A spacelike surface with cylinder topology can be described by various sets of canonical variables within pure AdS3 gravity. Each is made of one real coordinate and one real momentum. The Hamiltonian can be either $H=0$ or it can be nonzero and we display the canonical transformations that map one into the other, in two relevant cases. In a choice of canonical coordinates, one of them is the cylinder aspect $q$, which evolves nontrivially in time. The time dependence of the aspect is an analytic function of time $t$ and an "angular momentum" $J$. By analytic continuation in both $t$ and $J$ we obtain a Euclidean evolution that can be described geometrically as the motion of a cylinder inside the region of the 3D hyperbolic space bounded by two "domes" (i.e. half spheres), which is topologically a solid torus. We find that for a given $J$ the Euclidean evolution cannot connect an initial aspect to an arbitrary final aspect; moreover, there are infinitely many Euclidean trajectories that connect any two allowed initial and final aspects. We compute the transition amplitude in two independent ways; first by solving exactly the time-dependent Schrödinger equation, then by summing in a sensible way all the saddle contributions, and we discuss why both approaches are mutually consistent.
We show that the entanglement entropy of $D=4$ linearized gravitons across a sphere recently computed by Benedetti and Casini coincides with that obtained using the Kaluza-Klein tower of traceless transverse massive spin-2 fields on $S^1\times AdS_3$. The mass of the constant mode on $S^1$ saturates the Brietenholer-Freedman bound in $AdS_3$. This condition also ensures that the entanglement entropy of higher spins determined from partition functions on the hyperbolic cylinder coincides with their recent conjecture. Starting from the action of the 2-form on $S^1\times AdS_5$ and fixing gauge, …
Starting from the averaged null energy condition (ANEC) in Minkowski we show that conformal symmetry implies the ANEC for a conformal field theory (CFT) in a de Sitter and anti-de Sitter background. A similar and novel bound is also obtained for a CFT in the Lorentzian cylinder. Using monotonicity of relative entropy, we rederive these results for dS and the cylinder. As a byproduct we obtain the vacuum modular Hamiltonian and entanglement entropy associated to null deformed regions of CFTs in (A)dS and the cylinder. A third derivation of the ANEC in dS is shown to follow from bulk causality i…
String theory on $\text{AdS}_3\times \text{S}^3\times \mathbb{T}^4$ with minimal $k=1$ NS-NS flux can be described in terms of a free field worldsheet theory in the hybrid formalism. We construct various D-branes of this string theory and calculate their associated cylinder amplitudes. We find that these amplitudes match with the cylinder correlators of certain boundary states of the dual symmetric orbifold CFT $\text{Sym}(\mathbb{T}^4)$, thus suggesting a direct correspondence between these boundary conditions. We also show that the disk amplitudes of these D-branes localise to those points i…
We describe the pure spinor string in the $AdS_5\times S^5$ using unconstrained matrices first used by Roiban and Siegel for the Green-Schwarz superstring.
We point out that pure supergravity theories in $AdS$ with enough supersymmetry lead, upon taking the large radius limit, to flat space quantum gravities with a nonperturbatively exact global symmetry, and are therefore in the Swampland. The argument applies to any $AdS$ supergravity with gauged R-symmetry group, including truncations of most well known examples, such as $AdS_5$ without the $S^5$ or $AdS_4$ without the $S^7$. This demonstrates that extreme scale separation, at least with enough supersymmetry, is not realizable. Moreover pure $AdS$ theories are also in conflict with some other …
We lift the set of classical non-local symmetries recently studied by Klose, Loebbert, and Münkler in the context of $\mathbb Z_2$ cosets to the pure spinor description of the superstring in the $AdS_5\times S^5$ background.
We present an integrable deformation of the $AdS_{5}\times S^{5}$ pure spinor action based on homological perturbation theory. Its equations of motion, Lax connection and BRST symmetry are discussed. The resulting model describes a pure spinor superstring in a generalized supergravity background.
We examine the surface term for the BRST transformation of the open pure spinor superstring in an AdS_5 x S^5 background. We find that the boundary condition to eliminate the surface term leads to a classification of possible configurations of 1/2 supersymmetric D-branes.
