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We study the two-point function of local operators in the presence of a defect in a generic conformal field theory. We define two pairs of cross ratios, which are convenient in the analysis of the OPE in the bulk and defect channel respectively. The new coordinates have a simple geometric interpretation, which can be exploited to efficiently compute conformal blocks in a power expansion. We illustrate this fact in the case of scalar external operators. We also elucidate the convergence properties of the bulk and defect OPE decompositions of the two-point function. In particular, we remark that the expansion of the two-point function in powers of the new cross ratios converges everywhere, a property not shared by the cross ratios customarily used in defect CFT. We comment on the crucial relevance of this fact for the numerical bootstrap.
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We study $mathrm{AdS}_3times S^3/mathbb{Z}_ktimes {tilde S}^3/mathbb{Z}_{k}$ solutions to M-theory preserving $mathcal{N}=(0,4)$ supersymmetries, arising as near-horizon limits of M2-M5 brane intersections ending on M5-branes, with both types of five-branes placed on A-type singularities. Solutions in this class asymptote locally to $mathrm{AdS}_7/mathbb{Z}_ktimes {tilde S}^3/mathbb{Z}_{k}$, and can thus be interpreted as holographic duals to surface defect CFTs within the $mathcal{N}=(1,0)$ 6d CFT dual to this solution. Upon reduction to Type IIA, we obtain a new class of solutions of the form $mathrm{AdS}_3times S^3/mathbb{Z}_ktimes S^2 times Sigma_2$ preserving (0,4) supersymmetries. We construct explicit 2d quiver CFTs dual to these solutions, describing D2-D4 surface defects embedded within the 6d (1,0) quiver CFT dual to the $mathrm{AdS}_7/mathbb{Z}_k$ solution to massless IIA. Finally, in the massive case, we show that the recently constructed $mathrm{AdS}_3times S^2times mathrm{CY}_2$ solutions with $mathcal{N}=(0,4)$ supersymmetries gain a defect interpretation when $mathrm{CY}_2=T^4$ as surface CFTs originating from D2-NS5-D6 defects embedded within the 5d CFT dual to the Brandhuber-Oz $mathrm{AdS}_6$ background.
A salient feature of the Schr{o}dinger equation is that the classical radial momentum term $p_{r}^{2}$ in polar coordinates is replaced by the operator $hat{P}^{dagger}_{r} hat{P}_{r}$, where the operator $hat{P}_{r}$ is not hermitian in general. This fact has important implications for the path integral and semi-classical approximations. When one defines a formal hermitian radial momentum operator $hat{p}_{r}=(1/2)((frac{hat{vec{x}}}{r}) hat{vec{p}}+hat{vec{p}}(frac{hat{vec{x}}}{r}))$, the relation $hat{P}^{dagger}_{r} hat{P}_{r}=hat{p}_{r}^{2}+hbar^{2}(d-1)(d-3)/(4r^{2})$ holds in $d$-dimensional space and this extra potential appears in the path integral formulated in polar coordinates. The extra potential, which influences the classical solutions in the semi-classical treatment such as in the analysis of solitons and collective modes, vanishes for $d=3$ and attractive for $d=2$ and repulsive for all other cases $dgeq 4$. This extra term induced by the non-hermitian operator is a purely quantum effect, and it is somewhat analogous to the quantum anomaly in chiral gauge theory.
In this work, we formulate a path-integral optimization for two dimensional conformal field theories perturbed by relevant operators. We present several evidences how this optimization mechanism works, based on calculations in free field theories as well as general arguments of RG flows in field theories. Our optimization is performed by minimizing the path-integral complexity functional that depends on the metric and also on the relevant couplings. Then, we compute the optimal metric perturbatively and find that it agrees with the time slice of the hyperbolic metric perturbed by a scalar field in the AdS/CFT correspondence. Last but not the least, we estimate contributions to complexity from relevant perturbations.
We construct classical theories for scalar fields in arbitrary Carroll spacetimes that are invariant under Carrollian diffeomorphisms and Weyl transformations. When the local symmetries are gauge fixed these theories become Carrollian conformal field theories. We show that generically there are at least two types of such theories: one in which only time derivatives of the fields appear and the other in which both space and time derivatives appear. A classification of such scalar field theories in three (and higher) dimensions up to two derivative order is provided. We show that only a special case of our theories arises in the ultra-relativistic limit of a covariant parent theory.
A local SL(2,Z) transformation on the Type IIB brane configuration gives rise to an interesting class of superconformal field theories, known as the S-fold CFTs. Previously it has been proposed that the corresponding quiver theory has a link involving the T(U(N)) theory. In this paper, we generalise the preceding result by studying quivers that contain a T(G) link, where G is self-dual under S-duality. In particular, the cases of G = SO(2N), USp(2N) and G_2 are examined in detail. We propose the theories that arise from an appropriate insertion of an S-fold into a brane system, in the presence of an orientifold threeplane or an orientifold fiveplane. By analysing the moduli spaces, we test such a proposal against its S-dual configuration using mirror symmetry. The case of G_2 corresponds to a novel class of quivers, whose brane construction is not available. We present several mirror pairs, containing G_2 gauge groups, that have not been discussed before in the literature.
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