We develop a new method for decomposing Witten diagrams into conformal blocks. The steps involved are elementary, requiring no explicit integration, and operate directly in position space. Central to this construction is an appealingly simple answer to the question: what object in AdS computes a conformal block? The answer is a "geodesic Witten diagram," which is essentially an ordinary exchange Witten diagram, except that the cubic vertices are not integrated over all of AdS, but only over bulk geodesics connecting the boundary operators. In particular, we consider the case of four-point functions of scalar operators, and show how to easily reproduce existing results for the relevant conformal blocks in arbitrary dimension.
We provide a new proof of Cachazo-Svrcek-Witten rules for tree-level gluonic amplitudes. As a key step, we explicitly show the cancellation of spurious poles originating from the maximally helicity violating vertices in these rules. To achieve this, we introduce specially-defined two-off-shell-line sub-amplitudes and study their residues at spurious poles.
We provide a uniform solution to 4d N=2 gauge theory with a single gauge group G=A,D,E when the one-loop contribution to the beta function from any irreducible component R of the hypermultiplets is less than or equal to half of that of the adjoint representation. The solution is given by a non-compact Calabi-Yau geometry, whose defining equation is built from explicitly known polynomials W_G and X_R, associated respectively to the gauge group G and each irreducible component R. We provide many pieces of supporting evidence, for example by analyzing the system from the point of view of the 6d N…
We have performed a direct calculation of Witten index in N = 1,2,3 supersymmetric Yang-Mills Chern-Simons 3d theories. We do it in the framework of Born-Oppenheimer (BO) approach by putting the system into a small spatial box and studying the effective Hamiltonian depending on the zero field harmonics. At the tree level, our results coincide with the results of Witten, but there is a difference in the way the loop effects are implemented. In Witten's approach, one has only take into account the fermion loops, which bring about a negative shift of the (chosen positive at the tree level) Chern-…
We describe a systematic approach for the evaluation of Witten diagrams for multi-loop scattering amplitudes of a conformally coupled scalar $ϕ^4$-theory in Euclidean AdS$_4$, by recasting the Witten diagrams as flat space Feynman integrals. We derive closed form expressions for the anomalous dimensions for all double-trace operators up to the second order in the coupling constant. We explain the relation between the flat space unitarity methods and the discontinuities of the short distance expansion on the boundary of Witten diagrams.
We calculate an unrefined limit of the superconformal index (the Schur-like index) of the Klebanov-Witten theory from the dual AdS side by using the recently developed giant graviton expansion method. Our formula includes multiple sums of the contribution of the D3-branes wrapped on three-cycles in the internal space. We numerically confirm the validity of our formula by comparing indices obtained by the formula with the gauge theory results.
In this paper we consider Witten diagrams at one loop in AdS space for scalar $ϕ^3+ϕ^4$ theory. After using Schwinger parametrization to trivialize the space-time loop integration, we extract the Mellin-Barnes representation for the one-loop corrections to the four-particle scattering up to an integration over the Schwinger parameters corresponding to the propagators of the internal particles running into the loop. We then discuss an approach to deal with those integrals.
Both celestial and momentum space amplitudes in four dimensions are beset by divergences resulting from spacetime translation and sometimes scale invariance. In this paper we consider a (linearized) marginal deformation of the celestial CFT for Yang-Mills theory which preserves 2D conformal invariance but breaks both spacetime translation and scale invariance and involves a chirally coupled massive scalar. The resulting celestial amplitudes are completely finite (apart from the usual soft and collinear divergences) and take the canonical CFT form. Moreover, we show they can be simply rewritten…
In this paper we find various new backgrounds in Type IIB, IIA and M-theory with an $AdS_3$-factor. The solutions are smooth and preserve small amounts of SUSY. These new backgrounds are found by application of non-Abelian T-duality (sometimes combined with T-duality) on the supergravity solution dual to the Klebanov-Witten CFT compactified to two dimensions. The field theory aspects encoded by these backgrounds are studied. We give a detailed account of conserved charges, central charges, entanglement entropy and Wilson loops. Further, we present a possible field theory interpretation for our…
我们进一步研究了在AdS_{4/7} x S^{7/4}背景下的开放超膜。开超膜可以有M5-膜和9-膜作为Dirichlet膜。在AdS和pp-波的情况下，Dirichlet膜的构型是受限制的。在hep-th/0310035中给出了一种可能的狄利克雷膜的分类，该分类直到并包括费米子变量的四阶，即使在全阶的情况下也是有效的。我们还讨论了AdS_{4/7} x S^{7/4}上的开M5-膜.
