scholarly journals The perturbative CFT optical theorem and high-energy string scattering in AdS at one loop

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
António Antunes ◽  
Miguel S. Costa ◽  
Tobias Hansen ◽  
Aaditya Salgarkar ◽  
Sourav Sarkar
Keyword(s):  
Vertex Function ◽  
Flat Space ◽  
String Tension ◽  
High Energy ◽  
Tree Level ◽  
Optical Theorem ◽  
Space Limit ◽  
The One ◽  
High Energy Scattering ◽  
Regge Limit

Abstract We derive an optical theorem for perturbative CFTs which computes the double discontinuity of conformal correlators from the single discontinuities of lower order correlators, in analogy with the optical theorem for flat space scattering amplitudes. The theorem takes a purely multiplicative form in the CFT impact parameter representation used to describe high-energy scattering in the dual AdS theory. We use this result to study four-point correlation functions that are dominated in the Regge limit by the exchange of the graviton Regge trajectory (Pomeron) in the dual theory. At one-loop the scattering is dominated by double Pomeron exchange and receives contributions from tidal excitations of the scattering states which are efficiently described by an AdS vertex function, in close analogy with the known Regge limit result for one-loop string scattering in flat space at finite string tension. We compare the flat space limit of the conformal correlator to the flat space results and thus derive constraints on the one-loop vertex function for type IIB strings in AdS and also on general spinning tree level type IIB amplitudes in AdS.

scholarly journals CFT unitarity and the AdS Cutkosky rules

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
David Meltzer ◽  
Allic Sivaramakrishnan
Keyword(s):  
Flat Space ◽  
Tree Level ◽  
Optical Theorem ◽  
Conformal Field Theories ◽  
Strongly Coupled ◽  
Conformal Field ◽  
Weakly Coupled ◽  
S Matrix ◽  
Space Limit ◽  
Diagrammatic Method

Abstract We derive the Cutkosky rules for conformal field theories (CFTs) at weak and strong coupling. These rules give a simple, diagrammatic method to compute the double-commutator that appears in the Lorentzian inversion formula. We first revisit weakly-coupled CFTs in flat space, where the cuts are performed on Feynman diagrams. We then generalize these rules to strongly-coupled holographic CFTs, where the cuts are performed on the Witten diagrams of the dual theory. In both cases, Cutkosky rules factorize loop diagrams into on-shell sub-diagrams and generalize the standard S-matrix cutting rules. These rules are naturally formulated and derived in Lorentzian momentum space, where the double-commutator is manifestly related to the CFT optical theorem. Finally, we study the AdS cutting rules in explicit examples at tree level and one loop. In these examples, we confirm that the rules are consistent with the OPE limit and that we recover the S-matrix optical theorem in the flat space limit. The AdS cutting rules and the CFT dispersion formula together form a holographic unitarity method to reconstruct Witten diagrams from their cuts.

scholarly journals High Energy Scattering of Non-Critical Strings

1997 ◽  
Vol 12 (06) ◽  
pp. 1253-1263 ◽  
Author(s):  
Kenichiro Aoki ◽  
Eric D'Hoker
Keyword(s):  
Central Charge ◽  
String Tension ◽  
High Energy ◽  
Tree Level ◽  
Energy Limit ◽  
Electrostatic Problem ◽  
High Energy Limit ◽  
On Line ◽  
High Energy Scattering ◽  
Branch Cuts

We summarize recent work, in which we consider scattering amplitudes of non-critical strings in the limit where the energy of all external states is large compared to the string tension. We show that the high energy limit is dominated by a saddle point that can be mapped onto an electrostatic equilibrium configuration of an assembly of charges associated with the external states, together with a density of charges arising from the Liouville field. The Liouville charges accumulate on line segments, which produce quadratic branch cuts on the worldsheet. The electrostatic problem is solved for string tree level in terms of hyperelliptic integrals and is given explicitly for the 3- and 4-point functions. For generic values of the central charge, the high energy limit behaves in a string-like fashion, with exponential energy dependence.

scholarly journals Simplicity of AdS supergravity at one loop

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Luis F. Alday ◽  
Xinan Zhou
Keyword(s):  
Closed Form ◽  
Conformal Symmetry ◽  
Flat Space ◽  
Tree Level ◽  
Loop Level ◽  
Level Data ◽  
Space Limit ◽  
Loop Amplitude

