A. Fotopoulos, M. Tsulaia
We show how to decompose a Lagrangian for reducible massless bosonic Higher Spin modes into the ones describing irreducible (Fronsdal) Higher Spin modes on a D dimensional AdS space. Using this decomposition we construct a new Nonabelian cubic interaction vertex for reducible higher spin modes and two scalars on AdS from the already known vertex which involves irreducible (Fronsdal) modes.
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We consider the frame-like formulation of reducible sets of totally symmetric bosonic and fermionic higher-spin fields in flat and AdS backgrounds of any dimension, that correspond to so-called higher-spin triplets resulting from the string-inspired BRST approach. The explicit relationship of the fields of higher-spin triplets to the higher-spin vielbeins and connections is found. The gauge invariant actions are constructed including, in particular, the reducible (i.e. triplet) higher-spin fermion case in AdS_D space.
Adjustment of Faddeev-Popov quantization to reducible gauge theories: antisymmetric tensor fermion in $AdS_d$ space
本文提出一种调整Faddeev-Popov因式分解的方法，用于量子化具有线性相关生成元的可约化规范理论，并在d维AdS时空中应用于二阶反对称费米子模型，证明其与BV形式等价且泛函积分中鬼场数量更少，最终推导出有效作用量。
We compute the current exchanges between triplets of higher spin fields which describe reducible representations of the Poincare group. Through this computation we can extract the propagator of the reducible higher spin fields which compose the triplet. We show how to decompose the triplet fields into irreducible HS fields which obey Fronsdal equations, and how to compute the current-current interaction for the cubic couplings which appear in ArXiv:0708.1399 [hep-th] using the decomposition into irreducible modes. We compare this result with the same computation using a gauge fixed (Feynman) v…
We develop further the general light-cone gauge approach in AdS space and apply it for studying continuous-spin field. For such field, we find light-cone gauge Lagrangian and realization of relativistic symmetries. We find a simple realization of spin operators entering our approach. Generalization of our results to the gauge invariant Lagrangian formulation is also described. We conjecture that, in the framework of AdS/CFT, the continuous-spin AdS field is dual to light-ray conformal operator. For some particular cases, our continuous-spin field leads to reducible models. We note two reducibl…
In this short note we present a Lagrangian formulation for free bosonic Higher Spin fields which belong to massless reducible representations of D-dimensional Anti de Sitter group using an ambient space formalism.
We discuss the analytic properties of AdS scalar exchange graphs in the crossed channel. We show that the possible non-analytic terms drop out by virtue of non-trivial properties of generalized hypergeometric functions. The absence of non-analytic terms is a necessary condition for the existence of an operator product expansion for CFT amplitudes obtained from AdS/CFT correspondence.
In this note we explicitly compute the graviton exchange graph for scalar fields with arbitrary conformal dimension Δin arbitrary spacetime dimension d. This results in an analytical function in Δas well as in d.
We explicitly calculate a Witten diagram with general spinor field exchange on $(d+1)$-dimensional Euclidean Anti-de Sitter space, which is necessary to evaluate four-point correlation functions with spinor fields when we make use of the AdS/CFT correspondence, especially in supersymmetric cases. We also show that the amplitude can be reduced to a scalar exchange amplitude. We discuss the operator product expansion of the dual conformal field theory by interpreting the short distance expansion of the amplitude according to the AdS/CFT correspondence.
A classical exchange algebra of the superstring on S^5 with the AdS-time is shown on the light-like plane. To this end we use the geometrical method of which consistency is guaranteed by the classical Yang-Baxter equation. The Dirac method does not work, there being constraints which contain first-class and second-class and one can disentangle with each other keeping the isometry hardly.
