We study compactifications of $6d$ non minimal $(D_{p+3},D_{p+3})$ type conformal matter. These can be described by $N$ M5-branes probing a $D_{p+3}$-type singularity. We derive $4d$ Lagrangians corresponding to compactifications of such $6d$ SCFTs on three punctured spheres (trinions) with two maximal punctures and one minimal puncture. The trinion models are described by simple $\mathcal{N}=1$ quivers with $SU(2N)$ gauge nodes. We derive the trinion Lagrangians using RG flows between the aforementioned $6d$ SCFTs with different values of $p$ and their relations to matching RG flows in their compactifications to $4d$. The suggested trinions are shown to reduce to known models in the minimal case of $N=1$. Additional checks are made to show the new minimal punctures uphold the expected S-duality between models in which we exchange two such punctures. We also show that closing the new minimal puncture leads to expected flux tube models.
We study holographic conformal order compactified on $S^3$. The corresponding boundary CFT$ _4$ has a thermal phase with a nonzero expectation value of a certain operator. The gravitational dual to the ordered phase is represented by a black hole in asymptotically $AdS_5$ that violates the no-hair theorem. While the compactification does not destroy the ordered phase, it does not cure its perturbative instability: we identify the scalar channel QNM of the hairy black hole with Im$[w]>0$. On the contrary, we argue that the disordered thermal phase of the boundary CFT is perturbatively stable in…
The Chamblin-Reall background is a static solution of Einstein gravity coupled with a background scalar field and a dynamical domain wall, with the potential of the scalar field being of Liouville type. It can be got by dimensionally reducing a higher dimensional background with a constant potential. Compactified AdS black holes are black hole backgrounds constructed by wrapping one or more spatial directions of a higher dimensional AdS black hole on a torus and then integrating them out. The compactified AdS black hole background is asymptotically flat, non-conformal, and of Chamblin-Reall ty…
We provide explicit holographic duals of M5-branes wrapped on a sphere with one irregular puncture and one regular puncture of arbitrary type. The solutions generalise the solutions corresponding to M5-branes wrapped on a disc recently constructed by Bah-Bonetti-Minasian-Nardoni by allowing for a general choice of regular puncture. We show that the central charges, flavour central charges and conformal dimensions of BPS operators match with a class of Argyres-Douglas theory.
We present the formulation of the bosonic Hamiltonian M2-brane compactified on a twice punctured torus following the procedure proposed in \cite{mpgm14}. In this work we analyse two possible metric choice, different from the one used in \cite{mpgm14}, over the target space and study some of the properties of the corresponding Hamiltonian.
The leading classical asymptotics of Virasoro conformal blocks on the Riemann sphere with n generic and n-3 "heavy" degenerate field insertions can be described in terms of the geometry of Garnier system describing the monodromy preserving deformations of second order Fuchsian differential equations on an n-punctured sphere. This allows us to characterise the leading classical asymptotics of Virasoro conformal blocks completely, and to clarify in which sense conformal field theory represents a quantisation of the isomonodromic deformation problem.
Entanglement or modular Hamiltonians play a crucial role in the investigation of correlations in quantum field theories. In particular, in 1+1 space-time dimensions, the spectra of entanglement Hamiltonians of conformal field theories (CFTs) for certain geometries are related to the spectra of the physical Hamiltonians of corresponding boundary CFTs. As a result, conformal invariance allows exact computation of the spectra of the entanglement Hamiltonians for these models. In this work, we perform this computation of the spectrum of the entanglement Hamiltonian for the free compactified boson …
We extend the scope of the Klein bottle entropy, originally introduced by [Tu, Phys. Rev. Lett. 119, 261603 (2017)] in the rational conformal field theory (CFT), to the compactified boson CFT, which are relevant to the studies of Luttinger liquids. We first review the Klein bottle entropy in rational CFT and discuss details of how to extract the Klein bottle entropy from lattice models using the example of the transverse field Ising model. We then go beyond the scope of rational CFT and study the Klein bottle entropy $\ln g$ in the compactified boson CFT, which turns out to have a straightforw…
We obtain the Hamiltonian formulation of the 11D Supermembrane theory non-trivially compactified on a twice-punctured torus times a 9D Minkowski space-time. It corresponds to a M2-brane formulated in 11D space with ten non-compact dimensions. The critical points like the poles and the zeros of the fields describing the embedding of the Supermembrane in the target space are treated rigorously. The non-trivial compactification generates non-trivial mass terms appearing in the bosonic potential, which dominate the full supersymmetric potential and should render the spectrum of the (regularized) S…
We construct five-dimensional non-Lorentzian Lagrangian gauge field theories with an SU(1,3) conformal symmetry and 12 (conformal) supersymmetries. Such theories are interesting in their own right but can arise from six-dimensional (1,0) superconformal field theories on a conformally compactified Minkowski spacetime. In the limit that the conformal compactification is removed the Lagrangians we find give field theory formulations of DLCQ constructions of six-dimensional (1,0) conformal field theories.
