scholarly journals Plahte diagrams for string scattering amplitudes

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Pongwit Srisangyingcharoen ◽  
Paul Mansfield
Keyword(s):  
Scattering Amplitudes ◽  
Analytic Continuation ◽  
Complex Plane ◽  
Open String ◽  
Tree Level ◽  
Recursion Relations ◽  
Sign Changes ◽  
String Amplitudes

Abstract Plahte identities are monodromy relations between open string scattering amplitudes at tree level derived from the Koba-Nielsen formula. We represent these identities by polygons in the complex plane. These diagrams make manifest the appearance of sign changes and singularities in the analytic continuation of amplitudes. They provide a geometric expression of the KLT relations between closed and open string amplitudes. We also connect the diagrams to the BCFW on-shell recursion relations and generalise them to complex momenta resulting in a relation between the complex phases of partial amplitudes.

scholarly journals KLT factorization of winding string amplitudes

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Jaume Gomis ◽  
Ziqi Yan ◽  
Matthew Yu
Keyword(s):  
Scattering Amplitudes ◽  
Open String ◽  
Closed String ◽  
Open Strings ◽  
Toroidal Compactifications ◽  
Quantum Numbers ◽  
String Amplitudes

Abstract We uncover a Kawai-Lewellen-Tye (KLT)-type factorization of closed string amplitudes into open string amplitudes for closed string states carrying winding and momentum in toroidal compactifications. The winding and momentum closed string quantum numbers map respectively to the integer and fractional winding quantum numbers of open strings ending on a D-brane array localized in the compactified directions. The closed string amplitudes factorize into products of open string scattering amplitudes with the open strings ending on a D-brane configuration determined by closed string data.

scholarly journals Extracting bigravity from string theory

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Dieter Lüst ◽  
Chrysoula Markou ◽  
Pouria Mazloumi ◽  
Stephan Stieberger
Keyword(s):  
Scattering Amplitudes ◽  
String Theory ◽  
Open String ◽  
Closed String ◽  
Bimetric Theory ◽  
Low Energy ◽  
Tree Level ◽  
Dark Matter Candidate ◽  
Massive Spin ◽  
Numerical Coefficient

Abstract The origin of the graviton from string theory is well understood: it corresponds to a massless state in closed string spectra, whose low-energy effective action, as extracted from string scattering amplitudes, is that of Einstein-Hilbert. In this work, we explore the possibility of such a string-theoretic emergence of ghost-free bimetric theory, a recently proposed theory that involves two dynamical metrics, that around particular backgrounds propagates the graviton and a massive spin-2 field, which has been argued to be a viable dark matter candidate. By choosing to identify the latter with a massive spin-2 state of open string spectra, we compute tree-level three-point string scattering amplitudes that describe interactions of the massive spin-2 with itself and with the graviton. With the mass of the external legs depending on the string scale, we discover that extracting the corresponding low-energy effective actions in four spacetime dimensions is a subtle but consistent process and proceed to appropriately compare them with bimetric theory. Our findings consist in establishing that string and bimetric theory provide to lowest order the same set of two-derivative terms describing the interactions of the massive spin-2 with itself and with the graviton, albeit up to numerical coefficient discrepancies, a fact that we analyze and interpret. We conclude with a mention of future investigations.

scholarly journals LOOP VARIABLES AND GAUGE INVARIANCE IN CLOSED BOSONIC STRING THEORY

2004 ◽  
Vol 19 (38) ◽  
pp. 2857-2870 ◽  
Author(s):  
B. SATHIAPALAN
Keyword(s):  
Gauge Invariance ◽  
Open String ◽  
Closed String ◽  
Bosonic String ◽  
Tree Level ◽  
Gauge Invariant ◽  
Open Strings ◽  
Invariant Description ◽  
String Amplitudes ◽  
Closed Bosonic String

We extend an earlier proposal for a gauge-invariant description of off-shell open strings (at tree level), using loop variables, to off-shell closed strings (at tree level). The basic idea is to describe the closed string amplitudes as a product of two open string amplitudes (using the technique of Kawai, Lewellen and Tye). The loop variable techniques that were used earlier for open strings can be applied here mutatis mutandis. It is a proposal for a theory whose on-shell amplitudes coincide with those of the closed bosonic string in 26 dimensions. It is also gauge-invariant off-shell. As was the case with the open string, the interacting closed string looks like a free closed string thickened to a band.