We apply the BRST approach, developed for higher spin field theories, to Lagrangian construction for totally antisymmetric massive fermionic fields in AdS_d space. As well as generic higher spin massive theories, the obtained Lagrangian theory is a reducible gauge model containing, besides the basic field, a number of auxiliary (Stuckelberg) fields and the order of reducibility grows with the value of the rank of the antisymmetric field. However, unlike the generic higher spin theory, for the special case under consideration we show that one can get rid of all the auxiliary fields and the fina…
The graviton exchange diagram for the correlation function of arbitrary scalar operators is evaluated in anti-de Sitter space, AdS(d+1). This enables us to complete the computation of the 4-point amplitudes of dilaton and axion fields in IIB supergravity on AdS5 X S5. By the AdS/CFT correspondence, we obtain the 4-point functions of the marginal operators Tr (F^2+...) and Tr(F F~ +...) in N=4, d=4 SU(N) SYM at large N, large g^2 N. The short distance asymptotics of the amplitudes are studied. We find that in the direct channel the leading power singularity agrees with the expected contribution…
We study the amplitude for exchange of massless gauge bosons between pairs of massive scalar fields in Anti-de Sitter space. In the AdS/CFT correspondence this amplitude describes the contribution of conserved flavor symmetry currents to 4-point functions of scalar operators in the boundary conformal theory. A concise, covariant (Y2K-compatible) derivation of the gauge boson propagator in $\AdS_{d+1}$ is given. Techniques are developed to calculate the two bulk integrals over AdS space leading to explicit expressions or convenient, simple integral representations for the amplitude. The amplitu…
We study the exchange diagrams in the computation of four-point functions of all chiral primary operators in D=4, $\mathcal{N}=4$ Super-Yang-Mills using AdS/CFT correspondence. We identify all supergravity fields that can be exchanged and compute the cubic couplings. As a byproduct, we also rederive the normalization of the quadratic action of the exchanged fields. The cubic couplings computed in this paper and the propagators studied extensively in the literature can be used to compute almost all the exchange diagrams explicitly. Some issues in computing the complete four-point function in th…
In this paper we compute the tree-level four-point scattering amplitude of two dilatini and two axion-dilaton fields in type IIB supergravity in AdS5 x S5. A special feature of this process is that there is an "exotic" channel in which there are no singleparticle poles. Another novelty is that this process involves the exchange of a bulk gravitino. The amplitude is interpreted in terms of N = 4 supersymmetric Yang-Mills theory at large 't Hooft coupling. Properties of the Operator Product Expansion are used to analyze the various contributions from single- and double-trace operators in the wea…
A new method is discussed which vastly simplifies one of the two integrals over AdS(d+1) required to compute exchange graphs for 4-point functions of scalars in the AdS/CFT correspondence. The explicit form of the bulk-to-bulk propagator is not required. Previous results for scalar, gauge boson and graviton exchange are reproduced, and new results are given for massive vectors. It is found that precisely for the cases that occur in the AdS(5) X S(5) compactification of Type IIB supergravity, the exchange diagrams reduce to a finite sum of graphs with quartic scalar vertices. The analogous inte…
Wilson network expansion for four-point contact and exchange scalar Feynman diagrams in AdS$_2$
论文推导了AdS传播子的新积分恒等式，并发展了AdS费曼图的Wilson网络扩展方法，展示了二维四点接触和交换标量图可展开为Wilson线网络算子的矩阵元无穷级数，每级由特定的多迹算子表征，结果在共形边界附近重现了四点Witten图分解为共形块的已知分解。
The scalar field exchange diagram for the correlation function of four scalar operators is evaluated in anti-de Sitter space, $AdS_{d+1}$. The conformal dimensions $Δ_i$, $i=1,...,4$ of the scalar operators and the dimension $Δ$ of the exchanged field are arbitrary, constrained only to obey the unitarity bound. Techniques similar to those developed earlier for gauge boson exchange are used, but results are generally more complicated. However, for integer $Δ_i, Δ$, the amplitude can be presented as a multiple derivative of a simple universal function. Results simplify if further conditions hold…
We present a simple general relation between tree-level exchanges in AdS and dS. This relation allows to directly import techniques and results for AdS Witten diagrams, both in position and momentum space, to boundary correlation functions in dS. In this work we apply this relation to define Mellin amplitudes and a spectral representation for exchanges in dS. We also derive the conformal block decomposition of a dS exchange, both in the direct and crossed channels, from their AdS counterparts. The relation between AdS and dS exchanges itself is derived using a recently introduced Mellin-Barnes…