We revisit the microscopic description of AdS$_3$ black holes in light of recent progress on their higher dimensional analogues. The grand canonical partition function that follows from the AdS$_3$/CFT$_2$ correspondence describes BPS and nearBPS black hole thermodynamics. We formulate an entropy extremization principle that accounts for both the black hole entropy and a constraint on its charges, in close analogy with asymptotically AdS black holes in higher dimensions. We are led to interpret supersymmetric black holes as ensembles of BPS microstates satisfying a charge constraint that is no…
We investigate the absorption cross section for minimal-coupled scalars in the warped AdS_3 black hole. According to our calculation, the cross section reduces to the horizon area in the low energy limit as usually expected in contrast to what was previously found. We also calculate the greybody factor and find that the effective temperatures for the two chiral CFT's are consistent with that derived from the quasinormal modes. Observing the conjectured warped AdS/CFT correspondence, we suspect that a specific sector of the CFT operators with the desired conformal dimension could be responsible…
In this paper we study an $AdS_5$ solution constructed using non-Abelian T-duality, acting on the Klebanov-Witten background. We show that this is dual to a linear quiver with two tails of gauge groups of increasing rank. The field theory dynamics arises from a D4-NS5-NS5' brane set-up, generalizing the constructions discussed by Bah and Bobev. These realize $\mathcal{N}=1$ quiver gauge theories built out of $\mathcal{N}=1$ and $\mathcal{N}=2$ vector multiplets flowing to interacting fixed points in the infrared. We compute the central charge using $a$-maximization, and show its precise agreem…
We apply the new thermodynamical method proposed initially by Hindi. et al \cite{base} to revisit the phase structure of the AdS black hole in the massive gravity framework. In comparison to the standard thermodynamical method used in literature \cite{mass}, we show that this new technical approach can easily reproduce the critical behavior inherent to this black hole configuration and addresses some of the shortcomings of the standard method. We also show the ability of this new perception to find all possible critical points and regions in which phase transitions occur, an impossible task in…
We show the AdS/CFT correspondence between the conformal partial wave and the geodesic Witten diagram with anti-symmetric exchange. To this end, we introduce the embedding space formalism for anti-symmetric fields in AdS. Then we prove that the geodesic Witten diagram satisfies the conformal Casimir equation and the appropriate boundary condition. Furthermore, we discuss the connection between the geodesic Witten diagram and the shadow formalism by using the split representation of harmonic function for anti-symmetric fields. We also discuss the 3pt geodesic Witten diagrams and its extension t…
We present a formula for the holographic 4-point correlators in AdS$_3 \times S^3$ involving four single-trace operators of dimension $k, k, l, l$. As an input we use the supergravity results for the Heavy-Heavy-Light-Light correlators that can be derived by studying the linear fluctuations around known asymptotically AdS$_3 \times S^3$ geometries. When the operators of dimension $k$ and $l$ are in the same multiplet there are contributions due to the exchange of single-trace operators in the $t$ and $u$ channels, which are not captured by the approach mentioned above. However by rewriting the…
We develop a new embedding-space formalism for AdS$_4$ and CFT$_3$ that is useful for evaluating Witten diagrams for operators with spin. The basic variables are Killing spinors for the bulk AdS$_4$ and conformal Killing spinors for the boundary CFT$_3$. The more conventional embedding space coordinates $X^I$ for the bulk and $P^I$ for the boundary are bilinears in these new variables. We write a simple compact form for the general bulk-boundary propagator, and, for boundary operators of spin $\ell \geq 1$, we determine its conservation properties at the unitarity bound. In our CFT$_3$ formali…
In this sequel to [L-Y1], [L-L-S-Y], and [L-Y2] (respectively arXiv:0709.1515 [math.AG], arXiv:0809.2121 [math.AG], and arXiv:0901.0342 [math.AG]), we study a D-brane probe on a conifold from the viewpoint of the Azumaya structure on D-branes and toric geometry. The details of how deformations and resolutions of the standard toric conifold $Y$ can be obtained via morphisms from Azumaya points are given. This should be compared with the quantum-field-theoretic/D-brany picture of deformations and resolutions of a conifold via a D-brane probe sitting at the conifold singularity in the work of Kle…
We initiate the study of bound state scattering in AdS space at the level of Witten diagrams. For concreteness, we focus on the case with only scalar fields and analyze several basic diagrams which more general diagrams reduce to. We obtain closed form expressions for their Mellin amplitudes with arbitrary conformal dimensions, which exhibit interesting behavior. In particular, we observe that certain tree-level bound state Witten diagrams have the same structure as loop diagrams in AdS.
