Laszlo Palla
The reflection matrices of multi magnon bound states are obtained explicitely by exploiting the Yangian symmetry of boundary scattering on the Y=0 maximal giant graviton brane.
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We review the study of Hopf algebras, classical and quantum R-matrices, infinite-dimensional Yangian symmetries and their representations in the context of integrability for the N=4 vs AdS5xS5 correspondence.
We consider the problem of boundary scattering for Y=0 maximal giant graviton branes. We show that the boundary S-matrix for the fundamental excitations has a Yangian symmetry. We then exploit this symmetry to determine the boundary S-matrix for two-particle bound states. We verify that this boundary S-matrix satisfies the boundary Yang-Baxter equations.
We express the classical r-matrix of AdS/CFT in terms of tensor products involving an infinite family of generators, which takes a form suggestive of the universal expression obtained from a Yangian double. This should provide an insight into the structure of the infinite dimensional symmetry algebra underlying the integrability of the model, and give a clue to the construction of its universal R-matrix. We derive the commutation relations under which the algebra of these new generators close.
In the su(2|2) spin chain motivated by the AdS/CFT correspondence, a novel symmetry extending the superalgebra su(2|2) into u(2|2) was found. We pursue the origin of this symmetry in the exceptional superalgebra d(2,1;epsilon), which recovers su(2|2) when the parameter epsilon is taken to zero. Especially, we rederive the Yangian symmetries of the AdS/CFT spin chain using the exceptional superalgebra and find that the epsilon-correction corresponds to the novel symmetry. Also, we reproduce the non-canonical classical r-matrix of the AdS/CFT spin chain expressed with this symmetry from the cano…
This review is meant to be an account of the properties of the infinite-dimensional quantum group (specifically, Yangian) symmetry lying behind the integrability of the AdS/CFT spectral problem. In passing, the chance is taken to give a concise anthology of basic facts concerning Yangians and integrable systems, and to store a series of remarks, observations and proofs the author has collected in a five-year span of research on the subject. We hope this exercise will be useful for future attempts to study Yangians in field and string theories, with or without supersymmetry.
It was shown that the spin chain model coming from AdS/CFT correspondence satisfies the Yangian symmetry if we assume evaluation representation, though so far there is no explicit proof that the evaluation representation satisfies the Serre relation, which is one of the defining equations of the Yangian algebra imposing constraints on the whole algebraic structure. We prove completely that the evaluation representation adopted in the model satisfies the Serre relation by introducing a three-dimensional gamma matrix. After studying the Serre relation, we proceed to the whole Yangian algebraic s…
We discuss the relation between the recently derived bound state S-matrices for the AdS5 x S5 superstring and Yangian symmetry. We will study the relation between this Yangian symmetry and the Bethe ansatz. In particular we can use it to derive the Bethe equations for bound states.
We find new twisted Yangian symmetries of the AdS/CFT reflection matrices for the Y=0 maximal giant graviton and D5-brane. These new symmetries originate from the known secret symmetries of the Yangian symmetry of the AdS/CFT S-matrix.
We find the Yangian symmetry underlying the integrability of type IIB superstrings on $AdS_3 \times S^3 \times S^3 \times S^1$ with mixed Ramond-Ramond and Neveu-Schwarz-Neveu-Schwarz flux. The abstract commutation relations of the Yangian are formulated via RTT realisation, while its matrix realisation is in an evaluation representation depending on the quantised coefficient of the Wess-Zumino term. The construction naturally encodes a secret symmetry of the worldsheet scattering matrix whose generators map different Yangian levels to each other. We show that in the large effective string ten…
We present the `Heisenberg picture' of the reflection algebra by explicitly constructing the boundary Yangian symmetry of an AdS/CFT superstring which ends on a boundary with non-trivial degrees of freedom and which preserves the full bulk Lie symmetry algebra. We also consider the spectrum of bulk and boundary states and some automorphisms of the underlying algebras.
We find a new quantum Yangian symmetry of the AdS/CFT S-matrix, which complements the original su(2|2) symmetry to gl(2|2) and does not have a Lie algebra analog. Our finding is motivated by the Yangian double structure discovered at the classical level.