The character integral representation of one loop partition functions is useful to establish the relation between partition functions of conformal fields on Weyl equivalent spaces. The Euclidean space $S^a\times AdS_b$ can be mapped to $S^{a+b}$ provided $S^a$ and $AdS_b$ are of the same radius. As an example, to begin with, we show that the partition function in the character integral representation of conformally coupled free scalars and fermions are identical on $S^a\times AdS_b$ and $S^{a+b}$. We then demonstrate that the partition function of higher derivative conformal scalars and fermio…
We calculate the expectation value of the Wilson line in the pure AdS$_3$ Einstein gravity theory and also the entanglement entropy in the boundary theory. Our one-loop calculation of entanglement entropy shows a shift of the central charge 26. Finally, we show that the Wilson line provides the equivalent description to the boundary entanglement entropy. This equivalence leads to a concrete example of the building of "minimum surface=entanglement entropy".
The three-dimensional pure quantum gravity with negative cosmological constant is supposed to be dual to the extremal conformal field theory of central charge $c=24k$ in two dimensions. We employ the conformal bootstrap method to analyze the extremal CFTs, and find numerical evidence for the non-existence of the extremal CFTs for sufficiently large central charge ($k \ge 20$). We also explore near-extremal CFTs, a small modification of extremal ones, and find similar evidence for their non-existence for large central charge. This indicates, under the assumption of holomorphic factorization, th…
The $b$-ghost of the pure spinor formalism in a general curved background is not holomorphic. For such theories, the construction of the string measure requires the knowledge of the action of diffeomorphisms on the BV phase space. We construct such an action for the pure spinor sigma-model in $AdS_5\times S^5$. From the point of view of the BV formalism, this sigma-model belongs to the class of theories where the expansion of the Master Action in antifields terminates at the quadratic order. We show that it can be reduced to a simpler degenerate sigma-model, preserving the AdS symmetries. We c…
Revisiting the tensionless limit of pure-Ramond-Ramond AdS3/CFT2
Technical University of Munich（慕尼黑工业大学）；HUN-REN Wigner Research Centre for Physics（匈牙利科学院维格纳物理研究所）；University of Birmingham（伯明翰大学）；INFN, Sezione di Padova（意大利国家核物理学院帕多瓦分部）
We express one-loop string amplitudes involving both open and closed strings as sum over pure open string amplitudes. These findings generalize the analogous tree-level result to higher loops and extend the tree-level observation that in gravitational amplitudes a graviton can be traded for two gluons. Our results are derived from analytic continuation of closed string world-sheet coordinates on the cylinder resulting in pairs of real open string coordinates located at the two cylinder boundaries subject to a one-loop kernel. The latter depends on the loop momentum flowing between the two cyli…
The pure spinor formalism for the superstring can be formulated as a twisted N=2 worldsheet theory with fermionic generators $j_{BRST}$ and composite $b$ ghost. After untwisting the formalism to an N=1 worldsheet theory with fermionic stress tensor $j_{BRST}+b$, the worldsheet variables combine into N=1 worldsheet superfields $X^m$ and $Θ^α$ together with a superfield constraint relating $DX^m$ and $DΘ^α$. The constraint implies that the worldsheet superpartner of $θ^α$ is a bosonic twistor variable, and different solutions of the constraint give rise to the pure spinor or extended RNS formali…
We construct new Euclidean wormhole solutions in AdS(d+1) and discuss their role in UV-complete theories, without ensemble averaging. The geometries are interpreted as overlaps of GHZ-like entangled states, which arise naturally from coarse graining the density matrix of a pure state in the dual CFT. In several examples, including thin-shell collapsing black holes and pure black holes with an end-of-the-world brane behind the horizon, the coarse-graining map is found explicitly in CFT terms, and used to define a coarse-grained entropy that is equal to one quarter the area of a time-symmetric a…
