scholarly journals Scattering equations in AdS: scalar correlators in arbitrary dimensions

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Lorenz Eberhardt ◽  
Shota Komatsu ◽  
Sebastian Mizera
Keyword(s):  
Moduli Space ◽  
Classical Limit ◽  
Natural Extension ◽  
Flat Space ◽  
Tree Level ◽  
Quantum Level ◽  
S Matrix ◽  
Arbitrary Space ◽  
Sutherland Model ◽  
Arbitrary Dimensions

Abstract We introduce a bosonic ambitwistor string theory in AdS space. Even though the theory is anomalous at the quantum level, one can nevertheless use it in the classical limit to derive a novel formula for correlation functions of boundary CFT operators in arbitrary space-time dimensions. The resulting construction can be treated as a natural extension of the CHY formalism for the flat-space S-matrix, as it similarly expresses tree-level amplitudes in AdS as integrals over the moduli space of Riemann spheres with punctures. These integrals localize on an operator-valued version of scattering equations, which we derive directly from the ambitwistor string action on a coset manifold. As a testing ground for this formalism we focus on the simplest case of ambitwistor string coupled to two cur- rent algebras, which gives bi-adjoint scalar correlators in AdS. In order to evaluate them directly, we make use of a series of contour deformations on the moduli space of punctured Riemann spheres and check that the result agrees with tree level Witten diagram computations to all multiplicity. We also initiate the study of eigenfunctions of scattering equations in AdS, which interpolate between conformal partial waves in different OPE channels, and point out a connection to an elliptic deformation of the Calogero-Sutherland model.

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 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 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 6d (2, 0) and M-theory at 1-loop

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Luis F. Alday ◽  
Shai M. Chester ◽  
Himanshu Raj
Keyword(s):  
Flat Space ◽  
Lagrangian Description ◽  
Loop Correction ◽  
Higher Derivative ◽  
Weakly Coupled ◽  
S Matrix ◽  
Space Limit ◽  
Tensor Multiplet ◽  
First Time ◽  
M Theory

Abstract We study the stress tensor multiplet four-point function in the 6d maximally supersymmetric (2, 0) AN−1 and DN theories, which have no Lagrangian description, but in the large N limit are holographically dual to weakly coupled M-theory on AdS7× S4 and AdS7× S4/ℤ2, respectively. We use the analytic bootstrap to compute the 1-loop correction to this holographic correlator coming from Witten diagrams with supergravity R and the first higher derivative correction R4 vertices, which is the first 1-loop correction computed for a non-Lagrangian theory. We then take the flat space limit and find precise agreement with the corresponding terms in the 11d M-theory S-matrix, some of which we compute for the first time using two-particle unitarity cuts.

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.

scholarly journals On TCS G2 manifolds and 4D emergent strings

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Fengjun Xu
Keyword(s):  
Moduli Space ◽  
Quantum Corrections ◽  
Type Ii ◽  
Quantum Level ◽  
Weakly Coupled ◽  
G2 Manifolds ◽  
Fundamental Type ◽  
M Theory ◽  
Distance Limit ◽  
Refined Version

Abstract In this note, we study the Swampland Distance Conjecture in TCS G2 manifold compactifications of M-theory. In particular, we are interested in testing a refined version — the Emergent String Conjecture, in settings with 4d N = 1 supersymmetry. We find that a weakly coupled, tensionless fundamental heterotic string does emerge at the infinite distance limit characterized by shrinking the K3-fiber in a TCS G2 manifold. Such a fundamental tensionless string leads to the parametrically leading infinite tower of asymptotically massless states, which is in line with the Emergent String Conjecture. The tensionless string, however, receives quantum corrections. We check that these quantum corrections do modify the volume of the shrinking K3-fiber via string duality and hence make the string regain a non-vanishing tension at the quantum level, leading to a decompactification. Geometrically, the quantum corrections modify the metric of the classical moduli space and are expected to obstruct the infinite distance limit. We also comment on another possible type of infinite distance limit in TCS G2 compactifications, which might lead to a weakly coupled fundamental type II string theory.