Integrability is believed to underlie the AdS3/CFT2 correspondence with sixteen supercharges. We elucidate the role of massless modes within this integrable framework. Firstly, we find the dressing factors that enter the massless and mixed-mass worldsheet S matrix. Secondly, we derive a set of all-loop Bethe Equations for the closed strings, determine their symmetries and weak-coupling limit. Thirdly, we investigate the underlying Yangian symmetry in the massless sector and show that it fits into the general framework of Yangian integrability. In addition, we compare our S matrix in the near-r…
We show that the recently found S-matrices describing the scattering of two-particle bound states of the light-cone string sigma model on AdS5 x S5 are compatible with Yangian symmetry. In case the invariance with respect to the centrally extended su(2|2) algebra is not sufficient to fully specify the scattering matrix, the requirement of Yangian symmetry provides an alternative to the Yang-Baxter equation and leads to a complete, up to an overall phase, determination of the S-matrix. We then compare the semi-classical limit of the bound state S-matrices with the universal classical r-matrix b…
We review the algebraic construction of the S-matrix of AdS/CFT. We also present its symmetry algebra which turns out to be a Yangian of the centrally extended su(2|2) superalgebra.
We discuss a classical integrability in the type IIB string theory on the AdS_5 x S^5 background. By using the Roiban-Siegel formulation of the superstring on the AdS_5 x S^5, we carefully treat the Wess-Zumino term and the constraint conditions intrinsic to the supersymmetric case, and construct explicitly non-local charges for a hidden infinite-dimensional symmetry. The existence of the symmetry is shown by Bena-Polchinski-Roiban. Then the super Yangian algebra is calculated. We also show the Serre relation ensuring the structure of the Hopf algebra. In addition, the classical integrability …
We construct highest-weight modules and a Yangian extension of the centrally extended sl(1|1)^2 superalgebra, that is a symmetry of the worldsheet scattering associated with the AdS3/CFT3 duality. We demonstrate that the R-matrix intertwining atypical modules is of a trigonometric type. We also consider a quantum deformation of this superalgebra, its modules, and obtain a quantum affine extension of the Drinfeld-Jimbo type that describes a deformed worldsheet scattering.
We study the remnants of Yangian symmetry of AdS/CFT magnons reflecting from boundaries with no degrees of freedom. We present the generalized twisted boundary Yangian of open strings ending on boundaries which preserve only a subalgebra h of the bulk algebra g, where (g,h) is a symmetric pair. This is realized by open strings ending on the D3 brane known as the Y=0 maximal giant graviton in AdS_5 x S^5. We also consider the Yangian symmetry of the boundary which preserves an su(1|2) subalgebra only.
We consider integrable field theories with achiral boundary conditions and uncover the underlying achiral twisted Yangian algebra. This construction arises from old work on the bosonic principal chiral model on a half-line, but finds a modern realization as the hidden symmetry in the planar limit of the scattering of worldsheet excitations of the AdS/CFT light-cone superstring off a D5-brane.
We construct Drinfeld's second realization of the Yangian based on psu(2|2)xR^3 symmetry. The second realization is traditionally more suitable for deriving the quantum double and the universal R matrix with respect to the first realization, originally obtained by Beisert, and it is generically more useful in order to study finite dimensional representations. We show that the two realization are isomorphic, where the isomorphism is almost the standard one given by Drinfeld for simple Lie algebras, but needs some crucial corrections to account for the central charges. We also evaluate the gener…
We identify certain blocks in the S-matrix describing the scattering of bound states of the AdS5 x S5 superstring that allow for a representation in terms of universal R-matrices of Yangian doubles. For these cases, we use the formulas for Drinfeld's second realization of the Yangian in arbitrary bound-state representations to obtain the explicit expressions for the corresponding R-matrices. We then show that these expressions perfectly match with the previously obtained S-matrix blocks.
