scholarly journals S matrix for a three-parameter integrable deformation of AdS3 × S3 strings

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Marco Bocconcello ◽  
Isari Masuda ◽  
Fiona K. Seibold ◽  
Alessandro Sfondrini
Keyword(s):  
Tree Level ◽  
Integrable Deformation ◽  
S Matrix ◽  
String Worldsheet

Abstract We consider the three-parameter integrable deformation of the AdS3 × S3 superstring background constructed in arXiv:1811.00453. Working on the string worldsheet in uniform lightcone gauge, we find the tree-level bosonic S matrix of the model and study some of its limits.

scholarly journals The twisted story of worldsheet scattering in η-deformed AdS5 × S5

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Fiona K. Seibold ◽  
Stijn J. van Tongeren ◽  
Yannik Zimmermann
Keyword(s):  
Light Cone ◽  
Dynkin Diagram ◽  
Symmetry Algebra ◽  
Perturbative Expansion ◽  
Tree Level ◽  
Baxter Equation ◽  
Light Cone Gauge ◽  
Integrable Deformation ◽  
S Matrix ◽  
Quadratic Order

Abstract We study the worldsheet scattering theory of the η deformation of the AdS5 × S5 superstring corresponding to the purely fermionic Dynkin diagram. This theory is a Weyl-invariant integrable deformation of the AdS5 × S5 superstring, with trigonometric quantum-deformed symmetry. We compute the two-body worldsheet S matrix of this string in the light-cone gauge at tree level to quadratic order in fermions. The result factorizes into two elementary blocks, and solves the classical Yang-Baxter equation. We also determine the corresponding exact factorized S matrix, and show that its perturbative expansion matches our tree-level results, once we correctly identify the deformed light-cone symmetry algebra of the string. Finally, we briefly revisit the computation of the corresponding S matrix for the η deformation based on the distinguished Dynkin diagram, finding a tree-level S matrix that factorizes and solves the classical Yang-Baxter equation, in contrast to previous results.

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 On string theory on with mixed 3-form flux: Tree-level S-matrix

2013 ◽  
Vol 873 (3) ◽  
pp. 682-727 ◽  
Author(s):  
B. Hoare ◽  
A.A. Tseytlin
Keyword(s):  
String Theory ◽  
Tree Level ◽  
S Matrix

A REMARK ON THE CONNECTION BETWEEN THE C-THEOREM AND THE CENTRAL CHARGE ACTION IN CLOSED BOSONIC σ-MODELS

1988 ◽  
Vol 03 (11) ◽  
pp. 1079-1083 ◽  
Author(s):  
N.E. MAVROMATOS
Keyword(s):  
Local Field ◽  
Central Charge ◽  
Scalar Function ◽  
Tree Level ◽  
Coupling Constant ◽  
World Sheet ◽  
Generating Functional ◽  
S Matrix ◽  
The World ◽  
Field Redefinition

In the case of closed bosonic σ-models propagating in massless backgrounds (at tree level in the world-sheet), there exists a real scalar function (in coupling constant space) whose variations are associated with the Weyl anomaly coefficients as a consequence of Zamolodchikov’s c-theorem. In this note, we prove that this function is related to the central charge action via a local field redefinition of the corresponding couplings. Modulo the equivalence conjecture, according to which the generating functional of the S-matrix of the central charge action and of the corresponding string theory (for massless tree level emissions) coincide, we thus represent the string effective action as an object in σ-model theory.

scholarly journals Perturbative S-matrix unitarity (S†S = 1) in Rμν2 gravity

2021 ◽  
pp. 2150105
Author(s):  
Yugo Abe ◽  
Takeo Inami ◽  
Keisuke Izumi
Keyword(s):  
Tree Level ◽  
Unitarity Bound ◽  
Counter Example ◽  
S Matrix ◽  
Curvature Theory ◽  
Theory Of Gravity