We consider three-parameter Yang-Baxter deformations of the $AdS_5\times T^{1,1}$ superstring for abelian $r$-matrices which are solutions of the classical Yang-Baxter equation. We find two new backgrounds which are dual to the dipole deformed Klebanov-Witten gauge theory and to the nonrelativistic Klebanov-Witten gauge theory with Schrödinger symmetry
The computation of CFT correlation functions via Witten diagrams in AdS space can be simplified via the Mellin transform. Recently a set of Feynman rules for tree-level Mellin space amplitudes has been proposed for scalar theories. In this note we derive these rules by explicitly evaluating all of the relevant Witten diagram integrals for the scalar phi^n theory. We also check that the rules reduce to the usual Feynman rules in the flat space limit.
We develop a framework for the reconstruction of the bulk theory dual to conformal field theory (CFT) without any assumption by means of a flow equation. To this end we investigate a minimal extension of the free flow equation and find that at a special parametrization the conformal transformation for a normalized smeared operator exactly becomes the isometry of anti-de Sitter space (AdS). By employing this special flow equation to O$(N)$ vector models, we explicitly show that the AdS geometry as well as the scalar field satisfying the GKP-Witten relation concurrently emerge in this framework.
We give a systematic procedure to evaluate conformal partial waves involving symmetric tensors for an arbitrary CFT$_d$ using geodesic Witten diagrams in AdS$_{d+1}$. Using this procedure we discuss how to draw a line between the tensor structures in the CFT and cubic interactions in AdS. We contrast this map to known results using three-point Witten diagrams: the maps obtained via volume versus geodesic integrals differ. Despite these differences, we show how to decompose four-point exchange Witten diagrams in terms of geodesic diagrams, and we discuss the product expansion of local bulk fiel…
The generating functional of stress tensor correlation functions in two-dimensional conformal field theory is the nonlocal Polyakov action, or equivalently, the Liouville or Alekseev-Shatashvili action. I review its holographic derivation within the AdS$_3$/CFT$_2$ correspondence, both in metric and Chern-Simons formulations. I also provide a detailed comparison with the well-known Hamiltonian reduction of three-dimensional gravity to a flat Liouville theory, and conclude that the two results are unrelated. In particular, the flat Liouville action is still off-shell with respect to bulk equati…
In this paper we discuss geodesic Witten diagrams in generic holographic conformal field theories with boundary or defect. Boundary CFTs allow two different decompositions of two-point functions into conformal blocks: boundary channel and ambient channel. Building on earlier work, we derive a holographic dual of the boundary channel decomposition in terms of bulk-to-bulk propagators on lower dimensional AdS slices. In the situation in which we can treat the boundary or defect as a perturbation around pure AdS spacetime, we obtain the leading corrections to the two-point function both in bounda…
We reconsidered the quantum gravity description of the near horizon extremal Reissner-Nordstrøm black hole in the viewpoint of the AdS$_2$/CFT$_1$ correspondence. We found that, for pure electric case, the right moving central charge of dual 1D CFT is $6 Q^2$ which is different from the previous result $6 Q^3$ of left moving sector obtained by warped AdS$_3$/CFT$_2$ description. We discussed the discrepancy in these two approaches and examined novel properties of our result.
The Schwinger-Dyson equations for Green functions and 3-vertexes in planar approximation used 50 years ago in the earlier theory of conformal bootstrap are written in frames of the AdS/CFT correspondence. The technique of "Wightman-Witten" diagrams is used in calculations of the bubble bulk diagrams that permitted to obtain the values of conformal dimensions of primary operators in two models of the interacting bulk scalar fields which conformal dimensions obey "extremal" relation. Simple expressions for the four-point tree "Wightman-Witten" correlators of these primary operators are obtained …
We construct a generalization of Witten's Kaluza-Klein instanton, where a higher-dimensional sphere (rather than a circle as in Witten's instanton) collapses to zero size and the geometry terminates at a bubble of nothing, in a low energy effective theory of M theory. We use the solution to exhibit instability of non-supersymmetric AdS_5 vacua in M Theory compactified on positive Kaehler-Einstein spaces, providing a further evidence for the recent conjecture that any non-supersymmetric anti-de Sitter vacuum supported by fluxes must be unstable.
