal field theories (CFTs) with slightly broken higher spin symmetry provide an interesting laboratory to study general properties of CFTs and their roles in the AdS/CFT correspondence. In this work we compute the…
We demonstrate that various aspects of Conformal Field Theory are amenable to machine learning. Relatively modest feed-forward neural networks are able to distinguish between scale and conformal invariance of a three-point function and…
We demonstrate that simple feed-forward neural networks (NNs) can accurately compute correlation functions of conformal field theories (CFTs) on a line. Strikingly, by optimising a NN solely on crossing symmetry and providing only the…
The 3D Bondi-Metzner-Sachs (BMS$_3$) algebra that is the asymptotic symmetry algebra at null infinity of the $1+2$D asymptotically flat space-time is isomorphic to the $1+1$D Carrollian conformal algebra. Building on this connection,…
In this paper, we use crossing symmetry and unitarity constraints to put a lower bound on the central charge of conformal field theories in large space-time dimensions $D$. Specifically, we work with the four-point function of identical…
We consider the problem of computing N=2 superconformal block functions. We argue that the Kazama-Suzuki coset realization of N=2 superconformal algebra in terms of the affine sl(2) algebra provides relations between N=2 and affine sl(2)…
AdS/CFT duality is a conjectured dual correspondence between the large $N$ limit of Conformal Field Theory (CFT) in $d$-dimensions and the supergravity (SUGRA) in $d+1$-dimensional Anti de Sitter (AdS) space. By using this conjecture, we…
Conformal properties of the topological gravitational terms in $D=2$, $D=4$ and $D=6$ are discussed. It is shown that in the last two cases the integrands of these terms, when being settled into the dimension $D-1$ and multiplied by a…