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 On quantum deformations of AdS3 × S3 × T4 and mirror duality

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Fiona K. Seibold ◽  
Stijn J. van Tongeren ◽  
Yannik Zimmermann
Keyword(s):  
Group Symmetry ◽  
Tree Level ◽  
Light Cone Gauge ◽  
Deformation Limit ◽  
S Matrix ◽  
Quantum Deformations ◽  
The One ◽  
Two Parameter ◽  
Quadratic Order ◽  
Massive Tree

Abstract We consider various integrable two-parameter deformations of the AdS3 × S3 × T4 superstring with quantum group symmetry. Working on the string worldsheet in light-cone gauge and to quadratic order in fermions, we obtain their common massive tree-level two-body S matrix, which matches the expansion of the conjectured exact q-deformed S matrix. We then analyze the behavior of the exact S matrix under mirror transformation — a double Wick rotation on the worldsheet — and find that it satisfies a mirror duality relation analogous to the distinguished q-deformed AdS5 × S5 S matrix in the one parameter deformation limit. Finally, we show that the fermionic q-deformed AdS5 × S5 S matrix also satisfies such a relation.

SYMMETRY IN TWO-DIMENSIONAL GRAVITY

1991 ◽  
Vol 06 (13) ◽  
pp. 2331-2346 ◽  
Author(s):  
KAI-WEN XU ◽  
CHUAN-JIE ZHU
Keyword(s):  
Light Cone ◽  
Integration Method ◽  
Symmetry Algebra ◽  
Two Dimensional ◽  
Light Cone Gauge ◽  
Simple Interpretation ◽  
Brst Charge ◽  
Dimensional Gravity ◽  
Covariant Gauge ◽  
Liouville Action

We study the symmetry of two-dimensional gravity by choosing a generic gauge. A local action is derived which reduces to either the Liouville action or the Polyakov one by reducing to the conformal or light-cone gauge respectively. The theory is also solved classically. We show that an SL (2, R) covariant gauge can be chosen so that the two-dimensional gravity has a manifest Virasoro and the sl (2, R)-current symmetry discovered by Polyakov. The symmetry algebra of the light-cone gauge is shown to be isomorphic to the Beltrami algebra. By using the contour integration method we construct the BRST charge QB corresponding to this algebra following the Fradkin-Vilkovisky procedure and prove that the nilpotence of QB requires c=28 and α0=1. We give a simple interpretation of these conditions.

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 A new Wilson line-based action for gluodynamics

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Hiren Kakkad ◽  
Piotr Kotko ◽  
Anna Stasto
Keyword(s):  
Canonical Transformation ◽  
Light Cone ◽  
Wilson Line ◽  
Functional Derivative ◽  
Tree Level ◽  
Classical Action ◽  
Light Cone Gauge ◽  
Standard Methods ◽  
Yang Mills ◽  
Negative Helicity

Abstract We perform a canonical transformation of fields that brings the Yang-Mills action in the light-cone gauge to a new classical action, which does not involve any triple-gluon vertices. The lowest order vertex is the four-point MHV vertex. Higher point vertices include the MHV and $$ \overline{\mathrm{MHV}} $$ MHV ¯ vertices, that reduce to the corresponding amplitudes in the on-shell limit. In general, any n-leg vertex has 2 ≤ m ≤ n − 2 negative helicity legs. The canonical transformation of fields can be compactly expressed in terms of path-ordered exponentials of fields and their functional derivative. We apply the new action to compute several tree-level amplitudes, up to 8-point NNMHV amplitude, and find agreement with the standard methods. The absence of triple-gluon vertices results in fewer diagrams required to compute amplitudes, when compared to the CSW method and, obviously, considerably fewer than in the standard Yang-Mills action.

scholarly journals Graviton-Scalar Interaction in the pp-Wave Background

2003 ◽  
Vol 18 (21) ◽  
pp. 1441-1462
Author(s):  
K. Bobkov
Keyword(s):  
Field Theory ◽  
String Field Theory ◽  
Light Cone ◽  
Tree Level ◽  
Scalar Interaction ◽  
Superstring Theory ◽  
Light Cone Gauge ◽  
Interaction Vertex ◽  
Pp Wave