We show that in the quadratic curvature theory of gravity, or simply [Formula: see text] gravity, the tree-level unitarity bound (tree unitarity) is violated in the UV region but an analog for [Formula: see text]-matrix unitarity [Formula: see text] is satisfied. This theory is renormalizable, and hence the failure of tree unitarity is a counter example of Llewellyn Smith’s conjecture on the relation between them. We have recently proposed a new conjecture that [Formula: see text]-matrix unitarity gives the same conditions as renormalizability. We verify that [Formula: see text]-matrix unitarity holds in the matter-graviton scattering at the tree level in the [Formula: see text] gravity, demonstrating our new conjecture.

scholarly journals On the massless tree-level S-matrix in 2d sigma models

2019 ◽  
Vol 52 (14) ◽  
pp. 144005 ◽  
Author(s):  
Ben Hoare ◽  
Nat Levine ◽  
Arkady A Tseytlin
Keyword(s):  
Sigma Models ◽  
Tree Level ◽  
S Matrix

scholarly journals Toward the stabilization of extra dimensions by brane dynamics

2015 ◽  
Vol 30 (11) ◽  
pp. 1550055 ◽  
Author(s):  
Noriaki Kitazawa
Keyword(s):  
Compact Space ◽  
Dimensional Space ◽  
Scalar Fields ◽  
Open String ◽  
Closed String ◽  
Tree Level ◽  
Internal Space ◽  
Massless Scalar ◽  
Dimensional Space Time ◽  
String Worldsheet

All the models of elementary particles and their interactions derived from String Theory involve a compact six-dimensional internal space. Its volume and shape should be fixed or stabilized, since otherwise massless scalar fields (moduli) reflecting their deformations appear in our four-dimensional space–time, with sizable effects on known particles and fields. We propose a strategy toward stabilizing the compact space without fluxes of three-form fields from closed strings. Our main motivation and goal is to proceed insofar as possible within conventional string worldsheet theory. As we shall see, D-branes with magnetic flux ("magnetized D-branes") and the forces between them can be used to this end. We investigate here some necessary ingredients: open string one-loop vacuum amplitudes between magnetized D-branes, magnetized D-branes fixed at orbifold singularities, and potential energies among such D-branes in the compact space that result from tree-level closed string exchanges.

scholarly journals Tree-level S-matrix of superstring field theory with homotopy algebra structure

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Hiroshi Kunitomo
Keyword(s):  
Field Theory ◽  
String Field Theory ◽  
Heterotic String ◽  
Field Theories ◽  
Tree Level ◽  
Algebra Structure ◽  
Type Ii ◽  
S Matrix ◽  
Homotopy Algebra

Abstract We show that the tree-level S-matrices of the superstring field theories based on the homotopy-algebra structure agree with those obtained in the first-quantized formulation. The proof is given in detail for the heterotic string field theory. The extensions to the type II and open superstring field theories are straightforward.

scholarly journals Standard Model EFTs via on-shell methods

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Manuel Accettulli Huber ◽  
Stefano De Angelis
Keyword(s):  
Standard Model ◽  
Building Blocks ◽  
Effective Field ◽  
Tree Level ◽  
Matrix Elements ◽  
Effective Interactions ◽  
S Matrix ◽  
The Standard Model ◽  
Mass Dimension ◽  
Mixing Matrix

Abstract We present the Standard Model Effective Field Theories (SMEFT) from purely on-shell arguments. Starting from few basics assumptions such as Poincaré invariance and locality, we classify all the renormalisable and non-renormalisable interactions at lowest order in the couplings. From these building blocks, we review how locality and unitarity enforce Lie algebra structures to appear in the S-matrix elements together with relations among couplings (and hypercharges). Furthermore, we give a fully on-shell algorithm to compute any higher-point tree-level amplitude (or form factor) in generic EFTs, bypassing BCFW-like recursion relations which are known to be problematic when non-renormalisable interactions are involved. Finally, using known amplitudes techniques we compute the mixing matrix of SMEFT marginal interactions up to mass dimension 8, to linear order in the effective interactions.

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