Based on the perturbation expansion, we compute the noncommutative corrections to the minimal surface areas of the pure AdS spacetime and Schwarzschild-AdS black hole, where the noncommutative background is suitably constructed in terms of the Poincaré coordinate system. In particular, we find a reasonable tetrad with subtlety, which not only matches the metrics of the pure AdS spacetime and Schwarzschild-AdS black hole in the commutative case, but also makes the corrections real rather than complex in the noncommutative case. For the pure AdS spacetime, the nocommutative effect is only a loga…
The GS Type IIB Superstring Action on AdS(3) X S(3) X T(4)
我们用AdS_{3|4} x S_{3} x T ^{4}的势描述了AdS_{3} x S_{3} x T ^{4}上的IIB型超引力背景，并用与AdS_{3|4}相关的超可解代数计算了Kappa规范固定的IIB型弦作用量.从作用量的显式形式，我们可以清楚地看到，从纯NSNS背景到纯RR背景，WZW项是如何消失的。
We revisit the 1/2-BPS D-branes on the AdS$_5\times$S$^5$ background. Based only on the classification of 1/2-BPS D-branes obtained by the covariant open string description, we consider various purely static configurations of D-branes without any worldvolume flux on the AdS$_5\times$S$^5$ background. Under the covariant $κ$ symmetry fixing condition, we investigate which part the spacetime supersymmetries is preserved on the D-brane worldvolume and obtain the associated worldvolume supersymmetry transformation rules to leading order in the worldvolume fluctuating fields. It is shown that, for …
The string theory calculation of the 1/2-BPS circular Wilson loop of N=4 SYM in the planar limit at next to leading order at strong coupling is revisited in the ratio of its semiclassical string partition function and the one dual to a latitude Wilson loop with trivial expectation value. After applying a conformal transformation from the disk to the cylinder, this problem can be approached by means of the Gel'fand-Yaglom formalism. Using results from the literature and the exclusion of zero modes from a modified Gel'fand-Yaglom formula, we obtain matching with the known field theory result. As…
In recent times, a considerable effort has been dedicated to identify certain conditions -- the so-called swampland conjectures -- with an eye on identifying effective theories which have no consistent UV-completions in string theory. In this paper, we examine the anti-de Sitter vacua corresponding to solutions which arise from purely non-perturbative contributions to the superpotential and show that these solutions satisfy the (axionic) weak gravity conjecture and the AdS-moduli scale separation conjecture. We also sketch out their advantages over other constructions.
We compute the holographic entanglement entropy and subregion complexity of spherical boundary subregions in the uncharged and charged AdS black hole backgrounds, with the \textbf{change} in these quantities being defined with respect to the pure AdS result. This calculation is done perturbatively in the parameter $\frac{R}{z_{\rm h}}$, where $z_{\rm h}$ is the black hole horizon and $R$ is the radius of the entangling region. We provide analytic formulae for these quantities as functions of the boundary spacetime dimension $d$ including several orders higher than previously computed. We obser…
Constrained Supermanifolds for AdS M-Theory Backgrounds
AdS_4 x（G/H）_7或AdS_5 x（G/H）_5背景的超规范完备性是一个长期存在的问题，它保持了小于极大的超对称性。与基于卡帕对称性的AdS_4 x S^7背景的超可解实现并行，我们开发了一种技术，它相当于以一种对超膜和超弦的纯旋量量子化有用的方式解决上述问题。我们没有将某些超空间坐标规范固定为零，而是对它们施加了一个额外的约束，从而再现了超可解表示的简化。约束是二次的，齐次的，Sp（4，R）-协变的，并从量子的角度来看，在纯旋量的方法是一致的。在这里，我们提供的几何解决方案，在随后的工作中，将适用于膜和超弦西格玛模型。
We review recent developments in the study of the AdS/CFT correspondence in lower dimensions. We start summarising the classification of AdS$_3\times$S$^2$ solutions in massive Type IIA supergravity with (0,4) supersymmetries, and the construction of their 2d dual quiver CFTs. These theories are the seed for further developments, that we review next. First, we construct a new class of AdS$_3$ solutions in M-theory that describe M-strings in M5-brane intersections. Second, we generate a new class of AdS$_2\times$S$^3$ solutions in massive IIA with 4 supercharges that we interpret as describing …