We compute the graviton two scalar off-shell interaction vertex at tree level in Type IIB superstring theory on the pp-wave background using the light-cone string field theory formalism. We then show that the tree level vertex vanishes when all particles are on-shell and conservation of p+ and p- are imposed. We reinforce our claim by calculating the same vertex starting from the corresponding SUGRA action expanded around the pp-wave background in the light-cone gauge.

scholarly journals VERTEX OPERATORS FOR THE SUPERMEMBRANE AND BACKGROUND FIELD MATRIX THEORY

2001 ◽  
Vol 16 (05) ◽  
pp. 660-668 ◽  
Author(s):  
JAN PLEFKA
Keyword(s):  
Scattering Amplitudes ◽  
Ground State ◽  
Light Cone ◽  
Matrix Theory ◽  
Background Field ◽  
Tree Level ◽  
Vertex Operators ◽  
Light Cone Gauge ◽  
Linear Coupling ◽  
Definition Of

We derive the vertex operators that are expected to govern the emission of the massless d=11 supermultiplet from the supermembrane in the light cone gauge. Our results immediately imply the linear coupling of matrix theory to an arbitrary supergravity background to all orders in anticommuting coordinates. Finally we address the definition of n-point tree level and one-loop scattering amplitudes. The resulting 3-point tree level amplitudes turn out to agree with d=11 supergravity and are completely fixed by supersymmetry and the existence of a normalizable ground state.

scholarly journals The dipole picture and the non-relativistic expansion

2022 ◽  
Vol 258 ◽  
pp. 04006
Author(s):  
Miguel Ángel Escobedo ◽  
Tuomas Lappi
Keyword(s):  
Wave Function ◽  
Light Cone ◽  
Nonrelativistic Limit ◽  
Wave Functions ◽  
Tree Level ◽  
Leading Order ◽  
Light Cone Gauge ◽  
Quarkonium Production ◽  
Light Cone Wave Function ◽  
Dipole Picture

We study exclusive quarkonium production in the dipole picture at next-to-leading order (NLO) accuracy, using the non-relativistic expansion for the quarkonium wavefunction. The quarkonium light cone wave functions needed in the dipole picture have typically been available only at tree level, either in phenomenological models or in the nonrelativistic limit. Here, we discuss the compatibility of the dipole approach and the non-relativistic expansion and compute NLO relativistic corrections to the quarkonium light-cone wave function in light-cone gauge.

scholarly journals Quantum corrections to slow-roll inflation: scalar and tensor modes

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Jens O. Andersen ◽  
Magdalena Eriksson ◽  
Anders Tranberg
Keyword(s):  
Scalar Field ◽  
Quantum Corrections ◽  
Tree Level ◽  
Field Equations ◽  
Slow Roll ◽  
Scalar Field Equations ◽  
Slow Rolling ◽  
Different Sources ◽  
Suitable Potential ◽  
Quadratic Order

Abstract Inflation is often described through the dynamics of a scalar field, slow-rolling in a suitable potential. Ultimately, this inflaton must be identified with the expectation value of a quantum field, evolving in a quantum effective potential. The shape of this potential is determined by the underlying tree-level potential, dressed by quantum corrections from the scalar field itself and the metric perturbations. Following [1], we compute the effective scalar field equations and the corrected Friedmann equations to quadratic order in both scalar field, scalar metric and tensor perturbations. We identify the quantum corrections from different sources at leading order in slow-roll, and estimate their magnitude in benchmark models of inflation. We comment on the implications of non-minimal coupling to gravity in this context.

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 Flat self-dual gravity

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Kirill Krasnov ◽  
Evgeny Skvortsov
Keyword(s):  
Light Cone ◽  
Space Time ◽  
Kinetic Term ◽  
Light Cone Gauge ◽  
Yang Mills ◽  
Covariant Action ◽  
Chiral Interaction ◽  
Double Copy

Abstract We construct a new covariant action for “flat” self-dual gravity in four space-time dimensions. The action has just one term, but when expanded around an appropriate background gives rise to a kinetic term and a cubic interaction. Upon imposing the light-cone gauge, the action reproduces the expected chiral interaction of Siegel. The new action is in many ways analogous to the known covariant action for self-dual Yang-Mills theory. There is also a sense in which the new self-dual gravity action exhibits the double copy of self-dual Yang-Mills structure.

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