Abstract We demonstrate the simplicity of AdS5× S5 IIB supergravity at one loop level, by studying non-planar holographic four-point correlators in Mellin space. We develop a systematic algorithm for constructing one-loop Mellin amplitudes from the tree-level data, and obtain a simple closed form answer for the $$ \left\langle {\mathcal{O}}_2^{SG}{\mathcal{O}}_2^{SG}{\mathcal{O}}_p^{SG}{\mathcal{O}}_p^{SG}\right\rangle $$ O 2 SG O 2 SG O p SG O p SG correlators. The structure of this expression is remarkably simple, containing only simultaneous poles in the Mellin variables. We also study the flat space limit of the Mellin amplitudes, which reproduces precisely the IIB supergravity one-loop amplitude in ten dimensions. Our results provide nontrivial evidence for the persistence of the hidden conformal symmetry at one loop.

scholarly journals Notes on gravity multiplet correlators in AdS3 × S3

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Congkao Wen ◽  
Shun-Qing Zhang
Keyword(s):  
Recursion Relation ◽  
Conformal Symmetry ◽  
Flat Space ◽  
The Other ◽  
Tree Level ◽  
Space Limit ◽  
Compact Expression ◽  
Tensor Multiplet ◽  
R Symmetry

Abstract We present a compact formula in Mellin space for the four-point tree-level holographic correlators of chiral primary operators of arbitrary conformal weights in (2, 0) supergravity on AdS3× S3, with two operators in tensor multiplet and the other two in gravity multiplet. This is achieved by solving the recursion relation arising from a hidden six-dimensional conformal symmetry. We note the compact expression is obtained after carefully analysing the analytic structures of the correlators. Various limits of the correlators are studied, including the maximally R-symmetry violating limit and flat-space limit.

Collective phenomena in the one-dimensional three-particle model of high-energy potential scattering

1979 ◽  
Vol 57 (7) ◽  
pp. 974-980
Author(s):  
V. I. Inozemtsev
Keyword(s):  
Solvable Model ◽  
Impulse Approximation ◽  
High Energy ◽  
Potential Scattering ◽  
Particle Model ◽  
Collective Phenomena ◽  
Energy Potential ◽  
Exactly Solvable ◽  
The One ◽  
High Energy Scattering

Within the framework of an exactly solvable model of three particles interacting through zero-range forces it is shown that the high-energy scattering with high momentum transfer is due to collective phenomena. The spectrum of particles scattered through 180° is compared with the results of impulse approximation.

scholarly journals Nonperturbative approach to the parton model

2016 ◽  
Vol 31 (06) ◽  
pp. 1650016 ◽  
Author(s):  
Yu. A. Simonov
Keyword(s):  
Nonperturbative Effects ◽  
Parton Model ◽  
String Tension ◽  
High Energy ◽  
Wave Functions ◽  
Parton Distributions ◽  
Text String ◽  
Preliminary Discussion ◽  
High Energy Scattering

In this paper, the nonperturbative parton distributions, obtained from the Lorentz contracted wave functions, are analyzed in the formalism of many-particle Fock components and their properties are compared to the standard perturbative distributions. We show that the collinear and IR divergencies specific for perturbative evolution treatment are absent in the nonperturbative version, however for large momenta [Formula: see text] (string tension), the bremsstrahlung kinematics is restored. A preliminary discussion of possible nonperturbative effects in DIS and high energy scattering is given, including in particular a possible role of multihybrid states in creating ridge-type effects.

scholarly journals The Virasoro-Shapiro amplitude in AdS5 × S5 and level splitting of 10d conformal symmetry

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
F. Aprile ◽  
J. M. Drummond ◽  
H. Paul ◽  
M. Santagata
Keyword(s):  
Conformal Symmetry ◽  
Flat Space ◽  
Tree Level ◽  
Yang Mills ◽  
Anomalous Dimensions ◽  
Crossing Symmetry ◽  
String Correction ◽  
Space Limit ◽  
Fixed Order ◽  
Bootstrap Algorithm

Abstract The genus zero contribution to the four-point correlator $$ \left\langle {\mathcal{O}}_{p_1}{\mathcal{O}}_{p_2}{\mathcal{O}}_{p_3}{\mathcal{O}}_{p_4}\right\rangle $$ O p 1 O p 2 O p 3 O p 4 of half-BPS single-particle operators $$ {\mathcal{O}}_p $$ O p in $$ \mathcal{N} $$ N = 4 super Yang-Mills, at strong coupling, computes the Virasoro-Shapiro amplitude of closed superstrings in AdS5× S5. Combining Mellin space techniques, the large p limit, and data about the spectrum of two-particle operators at tree level in supergravity, we design a bootstrap algorithm which heavily constrains its α′ expansion. We use crossing symmetry, polynomiality in the Mellin variables and the large p limit to stratify the Virasoro-Shapiro amplitude away from the ten-dimensional flat space limit. Then we analyse the spectrum of exchanged two-particle operators at fixed order in the α′ expansion. We impose that the ten-dimensional spin of the spectrum visible at that order is bounded above in the same way as in the flat space amplitude. This constraint determines the Virasoro-Shapiro amplitude in AdS5× S5 up to a small number of ambiguities at each order. We compute it explicitly for (α′)5,6,7,8,9. As the order of α′ grows, the ten dimensional spin grows, and the set of visible two-particle operators opens up. Operators illuminated for the first time receive a string correction to their anomalous dimensions which is uniquely determined and lifts the residual degeneracy of tree level supergravity, due to ten-dimensional conformal symmetry. We encode the lifting of the residual degeneracy in a characteristic polynomial. This object carries information about all orders in α′. It is analytic in the quantum numbers, symmetric under an AdS5 ↔ S5 exchange, and it enjoys intriguing properties, which we explain and detail in various cases.