In this paper we study factorising twists of the massless AdS_3 and AdS_2 integrable R-matrices, and explore the programme of analysis of form factors which Maillet et al developed for ordinary spin-chains. We derive the factorising twists from the universal R-matrix of the gl(1|1) Yangian double, and discuss the RTT relations for the two- and three-site monodromy matrix. We show how the twist can be used to compute a simple scalar product. We then implement our construction in the language of free fermions. Finally, we show how to obtain the massless AdS_2 quantum R-matrix from the Yangian un…
We consider the worldsheet boundary scattering and the corresponding boundary algebras for the Z=0 giant graviton and the Z=0 D7-brane in the AdS/CFT correspondence. We consider two approaches to the boundary scattering, the usual one governed by the (generalized) twisted Yangians and the q-deformed model of these boundaries governed by the quantum affine coideal subalgebras. We show that the q-deformed approach leads to boundary algebras that are of a more compact form than the corresponding twisted Yangians, and thus are favourable to use for explicit calculations. We obtain the q-deformed r…
The AdS/CFT correspondence is established for the case of AdS$_3$ space compactified on a filled rectangular torus with the CFT field on the boundary.
We give a short introduction to AdS/CFT and its plane wave limit.
Conformal deformations manifest in the AdS/CFT correspondence as boundary conditions on the AdS field. Heretofore, double-trace deformations have been the primary focus in this context. To better understand multitrace deformations, we revisit the relationship between the generating AdS partition function for a free bulk theory and the boundary CFT partition function subject to arbitrary conformal deformations. The procedure leads us to a formalism that constructs bulk fields from boundary operators. Using this formalism, we independently replicate the holographic RG flow narrative to go on to …
We calculate the scalar quasinormal modes of warped $AdS_3$ black holes analytically. We find that in general they are not in agreement with the prediction of the usual AdS/CFT correspondence. Nevertheless, for the black hole not deviating far from BTZ black hole, the quasinormal frequencies are still well consistent with AdS/CFT correspondence.
In this letter we examine some structural aspects of the AdS/CFT such as the way of obtaining the expectation value of product of operators of the CFT, and ideas that should be considered when a proof of AdS/CFT is under consideration.
Integrable Feynman Graphs and Yangian Symmetry on the Loom
本文证明杨不变性扩展至对偶Baxter lattice的一大类共形不变平面费曼图，用Lax算子链表述对称性并推广至无穷维辅助空间，为非平凡费曼图导出新微分积分方程，统一并扩展了可积标量平面图的已知特例。
In the context of AdS3/CFT2, we address spacetimes with a certain sort of internal infinity as typified by the extreme BTZ black hole. The internal infinity is a null circle lying at the end of the black hole's infinite throat. We argue that such spacetimes may be described by a product CFT of the form CFT-L * CFT-R, where CFT-R is associated with the asymptotically AdS boundary while CFT-L is associated with the null circle. Our particular calculations analyze the CFT dual of the extreme BTZ black hole in a linear toy model of AdS3/CFT2. Since the BTZ black hole is a quotient of AdS3, the dua…
We introduce the AdS/CFT correspondence as a natural extension of QFT in a fixed AdS background. We start by reviewing some general concepts of CFT, including the embedding space formalism. We then consider QFT in a fixed AdS background and show that one can define boundary operators that enjoy very similar properties as in a CFT, except for the lack of a stress tensor. Including a dynamical metric in AdS generates a boundary stress tensor and completes the CFT axioms. We also discuss some applications of the bulk geometric intuition to strongly coupled QFT. Finally, we end with a review of th…
This is a write-up of two lectures on AdS/CFT correspondance given by the authors at the 1998 Spring School at the Abdus Salam ICTP
Mack has conjectured that all conformal field theories are equivalent to string theories. We explore the example of the two-dimensional minimal model CFTs and confirm that the Mellin transformed amplitudes have the desired properties of string theory in three-dimensional anti-de Sitter spacetime.
The AdS/CFT correspondence is established for the AdS_3 space compactified on a solid torus with the CFT field on the boundary. Correlation functions that correspond to the bulk theory at finite temperature are obtained in the regularization a'la Gubser, Klebanov, and Polyakov. The BTZ black hole solutions in AdS_3 are T-dual to the solution in the AdS_3 space without singularity.