scholarly journals COSET REALIZATION OF UNIFYING ${\mathcal W}$ ALGEBRAS

1995 ◽  
Vol 10 (16) ◽  
pp. 2367-2430 ◽  
Author(s):  
R. BLUMENHAGEN ◽  
W. EHOLZER ◽  
A. HONECKER ◽  
R. HÜBEL ◽  
K. HORNFECK
Keyword(s):  
Lie Algebras ◽  
Classical Limit ◽  
Classical Case ◽  
Quantum Level ◽  
Minimal Models ◽  
Classical Formula

We construct several quantum coset [Formula: see text] algebras, e.g. [Formula: see text] and [Formula: see text] and argue that they are finitely nonfreely generated. Furthermore, we discuss in detail their role as unifying [Formula: see text] algebras of Casimir [Formula: see text] algebras. We show that it is possible to give coset realizations of various types of unifying [Formula: see text] algebras; for example, the diagonal cosets based on the symplectic Lie algebras sp (2n) realize the unifying [Formula: see text] algebras which have previously been introduced as [Formula: see text]. In addition, minimal models of [Formula: see text] are studied. The coset realizations provide a generalization of level-rank duality of dual coset pairs. As further examples of finitely nonfreely generated quantum [Formula: see text] algebras, we discuss orbifolding of [Formula: see text] algebras which on the quantum level has different properties than in the classical case. We demonstrate through some examples that the classical limit — according to Bowcock and Watts — of these finitely nonfreely generated quantum [Formula: see text] algebras probably yields infinitely nonfreely generated classical [Formula: see text] algebras.

scholarly journals Amplituhedron-like geometries

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Gabriele Dian ◽  
Paul Heslop
Keyword(s):  
Canonical Form ◽  
Star Product ◽  
Natural Extension ◽  
Tree Level ◽  
Winding Number ◽  
Alternative Definition ◽  
Standard Definition ◽  
Definition Of ◽  
Intrinsic Definition ◽  
Simple Definition

Abstract We consider amplituhedron-like geometries which are defined in a similar way to the intrinsic definition of the amplituhedron but with non-maximal winding number. We propose that for the cases with minimal number of points the canonical form of these geometries corresponds to the product of parity conjugate amplitudes at tree as well as loop level. The product of amplitudes in superspace lifts to a star product in bosonised superspace which we give a precise definition of. We give an alternative definition of amplituhedron-like geometries, analogous to the original amplituhedron definition, and also a characterisation as a sum over pairs of on-shell diagrams that we use to prove the conjecture at tree level. The union of all amplituhedron-like geometries has a very simple definition given by only physical inequalities. Although such a union does not give a positive geometry, a natural extension of the standard definition of canonical form, the globally oriented canonical form, acts on this union and gives the square of the amplitude.

scholarly journals Landau diagrams in AdS and S-matrices from conformal correlators

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Shota Komatsu ◽  
Miguel F. Paulos ◽  
Balt C. van Rees ◽  
Xiang Zhao
Keyword(s):  
Flat Space ◽  
Momentum Conservation ◽  
Quantum Field Theories ◽  
Triangle Diagram ◽  
S Matrix ◽  
Space Limit ◽  
Anomalous Threshold ◽  
Delta Functions ◽  
Shell Particles ◽  
Do So

Abstract Quantum field theories in AdS generate conformal correlation functions on the boundary, and in the limit where AdS is nearly flat one should be able to extract an S-matrix from such correlators. We discuss a particularly simple position-space procedure to do so. It features a direct map from boundary positions to (on-shell) momenta and thereby relates cross ratios to Mandelstam invariants. This recipe succeeds in several examples, includes the momentum-conserving delta functions, and can be shown to imply the two proposals in [1] based on Mellin space and on the OPE data. Interestingly the procedure does not always work: the Landau singularities of a Feynman diagram are shown to be part of larger regions, to be called ‘bad regions’, where the flat-space limit of the Witten diagram diverges. To capture these divergences we introduce the notion of Landau diagrams in AdS. As in flat space, these describe on-shell particles propagating over large distances in a complexified space, with a form of momentum conservation holding at each bulk vertex. As an application we recover the anomalous threshold of the four-point triangle diagram at the boundary of a bad region.

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