scholarly journals Single-Valued Integration and Superstring Amplitudes in Genus Zero

2021 ◽  
Vol 382 (2) ◽  
pp. 815-874
Author(s):  
Francis Brown ◽  
Clément Dupont
Keyword(s):  
Open String ◽  
Closed String ◽  
Laurent Expansion ◽  
Tree Level ◽  
Multiple Zeta Values ◽  
Genus Zero ◽  
Period Map ◽  
Multiple Zeta ◽  
Zeta Values ◽  
String Amplitudes

AbstractWe study open and closed string amplitudes at tree-level in string perturbation theory using the methods of single-valued integration which were developed in the prequel to this paper (Brown and Dupont in Single-valued integration and double copy, 2020). Using dihedral coordinates on the moduli spaces of curves of genus zero with marked points, we define a canonical regularisation of both open and closed string perturbation amplitudes at tree level, and deduce that they admit a Laurent expansion in Mandelstam variables whose coefficients are multiple zeta values (resp. single-valued multiple zeta values). Furthermore, we prove the existence of a motivic Laurent expansion whose image under the period map is the open string expansion, and whose image under the single-valued period map is the closed string expansion. This proves the recent conjecture of Stieberger that closed string amplitudes are the single-valued projections of (motivic lifts of) open string amplitudes. Finally, applying a variant of the single-valued formalism for cohomology with coefficients yields the KLT formula expressing closed string amplitudes as quadratic expressions in open string amplitudes.

scholarly journals DIVERGENCES OF DISCRETE STATES AMPLITUDES AND EFFECTIVE LAGRANGIAN IN 2D STRING THEORY

1993 ◽  
Vol 08 (16) ◽  
pp. 1469-1476 ◽  
Author(s):  
I. YA. AREF’EVA ◽  
A.P. ZUBAREV
Keyword(s):  
Scattering Amplitudes ◽  
String Theory ◽  
Lie Algebra ◽  
Open String ◽  
Tree Level ◽  
Ward Identities ◽  
Effective Lagrangian ◽  
Discrete States

Scattering amplitudes for discrete states in 2D string theory are considered. Pole divergences of tree-level amplitudes are observed and residues are interpreted as renormalized amplitudes for discrete states. An effective Lagrangian generating renormalized amplitudes for open string is obtained and the corresponding Ward identities are presented. A relation of this Lagrangian with homotopy Lie algebra is discussed.

scholarly journals Weights, recursion relations and projective triangulations for positive geometry of scalar theories

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Renjan Rajan John ◽  
Ryota Kojima ◽  
Sujoy Mahato
Keyword(s):  
Scattering Amplitudes ◽  
Detailed Analysis ◽  
Tree Level ◽  
Massless Scalar ◽  
Weighted Sum ◽  
Canonical Forms ◽  
Factorization Property ◽  
Scalar Theory ◽  
Recursion Relations ◽  
Scalar Theories

Abstract The story of positive geometry of massless scalar theories was pioneered in [1] in the context of bi-adjoint ϕ3 theories. Further study proposed that the positive geometry for a generic massless scalar theory with polynomial interaction is a class of polytopes called accordiohedra [2]. Tree-level planar scattering amplitudes of the theory can be obtained from a weighted sum of the canonical forms of the accordiohedra. In this paper, using results of the recent work [3], we show that in theories with polynomial interactions all the weights can be determined from the factorization property of the accordiohedron. We also extend the projective recursion relations introduced in [4, 5] to these theories. We then give a detailed analysis of how the recursion relations in ϕp theories and theories with polynomial interaction correspond to projective triangulations of accordiohedra. Following the very recent development [6] we also extend our analysis to one-loop integrands in the quartic theory.

scholarly journals Relations between closed string amplitudes at higher-order tree level and open string amplitudes