The topology of closed manifolds forces interacting charges to appear in pairs. We take advantage of this property in the setting of the conformal boundary of $\mathrm{AdS}_5$ spacetime, topologically equivalent to the closed manifold $S^1\times S^3$, by considering the coupling of two massless opposite charges on it. Taking the interaction potential as the analog of Coulomb interaction (derived from a fundamental solution of the $S^3$ Laplace-Beltrami operator), a conformal $S^1\times S^3$ metric deformation is proposed, such that free motion on the deformed metric is equivalent to motion on …
In this paper we study compactifications of ADE type conformal matter, N M5 branes probing ADE singularity, on torus with flux for global symmetry. We systematically construct the four dimensional theories by first going to five dimensions and studying interfaces. We claim that certain interfaces can be associated with turning on flux in six dimensions. The interface models when compactified on a circle comprise building blocks for constructing four dimensional models associated to flux compactifications of six dimensional theories on a torus. The theories in four dimensions turn out to be qui…
The closed string field theory minimal-area problem asks for the conformal metric of least area on a Riemann surface with the condition that all non-contractible closed curves have length at least 2π. Through every point in such a metric there is a geodesic that saturates the length condition, and saturating geodesics in a given homotopy class form a band. The extremal metric is unknown when bands of geodesics cross, as it happens for surfaces of non-zero genus. We use recently proposed convex programs to numerically find the minimal-area metric on the square torus with a square boundary, for …
We study correlation functions in five-dimensional non-Lorentzian theories with an $SU(1,3)$ conformal symmetry. Examples of such theories have recently been obtained as $Ω$-deformed Yang-Mills Lagrangians arising from a null reduction of six-dimensional superconformal field theories on a conformally compactified Minkowski space. The correlators exhibit a rich structure with many novel properties compared to conventional correlators in Lorentzian conformal field theories. Moreover, identifying the instanton number with the Fourier mode number of the dimensional reduction offers a hope to formu…
Boundary Conformal Field Theory and Entanglement Entropy in Two-Dimensional Quantum Lifshitz Critical Point
讨论了二维量子Lifshitz临界点，即Rokhsar-Kivelson型临界波函数中的von Neumann纠缠熵。我遵循B. Hsu et al. [Phys.Rev.B79，115421（2009）]，但是指出了关于副本玻色子场的紧化的微妙问题：尽管可以通过原始场的线性组合来定义一组新的玻色子场，但是新的场不是独立紧化的。为了系统地研究多分量自由玻色子的边界共形场论，我采用了一种基于紧化格的几何表述。边界共形场论的结果与J. M. Stephan等人[Phys.Rev.B80，184421（2009）]，证实了它的普遍性，正如B. Hsu等人
ADE Little String Theory on a Riemann Surface (and Triality)
利用在ADE奇点上紧化的IIB弦的定义，我们开始了ADE型（2，0）小弦论的研究。作为一个应用，我们导出了一个5维ADE的量子规范理论，它描述了在低能量下，在一个有三个完整穿孔的球体上紧化的小弦。作为第二个应用，我们证明了这个理论的配分函数等于ADE Toda CFT的3点共形块，q-变形。为了建立这一点，我们将\cite{AHS}的A_n triality推广到所有的ADE李代数; IIB弦的观点也是至关重要的。