We discuss analytic continuation from d-dimensional Lorentzian de Sitter (dS$_d$) to d-dimensional Lorentzian anti-de Sitter (AdS$_{d}$) spacetime. We show that AdS$_{d}$, with opposite signature of the metric, can be obtained as analytic continuation of a portion of dS$_d$. This implies that the dynamics of (positive square-mass) scalar particles in AdS$_{d}$ can be obtained from the dynamics of tachyons in dS$_d$. We discuss this correspondence both at the level of the solution of the field equations and of the Green functions. The AdS/CFT duality is obtained as analytic continuation of the …
We study real-time correlators in the warped AdS/CFT correspondence. We apply the prescription used in the usual AdS/CFT correspondence and obtain the retarded Green's functions for the scalar and vector fields in the spacelike warped and the null warped black hole backgrounds. We find that the retarded Green's functions and the cross sections are well consistent with the predictions from dual CFT. Our results not only support strongly the conjectured warped AdS/CFT correspondence, but also show that the usual relativistic AdS/CFT prescription of obtaining the real-time correlators remain effe…
An interesting type of spin chain has appeared in the context of the planar AdS/CFT correspondence: It is based on an integrable nearest-neighbor spin chain, and it is perturbatively deformed by long-range interactions which apparently preserve the integrable structure. Similar models can be constructed by demanding the existence of merely one conserved local charge. Although the latter is not a sufficient integrability condition in general, the models often display convincing signs of full integrability. Here we consider a class of long-range spin chains with spins transforming in the fundame…
We discuss a possible relation between singletons in $AdS$ space and logarithmic conformal field theories at the boundary of $AdS$. It is shown that the bulk Lagrangian for singleton field (singleton dipole) induces on the boundary the two-point correlation function for logarithmic pair. Bulk interpretation of mixing between logarithmic operator $D$ and zero mode operator $C$ under the scale transformation is discussed as well as some other issues.
We discuss dilatonic gravity (bulk theory) from the point of view of (generalized) AdS/CFT correspondence. Self-consistent dilatonic background is considered. It may be understood as two boundaries space where AdS boundary appears as infinite boundary and new (singular) boundary occurs at short distances. The two-point correlation function and conformal dimension for minimal and dilaton coupled scalar are found. Even for minimal scalar, the conformal dimension is found to be different on above two boundaries. Hence, new CFT appears in AdS/CFT correspondence at short distances. AdS/CFT correspo…
By taking the interacting spinor-scalar theory on the $AdS_{d+1}$ space we calculate the boundary CFT correlation functions using AdS/CFT correspondence.
Paper withdrawn. The argument was based on a misconception
We discuss the role of singletons and logarithmic operators in AdS_3 string theory in the context of AdS_3/CFT_2 correspondence.
We extend the non-relativistic AdS/CFT correspondence to the fermionic fields. In particular we study the two point function of a fermionic operator in non-relativistic CFTs by making use of a massive fermion propagating in geometries with Schrodinger group isometry. Although the boundary of the geometries with Schrodinger group isometry differ from that in AdS geometries where the dictionary of AdS/CFT is established, using the general procedure of AdS/CFT correspondence, we see that the resultant two point function has the expected form for fermionic operators in non-relativistic CFTs, thoug…
We review the construction of the AdS/CFT dressing factor, its analytic properties and several checks of its validity.
This paper has been superseded by hep-th/0303164, "The Dirichlet Obstruction in AdS/CFT"
Using the AdS-CFT correspondence we calculate the two point function of CFT energy momentum tensors. The AdS gravitons are considered by explicitly solving the Dirichlet boundary value problem for $x_0=ε$. We consider this treatment as complementary to existing work, with which we make contact.
The renormalization of the boundary action in the AdS/CFT correspondence is considered and the breaking of conformal symmetry is discussed.
The dS/CFT correspondence differs from its AdS/CFT counterpart in some ways, yet is strikingly similar to it in many others. For example, both involve CFTs defined on connected spaces (despite the fact that the conformal boundary of deSitter space is not connected), and both impose constraints on scalar masses (Strominger's bound for deSitter, and the Breitenlohner-Freedman bound for Anti-deSitter). We argue that these similarities can be explored and exploited using a slight extension of the Euclidean approach to AdS/CFT. The methods are particularly compatible with Hull's embedding of deSitt…
We review some applications of Type 0 string theory in the context of the AdS/CFT correspondence.