Motivated by AdS/CFT, we address the following outstanding question in large $N$ conformal field theory: given the appearance of a single-trace operator in the ${\cal O}\times{\cal O}$ OPE of a scalar primary ${\cal O}$, what is its total contribution to the vacuum four-point function $\langle {\cal O}{\cal O}{\cal O}{\cal O}\rangle$ as dictated by crossing symmetry? We solve this problem in 4d conformal field theories at leading order in $1/N$. Viewed holographically, this provides a field theory reconstruction of crossing-symmetric, four-point exchange amplitudes in AdS$_5$. Our solution tak…
Extremal couplings, graviton exchange, and gluon scattering in AdS
本文研究了AdS中带七膜奇点的IIB型弦理论对偶理论，计算了引力子与胶子模间的极值耦合，利用引力子交换项解释了发散的3点图，并结合超对称局域化完全固定了特定4d $\mathcal{N}=2$规范理论在$1/N^2$阶的全息关联函数。
In the large 't Hooft coupling limit, the hadronic size of baryon is small and nucleon-nucleon potential is obtained from massless pseudo-scalar exchanges and an infinite tower of spin one mesons exchanges. In this paper we use the holographic nucleon-nucleon interaction and obtain the corresponding potential and binding energy for deuteron and tritium nuclei. The obtained potentials are repulsive at short distances and clearly become zero by increasing distance as we expected.
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…
Using the AdS/CFT correspondence in a confining backgroundand the worldline formalism of gauge field theories,we compute scattering amplitudes with an exchange of quark andantiquark in the $t$-channel corresponding to Reggeon exchange. Itrequires going beyond the eikonal approximation, which was used when studying Pomeron exchange. The wordline path integral is evaluated through the determination of minimal surfaces and their boundaries by the saddle-point method at large gauge coupling g^2N_c. We find a Regge behaviour with linear Regge trajectories. The slope is related to the $q\bar q$ stat…
We determine the AdS exchange diagrams needed for the computation of 4--point functions of chiral primary operators in the SCFT_2 dual to the D=6 N=4b supergravity on the AdS_3\times S^3 background and compute the corresponding cubic couplings. We also address the issue of consistent truncation.
Four-point functions of R-currents are discussed within Anti-de Sitter supergravity. In particular, we compute Witten diagrams with graviton and gauge boson exchange in the high energy Regge limit. Assuming validity of the AdS/CFT correspondence, our results apply to R-current four-point functions of N=4 super Yang-Mills theory at strong coupling.
We discuss the properties of four-point functions in the context of the correspondence between a classical supergravity theory in the bulk of the Anti de Sitter space and quantum conformal field theory at the boundary. The contribution to a four-point function from the exchange of a scalar field of arbitrary mass in AdS space is explicitly identified with that of the corresponding operator in the conformal partial wave expansion of a four-point function on the CFT side. Integral representations are found for the massless vector and graviton exchanges. We also discuss some aspects of the four-p…
A non-critical holographic QCD model constructed in the six dimensional Anti-de-Sitter ($AdS_6$) supergravity background is employed to study a the baryon. It is shown that the size of the baryon is of order one with respect to the $λ$, however, it is smaller than the scale of the dual QCD. An effective four dimensional action for the nucleon is obtained in terms of the meson exchange potentials. All meson-nucleon couplings in the non-critical $AdS_6$ background are calculated. Results obtained using our model are compared with predictions of four modern phenomenological interaction models. Al…
We analyze conformal field theory 4-point functions of the form A ~ O_1(x_1) O_2(x_2) O_1(x_3) O_2(x_4), where the operators O_i are scalar primaries. We show that, in the Lorentzian regime, the limit x_1 -> x_3 is dominated by the exchange of conformal partial waves of highest spin. When partial waves of arbitrary spin contribute to A, the behavior of the Lorentzian amplitude for x_1 -> x_3 must be analyzed using complex-spin techniques, leading to a generalized Regge theory for CFT's. Whenever the CFT is dual to a string theory, the string tree-level contribution A_tree to the amplitude A pr…
We derive an eikonal approximation to high energy interactions in Anti-de Sitter spacetime, by generalizing a position space derivation of the eikonal amplitude in flat space. We are able to resum, in terms of a generalized phase shift, ladder and cross ladder graphs associated to the exchange of a spin j field, to all orders in the coupling constant. Using the AdS/CFT correspondence, the resulting amplitude determines the behavior of the dual conformal field theory four point function < O_1 O_2 O_1 O_2 > for small values of the cross ratios, in a Lorentzian regime. Finally we show that the ph…
Within the conjectured duality between N=4 super Yang-Mills and Anti-deSitter string theory, the BFKL Pomeron of the gauge theory corresponds to the graviton mode of the dual string. As a first step towards analyzing multigraviton exchange, we investigate R-current six-point functions within the supergravity approximation. We compute the analogue of diffractive scattering, and we analyze the triple Regge limit. In the supergravity approximation the triple graviton vertex is found to vanish.