We calculate by a new way the two point function on the boundary of AdS spacetime in 1+2 dimensions for the massless conformal real scalar field. The result agrees with the answer provided by the Boundary-limit Holography and Witten recipe. This is done in Poincaré coordinates. The basic ingredients of this new method are conformal techniques, quantum fields defined on a half of Minkowski spacetime and a limit inspired by the Boundary-limit Holography. We also show that a state in AdS, the global vacuum, in three dimensions induces a state on the conformal boundary of AdS spacetime, which in t…
Recently there has been progress in the computation of the anomalous dimensions of gauge theory operators at strong coupling by making use of AdS/CFT correspondence. On string theory side they are given by dispersion relations in the semiclassical regime. We revisit the problem of large charges expansion of the dispersion relations for simple semiclassical strings in $AdS_4\times\mathbb{CP}^3$ background. We present the calculation of the corresponding anomalous dimensions of the gauge theory operators to an arbitrary order using three different methods. Although the results of the three metho…
In this paper we investigate the behavior of linearized gravitational excitation in the Born-Infeld Gravity in $AdS_3$ space. We obtain the linearized equation of motion and show that this higher order gravity propagate two gravitons, massless and massive, on the $AdS_3$ background. In contrast to the $R^2$ models, such as TMG or NMG, Born-Infeld Gravity does not have a critical point for any regular choice of parameters. So the logarithmic solution is not a solution of this model, due to this one can not find a logarithmic conformal field theory as a dual model for Born-Infeld Gravity.
In three-dimensional AdS space, we consider the gravitational collapse of dust shell and then investigate the quantum radiation from the collapsing shell by employing the functional Schrödinger formalism. In the formation of the BTZ black hole, the interior geometry of the shell can be chosen as either the massless black hole or the global AdS space. In the incipient black hole limit, we obtain the wave function exactly from the time-dependent Schrödinger equation for a massless scalar field. Then, we show that the occupation number of excited states can be written by analytic expressions, and…
Recalculating the Bogoliubov coefficients from the solutions in Phys. Rev. D 78, 103517 (2008), we obtain the mean number of boson pairs in a uniform electric field in the global coordinates dS_2 and AdS_2, which have the correct zero-field and zero-curvature limits, and study the vacuum persistence at one-loop. The mean number in AdS_2 gives the lowest limit to the Breitenloher-Freedman bound in the uniform electric field, and the mean numbers in dS_2 and AdS_2 satisfy the reciprocal relation N_{dS} (R, E) N_{AdS} (R, E) = 1 under the analytical continuation of the scalar curvature R.
We develop a systematic framework to compute the conformal partial wave expansions (CPWEs) of tree-level four-point Witten diagrams with totally symmetric external fields of arbitrary mass and integer spin in AdS$_{d+1}$. Employing this framework, we determine the CPWE of a generic exchange Witten diagram with spinning exchanged field. As an intermediate step, we diagonalise the linear map between spinning three-point conformal structures and spinning cubic couplings in AdS. As a concrete application, we compute all exchange diagrams in the type A higher-spin gauge theory on AdS$_{d+1}$, which…
We develop the embedding formalism for odd dimensional Dirac spinors in AdS and apply it to the (geodesic) Witten diagrams including fermionic degrees of freedom. We first show that the geodesic Witten diagram (GWD) with fermion exchange is equivalent to the conformal partial waves associated with the spin one-half primary field. Then, we explicitly demonstrate the GWD decomposition of the Witten diagram including the fermion exchange with the aid of the split representation. The geodesic representation of CPW indeed gives the useful basis for computing the Witten diagrams.