scholarly journals Modular invariant holographic correlators for $$ \mathcal{N} $$ = 4 SYM with general gauge group

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Luis F. Alday ◽  
Shai M. Chester ◽  
Tobias Hansen
Keyword(s):  
Gauge Group ◽  
Flat Space ◽  
Closed Form Expression ◽  
Tree Level ◽  
Modular Invariant ◽  
Higher Derivative ◽  
S Matrix ◽  
Space Limit ◽  
Type Iib String Theory ◽  
General Gauge

Abstract We study the stress tensor four-point function for $$ \mathcal{N} $$ N = 4 SYM with gauge group G = SU(N), SO(2N + 1), SO(2N) or USp(2N) at large N . When G = SU(N), the theory is dual to type IIB string theory on AdS5× S5 with complexified string coupling τs, while for the other cases it is dual to the orbifold theory on AdS5× S5/ℤ2. In all cases we use the analytic bootstrap and constraints from localization to compute 1-loop and higher derivative tree level corrections to the leading supergravity approximation of the correlator. We give perturbative evidence that the localization constraint in the large N and finite complexified coupling τ limit can be written for each G in terms of Eisenstein series that are modular invariant in terms of τs ∝ τ, which allows us to fix protected terms in the correlator in that limit. In all cases, we find that the flat space limit of the correlator precisely matches the type IIB S-matrix. We also find a closed form expression for the SU(N) 1-loop Mellin amplitude with supergravity vertices. Finally, we compare our analytic predictions at large N and finite τ to bounds from the numerical bootstrap in the large N regime, and find that they are not saturated for any G and any τ , which suggests that no physical theory saturates these bootstrap bounds.

scholarly journals The contribution of effective quantum gravity to the high energy scattering in the framework of modified perturbation theory and one loop approximation

2019 ◽  
Vol 79 (10) ◽  
Author(s):  
Nguyen Suan Han ◽  
Do Thu Ha ◽  
Nguyen Nhu Xuan
Keyword(s):  
Perturbation Theory ◽  
Quantum Gravity ◽  
Scattering Amplitude ◽  
High Energy ◽  
Effective Theory ◽  
Potential Equation ◽  
Scalar Particles ◽  
Loop Approximation ◽  
The One ◽  
High Energy Scattering

Abstract The asymptotic behavior of the scattering amplitude for two scalar particles at high energies with fixed momentum transfers is studied. The study is done within the effective theory of quantum gravity based on quasi-potential equation. By using the modified perturbation theory, a systematic method is developed to find the leading eikonal scattering amplitudes together with corrections to them in the one-loop gravitational approximation. The relation is established and discussed between the solutions obtained by means of the operator and functional approaches applied to quasi-potential equation. The first non-leading corrections to the leading eikonal amplitude are found.

scholarly journals Double copy structure of parity-violating CFT correlators

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Sachin Jain ◽  
Renjan Rajan John ◽  
Abhishek Mehta ◽  
Amin A. Nizami ◽  
Adithya Suresh
Keyword(s):  
Flat Space ◽  
Field Theories ◽  
Tree Level ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
Higher Spin ◽  
Space Limit ◽  
Double Copy ◽  
Conserved Currents ◽  
Massless Fields

Abstract We show that general parity-violating 3d conformal field theories show a double copy structure for momentum space 3-point functions of conserved currents, stress tensor and marginal scalar operators. Splitting up the CFT correlator into two parts — called homogeneous and non-homogeneous — we show that double copy relations exist for each part separately. We arrive at similar conclusions regarding double copy structures using tree-level correlators of massless fields in dS4. We also discuss the flat space limit of these correlators. We further extend the double copy analysis to correlators involving higher-spin conserved currents, which suggests that the spin-s current correlator can be thought of as s copies of the spin one current correlator.

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