In this talk we describe the application of the AdS/CFT correspondence for a confining background to the study of high energy scattering amplitudes in gauge theory. We relate the energy behaviour of scattering amplitudes to properties of minimal surfaces of the helicoidal type. We describe the results of hep-th/0003059 and hep-th/0010069 for amplitudes with vacuum quantum number exchange and, very briefly, hep-th/0110024 on the extension of this formalism to Reggeon exchange.
We present analyses on nucleon structure functions at the small Bjorken-$x$ in the framework of holographic QCD. In this study, we improve the description of the target nucleon in the current setup of the holographic model by introducing a soft-wall AdS/QCD model, in which the AdS geometry is smoothly cut off at IR. Combining the improved Pomeron-nucleon coupling and the wave function of the 5D U(1) vector field with the BPST Pomeron exchange kernel, then we obtain the structure functions. Here we focus on the nonperturbative kinematical region, where $10^{-6} \leq x \leq 10^{-2}$ and $0.1 \le…
We study heavy ion collisions at strong 't Hooft coupling using AdS/CFT correspondence. According to the AdS/CFT dictionary heavy ion collisions correspond to gravitational shock wave collisions in AdS_5. We construct the metric in the forward light cone after the collision perturbatively through expansion of Einstein equations in graviton exchanges. We obtain an analytic expression for the metric including all-order graviton exchanges with one shock wave, while keeping the exchanges with another shock wave at the lowest order. We read off the corresponding energy-momentum tensor of the produc…
In the past decade overwhelming evidence has emerged for a conjectured duality between a wide class of gauge theories in d dimensions and string theories on asymptotically AdS_{d+1} spaces. We apply this duality to scattering processes that occur via Pomeron exchange. First we develop the Pomeron in string theory, as done by Brower, Polchinski, Strassler and Tan, showing that it naturally emerges as the Regge Trajectory of the AdS graviton. Next we apply the AdS Pomeron to the study of Deeply Virtual Compton Scattering (DVCS), and see that our model gives good results when compared to HERA dat…
We consider correlators of N=4 super Yang Mills of the form A ~ < O_1 O_2 O*_1 O*_2 >, where the operators O_1 and O_2 are scalar primaries. In particular, we analyze this correlator in the planar limit and in a Lorentzian regime corresponding to high energy interactions in AdS. The planar amplitude is dominated by a Regge pole whose nature varies as a function of the 't Hooft coupling g^2. At large g, the pole corresponds to graviton exchange in AdS, whereas at weak g, the pole is that of the hard perturbative BFKL pomeron. We concentrate on the weak coupling regime and analyze pomeron exchan…
Towards Large-Spin Effective Theory I: Three-Particle States in AdS $ϕ^4$ Theory
本文提出在大自旋极限下利用 AdS 半径与粒子间距的尺度分离为 CFT 前导扭度态构造有效哈密顿量，并以 AdS $ϕ^4$ 玩具模型到 $O(λ^2)$ 阶为例，展示了长程非局域势与短程局域项的分离及与 CFT 数据的匹配方法。
Parametrization of GPDs from t-channel string exchange in AdS spaces
本文提出一种基于AdS空间中t通道弦交换的弦参数化方法，仅用五个Regge斜率参数即可对所有偏斜度生成核子夸克和胶子GPD，且与格点数据一致，首次避免了反卷积问题。
We examine the process of Deep Inelastic Scattering (DIS) in the small-x limit, where Pomeron exchange dominates. Using the AdS/CFT correspondence, we study Pomeron exchange in the dual string theory in AdS space, which allows us to study DIS at strong coupling. Two possibilities are examined, a purely conformal model, and a model with a hard-wall cutoff introduced to take into account the effects of confinement. Comparing our calculations with HERA DIS data, we find a very good agreement not only at large $Q^2$ dominated by conformal symmetry, but due to our strong coupling approach which all…