We study local operator insertions on 1/2-BPS line defects in ABJM theory. Specifically, we consider a class of four-point correlators in the CFT$_1$ with SU$(1, 1|3)$ superconformal symmetry defined on the 1/2-BPS Wilson line. The relevant insertions belong to the short supermultiplet containing the displacement operator and correspond to fluctuations of the dual fundamental string in AdS$_4 \times \mathbb{C}\textrm{P}^3$ ending on the line at the boundary. We use superspace techniques to represent the displacement supermultiplet and we show that superconformal symmetry determines the four-po…
Witten-O'Raifeartaigh potential revisited in the context of Warm Inflation
Ashoka University（阿肖卡大学）；University of Nottingham（诺丁汉大学）；Institute for Basic Science (IBS)（基础科学研究院）；Inter-University Centre for Astronomy and Astrophysics（大学间天文学与天体物理学中心）
Penrose limits of Lie Branes and a Nappi--Witten braneworld
从AdS_3 x S^3的Penrose极限是Inonu和Wigner意义下的群收缩这一观察出发，我们探讨了AdS_3 x S^3的对称D膜与其Penrose极限（一个类似于四维Nappi-Witten时空的六维对称平面波）的对称D膜之间的关系。这两个背景是李群承认双不变洛仑兹度量和对称的D-膜包裹他们的（扭曲）共轭类。我们确定了平面波背景下的（扭曲的和非扭曲的）对称D-膜，证明了充满空间的D5-膜的存在性，并分别证明了具有Nappi-Witten时空几何的D3-膜的叶理的存在性，这可以理解为AdS_3 x S^3中AdS_2 x S^2 D3-膜的彭罗斯极限。附带地，我们还得到了一个简单的标准对称平面波是等距的洛仑兹李群。特别地，我们观察到IIB弦论中的最大超对称平面波与洛伦兹李群等距，而M-理论中的最大超对称平面波与洛伦兹李群等距。
The Unruh temperature calculated from the global embedding of the Schwarzschild AdS spacetime into Minkowski spacetime was identified with the local temperature measured by a free-fall observer; however, it would be imaginary in a certain region outside the event horizon. So, the temperature was assumed to be zero of no thermal radiation for that region. In this paper, we revisit this issue in the exactly soluble two-dimensional Schwarzschild AdS black hole and present an alternative resolution to this problem by using the Tolman's procedure. However, the process is not straightforward in the …
We explore AdS/CFT correspondence between geodesic Witten diagrams and conformal blocks (conformal partial waves) with an external symmetric traceless tensor field. We derive an expression for the conformal partial wave with an external spin-1 field and show that this expression is equivalent to the amplitude of the geodesic Witten diagram. We also show the equivalence by using conformal Casimir equation in embedding formalism. Furthermore, we extend the construction of the amplitude of the geodesic Witten diagram to an external arbitrary symmetric traceless tensor field. We show our construct…
A large class of spherically symmetric static extremal black hole spacetimes possesses a stable null photon sphere on their horizons. For the extremal Kerr-Newman family, the photon sphere only really coincides with the horizon in the sense clarified by Doran. The condition under which photon orbit is stable on an asymptotically flat extremal Kerr-Newman black hole horizon has recently been clarified; it is found that a sufficiently large angular momentum destabilizes the photon orbit, whereas electrical charge tends to stabilize it. We investigated the effect of a negative cosmological consta…
The Witten-Yau theorem in the AdS/CFT correspondence conjectures that the conformal boundary to AdS space must possess a metric of non-negative scalar curvature for the conformal field theory defined thereon to be free of pathologies. By employing various tools from conformal geometry - such as almost Einstein structures, collapsing sphere products and tractor bundles - we rigorously prove this conjecture.
We investigate 1/2 BPS conformal surface operators in the Klebanov-Witten theory. These surface operators preserve certain parts of the conformal symmetry and R-symmetry as well as half of the supersymmetry. We propose the gravity dual of the surface operator as a configuration of a D3-brane in AdS_5 x T^{1,1}. This D3-brane preserves the same amount of the supersymmetry as the surface operator. We also compute the correlation function of the surface operator and a chiral primary operator.
Phenomenological AdS/QCD models, like hard wall and soft wall, provide hadronic mass spectra in reasonable consistency with experimental and (or) lattice results. These simple models are inspired in the AdS/CFT correspondence and assume that gauge/ gravity duality holds in a scenario where conformal invariance is broken through the introduction of an energy scale. Another important property of hadrons: the decay constant, can also be obtained from these models. However, a consistent formulation of an AdS/QCD model that reproduces the observed behavior of decay constants of vector meson excited…
Witten diagrams are basic objects for studying dynamics in AdS space, and also play key roles in the analytic functional bootstrap. However, these diagrams are notoriously hard to evaluate, making it extremely difficult to search for recursion relations among them. In this note, we present simple methods to obtain recursion relations for exchange Witten diagrams from conformal block recursion relations. We discover a variety of new relations, including the dimensional reduction formulae for exchange Witten diagrams. In particular, we find a five-term recursion relation relating exchange Witten…