We compute the boundary stress-energies of time-dependent asymptotically AdS spacetimes in 5 and 7 dimensions, and find that their traces are equal to the respective 4 and 6 dimensional field-theoretic trace anomalies. This provides good supporting evidence in favour of the AdS/CFT correspondence in time-dependent backgrounds.
Holographic Renormalization Group (RG) in nine dimensions is considered. The d8 holographic conformal anomaly is found. It should correspond to d8 CFT in AdS_9/CFT_8 correspondence. The comparison of holographic and QFT anomalies in d8 de Sitter space is done. It may give the indication for rigorous AdS_9/CFT_8 correspondence proposal.
We investigate the nature of the AdS/CFT duality between a subregion of the bulk and its boundary. In global AdS/CFT in the classical G_N=0 limit, the duality reduces to a boundary value problem that can be solved by restricting to one-point functions of local operators in the CFT. We show that the solution of this boundary value problem depends continuously on the CFT data. In contrast, the AdS-Rindler subregion cannot be continuously reconstructed from local CFT data restricted to the associated boundary region. Motivated by related results in the mathematics literature, we posit that a cont…
The loop expansion of the effective action is used to evaluate quantum corrections to a scalar field theory (massive phi^4 model) on AdS. We evaluate one loop corrections and show that they preserve conformal invariance of the boundary theory as conjectured by AdS/CFT correspondence.
The attempt to understand if AdS/CFT correspondence may be realized as the one between some AdS-like cosmological space and CFT living on the boundary is made. In order to obtain such cosmology we exchange the time and radial coordinates in d5 Schwarzschild-anti de Sitter (S-AdS) BH (with corresponding signature change). The test on proportionality of free energies from such d5 cosmological space (after AdS/CFT identification of parameters) and from ${\cal N}=4$ SU(N) super Yang-Mills quantum theory is successfully passed.
In this paper we resolve a contradiction posed in a recent paper by Horowitz and Hubeny. The contradiction concerns the way small objects in AdS space are described in the holographic dual CFT description.
It has been suggested that the quantum generalization of the Wald entropy for an extremal black hole is the logarithm of the ground state degeneracy of a dual quantum mechanics in a fixed charge sector. We test this proposal for supersymmetric extremal BTZ black holes for which there is an independent definition of the quantum entropy as the logarithm of the degeneracy of appropriate states in the dual 1+1 dimensional superconformal field theory. We find that the two proposals agree. This analysis also suggests a possible route to deriving the OSV conjecture.
We show that suitably regulated multi-trace primary states in large N CFTs behave like `in' and `out' scattering states in the flat-space limit of AdS. Their transition matrix elements approach the exact scattering amplitudes for the bulk theory, providing a natural CFT definition of the flat space S-Matrix. We study corrections resulting from the AdS curvature and particle propagation far from the center of AdS, and show that AdS simply provides an IR regulator that disappears in the flat space limit.
The prescription of the AdS/CFT correspondence is refined by using a regularization procedure, which makes is possible to calculate the divergent local terms in the CFT two-point function. We present the procedure for the example of the scalar field.
The strong subadditivity is the most important inequality which entanglement entropy satisfies. Based on the AdS/CFT conjecture, entanglement entropy in CFT is equal to the area of the minimal surface in AdS space. It is known that a Wilson loop can also be holographically computed from the minimal surface in AdS space. In this paper, we argue that Wilson loops also satisfy a similar inequality, and find several evidences of it.
$AdS/CFT$ to $dS/CFT$: Some Recent Developments
本文介绍了AdS/CFT对应关系及其在de Sitter和平直时空中的扩展，探讨了其基础理论和一致性检验。
We expand on Klebanov and Witten's recent proposal for formulating the AdS/CFT correspondence using irregular boundary conditions. The proposal is shown to be correct to any order in perturbation theory.
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