Within holography, we calculate the contribution of an arbitrary spin-s gauge boson exchange in $AdS_{d+1}$ to the four-point function with scalar operators on the boundary. As an important ingredient, we first compute the complete bulk-to-bulk propagators for massless bosonic higher-spin fields in the metric-like formulation, in any dimension and in various gauges. The split representation of the bulk-to-bulk propagators in terms of bulk-to-boundary propagators allows to present the higher-spin exchange diagram in the form of a conformal partial wave expansion. Our results provide a step towa…
The Virasoro algebra determines all `graviton' matrix elements in AdS$_3$/CFT$_2$. We study the explicit exchange of any number of Virasoro gravitons between heavy and light CFT$_2$ operators at large central charge. These graviton exchanges can be written in terms of new on-shell tree diagrams, organized in a perturbative expansion in $h_H/c$, the heavy operator dimension divided by the central charge. The Virasoro vacuum conformal block, which is the sum of all the tree diagrams, obeys a differential recursion relation generalizing that of the Catalan numbers. We use this recursion relation …
We derive non-linear commutator HS symmetry algebra, which encode unitary irreducible representations of AdS group subject to Young tableaux $Y(s_1,...,s_k)$ with $k\geq 2$ rows on $d$-dimensional anti-de-Sitter space. Auxiliary representations for specially deformed non-linear HS symmetry algebra in terms of generalized Verma module in order to additively convert a subsystem of second-class constraints in the HS symmetry algebra into one with first-class constraints are found explicitly for the case of HS fields for $k=2$ Young tableaux. The oscillator realization over Heisenberg algebra for …
We consider high energy collisions of two shock waves in AdS_5 as a model of ultrarelativistic nucleus-nucleus collisions in the boundary theory. We first calculate the graviton field produced in the collisions in the NLO and NNLO approximations, corresponding to three- and four-graviton exchanges with the shock waves. We then consider the asymmetric limit where the energy density in one shock wave is much higher than in the other one. In the boundary theory this setup corresponds to proton-nucleus collisions, with the nucleus being the denser of the two shock waves and the proton being the le…
Gauge Invariant Lagrangian Formulations for Mixed Symmetry Higher Spin Bosonic Fields in AdS Spaces
推导了AdS空间中混合对称高旋场的非线性对称代数与BRST算子，构建了规范不变拉格朗日表述，并发展了用于暗物质候选大质量高旋场的离壳三次相互作用顶点的BRST构建方法。
We introduce the impact-parameter representation for conformal field theory correlators of the form A ~ < O_1 O_2 O_1 O_2 >. This representation is appropriate in the eikonal kinematical regime, and approximates the conformal partial-wave decomposition in the limit of large spin and dimension of the exchanged primary. Using recent results on the two-point function < O_1 O_1 >_{shock} in the presence of a shock wave in Anti-de Sitter, and its relation to the discontinuity of the four-point amplitude A across a kinematical branch-cut, we find the high spin and dimension conformal partial- wave d…
We extend to its spin~3/2 supersymmetric partner the very recent demonstration that the massless limit of massive spin~2 exchange amplitudes can be made continuous in background AdS spaces, in contrast to the known flat space discontinuities for both systems. In an AdS background, unlike spin~2 where the limit m\to0 is the massless one, spin~3/2 ``masslessness'' requires m\to\sqrt{-Λ/3}, the supergravity value tuning the mass and cosmological constant that uniquely provides gauge invariance and two helicities. We find that continuity of the spin~3/2--mediated exchange amplitude can be regained…
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