2010 ◽  
Vol 824 (1-2) ◽  
pp. 314-330 ◽  
Author(s):  
Yi-Xin Chen ◽  
Yi-Jian Du ◽  
Qian Ma
Keyword(s):  
Open String ◽  
Closed String ◽  
Higher Order ◽  
Tree Level ◽  
String Amplitudes

BORDERED RIEMANN SURFACES, SCHOTTKY GROUPS AND OFF-SHELL STRING AMPLITUDES

1991 ◽  
Vol 06 (10) ◽  
pp. 1719-1747 ◽  
Author(s):  
M.A. MARTÍN-DELGADO ◽  
J. RAMÍREZ MITTELBRUNN
Keyword(s):  
Scattering Amplitudes ◽  
Partition Function ◽  
Moduli Space ◽  
Riemann Surfaces ◽  
Mass Shell ◽  
Tree Level ◽  
Schottky Groups ◽  
Functional Integrals ◽  
String Amplitudes ◽  
Closed Bosonic String

We propose an off-shell extension of the closed bosonic string scattering amplitudes as functional integrals over bordered Riemann surfaces. The tree level off-shell N-scalars amplitude is handled with the help of Schottky groups and the Burnside θ-series. Using these tools and the asymptotic behaviour of the partition function at the boundary of the moduli space, we show that the off-shell amplitudes exhibit the tachyon mass-shell poles in the external momenta. In addition, their residues are shown to be the semi-off-shell amplitudes and the well-known Koba-Nielsen amplitudes.

scholarly journals Gravity loop integrands from the ultraviolet

2021 ◽  
Vol 10 (1) ◽  
Author(s):  
Alex Edison ◽  
Enrico Herrmann ◽  
Julio Parra-Martinez ◽  
Jaroslav Trnka
Keyword(s):  
Scattering Amplitudes ◽  
Momentum Space ◽  
Indirect Evidence ◽  
Tree Level ◽  
Large Momentum ◽  
Recursion Relations ◽  
Yang Mills ◽  
The One ◽  
Geometric Picture ◽  
Super Yang Mills Theory

We demonstrate that loop integrands of (super-)gravity scattering amplitudes possess surprising properties in the ultraviolet (UV) region. In particular, we study the scaling of multi-particle unitarity cuts for asymptotically large momenta and expose an improved UV behavior of four-dimensional cuts through seven loops as compared to standard expectations. For N=8 supergravity, we show that the improved large momentum scaling combined with the behavior of the integrand under BCFW deformations of external kinematics uniquely fixes the loop integrands in a number of non-trivial cases. In the integrand construction, all scaling conditions are homogeneous. Therefore, the only required information about the amplitude is its vanishing at particular points in momentum space. This homogeneous construction gives indirect evidence for a new geometric picture for graviton amplitudes similar to the one found for planar N=4 super Yang-Mills theory. We also show how the behavior at infinity is related to the scaling of tree-level amplitudes under certain multi-line chiral shifts which can be used to construct new recursion relations.

scholarly journals Constraining the weights of Stokes polytopes using BCFW recursions for ϕ4

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Ishan Srivastava
Keyword(s):  
Scattering Amplitudes ◽  
Great Depth ◽  
Tree Level ◽  
Recursion Relations ◽  
3 Dimensional ◽  
Loop Level ◽  
Boundary Terms ◽  
Geometric Objects ◽  
The Relationship ◽  
Geometric Formulation

Abstract The relationship between certain geometric objects called polytopes and scattering amplitudes has revealed deep structures in QFTs. It has been developed in great depth at the tree- and loop-level amplitudes in $$ \mathcal{N} $$ N = 4 SYM theory and has been extended to the scalar ϕ3 and ϕ4 theories at tree-level. In this paper, we use the generalized BCFW recursion relations for massless planar ϕ4 theory to constrain the weights of a class of geometric objects called Stokes polytopes, which manifest in the geometric formulation of ϕ4 amplitudes. We see that the weights of the Stokes polytopes are intricately tied to the boundary terms in ϕ4 theories. We compute the weights of N = 1, 2, and 3 dimensional Stokes polytopes corresponding to six-, eight- and ten-point amplitudes respectively. We generalize our results to higher-point amplitudes and show that the generalized BCFW recursions uniquely fix the weights for an n-point amplitude.

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