scholarly journals Tree-level S-matrix of Pohlmeyer reduced form of AdS 5 × S 5 superstring theory

2010 ◽  
Vol 2010 (2) ◽  
Author(s):  
B. Hoare ◽  
A.A. Tseytlin
Keyword(s):  
Reduced Form ◽  
Tree Level ◽  
Superstring Theory ◽  
S Matrix

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 Relative entropy in scattering and the S-matrix bootstrap

2020 ◽  
Vol 9 (5) ◽  
Author(s):  
Anjishnu Bose ◽  
Parthiv Haldar ◽  
Aninda Sinha ◽  
Pritish Sinha ◽  
Shaswat Tiwari
Keyword(s):  
Relative Entropy ◽  
Cross Sections ◽  
High Energy ◽  
Quantum Field Theories ◽  
Superstring Theory ◽  
Information Theoretic ◽  
Pion Scattering ◽  
S Matrix ◽  
Information Theoretic Measures ◽  
Scattering Lengths

We consider entanglement measures in 2-2 scattering in quantum field theories, focusing on relative entropy which distinguishes two different density matrices. Relative entropy is investigated in several cases which include \phi^4ϕ4 theory, chiral perturbation theory (\chi PTχPT) describing pion scattering and dilaton scattering in type II superstring theory. We derive a high energy bound on the relative entropy using known bounds on the elastic differential cross-sections in massive QFTs. In \chi PTχPT, relative entropy close to threshold has simple expressions in terms of ratios of scattering lengths. Definite sign properties are found for the relative entropy which are over and above the usual positivity of relative entropy in certain cases. We then turn to the recent numerical investigations of the S-matrix bootstrap in the context of pion scattering. By imposing these sign constraints and the \rhoρ resonance, we find restrictions on the allowed S-matrices. By performing hypothesis testing using relative entropy, we isolate two sets of S-matrices living on the boundary which give scattering lengths comparable to experiments but one of which is far from the 1-loop \chi PTχPT Adler zeros. We perform a preliminary analysis to constrain the allowed space further, using ideas involving positivity inside the extended Mandelstam region, and other quantum information theoretic measures based on entanglement in isospin.

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 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 Massive S-matrix of AdS3×S3×T4 superstring theory with mixed 3-form flux

2013 ◽  
Vol 873 (2) ◽  
pp. 395-418 ◽  
Author(s):  
B. Hoare ◽  
A.A. Tseytlin
Keyword(s):  
Superstring Theory ◽  
S Matrix

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.

INFLATION FROM THE SUPERSTRING VACUUM

2009 ◽  
Vol 24 (20n21) ◽  
pp. 4021-4037
Author(s):  
M. D. POLLOCK
Keyword(s):  
Background Radiation ◽  
Physical Space ◽  
Reduction Process ◽  
Tree Level ◽  
Internal Space ◽  
De Sitter ◽  
Superstring Theory ◽  
Higher Derivative ◽  
Effective Lagrangian ◽  
Microwave Background Radiation

Quartic higher-derivative gravitational terms in the effective Lagrangian of the heterotic superstring theory renormalize the bare, four-dimensional gravitational coupling [Formula: see text], due to the reduction process [Formula: see text], according to the formula [Formula: see text], where A r and B r are the moduli for the physical space gij(xk) and internal space [Formula: see text], respectively. The Euler characteristic [Formula: see text] is negative for a three-generation Calabi–Yau manifold, and therefore both the additional terms, of tree-level and one-loop origin, produce a decrease in κ-2, which changes sign when κ-2 = 0. The corresponding tree-level critical point is [Formula: see text], if we set [Formula: see text] and λ = 15π2, for compactification onto a torus. Values [Formula: see text] yield the anti-gravity region κ-2 < 0, which is analytically accessible from the normal gravity region κ-2 > 0. The only non-singular, vacuum minimum of the potential [Formula: see text] is located at the point [Formula: see text], where [Formula: see text], the quadratic trace anomaly [Formula: see text] dominates over [Formula: see text], and a phase of de Sitter expansion may occur, as first envisaged by Starobinsky, in approximate agreement with the constraint due to the effect of gravitational waves upon the anisotropy of the cosmic microwave background radiation. There is no non-singular minimum of the potential [Formula: see text].

scholarly journals AN EXTENDED N=1 FERMIONIC SUPERCURRENT AND ITS ASSOCIATED N=2 SUPERCONFORMAL ALGEBRA

1995 ◽  
Vol 10 (38) ◽  
pp. 2967-2977
Author(s):  
DAVID M. PIERCE
Keyword(s):  
Superconformal Algebra ◽  
Tree Level ◽  
Intermediate Step ◽  
Superstring Theory ◽  
Massless Fermions

An extended free fermionic construction of the internal N=1 worldsheet supercurrent for four-dimensional superstring theory is given. We show how it can describe theories with massless fermions, and we discuss the corresponding N=2 superconformal algebra. As an intermediate step, we show that an internal N=2 global superconformal invariance occurs in any superstring theory with massless fermions at tree level. To demonstrate this fact, we give the N=2 supercurrents for a model with N=1 spacetime supersymmetry and a model without spacetime supersymmetry.

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