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.

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.

Subjective Time Preference and Willingness to Pay for an Energy-Saving Durable Good

2001 ◽  
Vol 32 (3) ◽  
pp. 133-141 ◽  
Author(s):  
Gerrit Antonides ◽  
Sophia R. Wunderink
Keyword(s):  
Willingness To Pay ◽  
Energy Saving ◽  
Subjective Time ◽  
Durable Good ◽  
Discount Function ◽  
Hyperbolic Discount ◽  
The One ◽  
Two Parameter ◽  
Difference Effect ◽  
Better Than

Summary: Different shapes of individual subjective discount functions were compared using real measures of willingness to accept future monetary outcomes in an experiment. The two-parameter hyperbolic discount function described the data better than three alternative one-parameter discount functions. However, the hyperbolic discount functions did not explain the common difference effect better than the classical discount function. Discount functions were also estimated from survey data of Dutch households who reported their willingness to postpone positive and negative amounts. Future positive amounts were discounted more than future negative amounts and smaller amounts were discounted more than larger amounts. Furthermore, younger people discounted more than older people. Finally, discount functions were used in explaining consumers' willingness to pay for an energy-saving durable good. In this case, the two-parameter discount model could not be estimated and the one-parameter models did not differ significantly in explaining the data.

Theoretical accuracy of the last squares method in the isotope dilution analysis

1984 ◽  
Vol 49 (4) ◽  
pp. 805-820
Author(s):  
Ján Klas
Keyword(s):  
Least Squares ◽  
Isotope Dilution ◽  
Least Squares Method ◽  
Isotope Dilution Analysis ◽  
Straight Line ◽  
The One ◽  
Two Parameter ◽  
Theoretical Accuracy

The accuracy of the least squares method in the isotope dilution analysis is studied using two models, viz a model of a two-parameter straight line and a model of a one-parameter straight line.The equations for the direct and the inverse isotope dilution methods are transformed into linear coordinates, and the intercept and slope of the two-parameter straight line and the slope of the one-parameter straight line are evaluated and treated.

scholarly journals Interplay of New Physics effects in (g − 2)ℓ and h → ℓ+ℓ− — lessons from SMEFT

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Svjetlana Fajfer ◽  
Jernej F. Kamenik ◽  
M. Tammaro
Keyword(s):  
Closed Operator ◽  
Higgs Doublet ◽  
New Physics ◽  
Effective Field ◽  
Tree Level ◽  
Electroweak Symmetry ◽  
Scalar Leptoquark ◽  
Doublet Model ◽  
The One ◽  
Two Higgs Doublet Model

Abstract We explore the interplay of New Physics (NP) effects in (g− 2)ℓ and h→ℓ+ℓ− within the Standard Model Effective Field Theory (SMEFT) framework, including one-loop Renormalization Group (RG) evolution of the Wilson coefficients as well as matching to the observables below the electroweak symmetry breaking scale. We include both the leading dimension six chirality flipping operators including a Higgs and SU(2)L gauge bosons as well as four-fermion scalar and tensor operators, forming a closed operator set under the SMEFT RG equations. We compare present and future experimental sensitivity to different representative benchmark scenarios. We also consider two simple UV completions, a Two Higgs Doublet Model and a single scalar LeptoQuark extension of the SM, and show how tree level matching to SMEFT followed by the one-loop RG evolution down to the electroweak scale can reproduce with high accuracy the (g−2)ℓ and h→ℓ+ℓ− contributions obtained by the complete one- and even two-loop calculations in the full models.

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 Symmetries and anomalies of (1+1)d theories: 2-groups and symmetry fractionalization

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Matthew Yu
Keyword(s):  
Spectral Sequence ◽  
Global Symmetries ◽  
Group Symmetry ◽  
Low Dimension ◽  
The One ◽  
Group Symmetries

Abstract We investigate the interactions of discrete zero-form and one-form global symmetries in (1+1)d theories. Focus is put on the interactions that the symmetries can have on each other, which in this low dimension result in 2-group symmetries or symmetry fractionalization. A large part of the discussion will be to understand a major feature in (1+1)d: the multiple sectors into which a theory decomposes. We perform gauging of the one-form symmetry, and remark on the effects this has on our theories, especially in the case when there is a global 2-group symmetry. We also implement the spectral sequence to calculate anomalies for the 2-group theories and symmetry fractionalized theory in the bosonic and fermionic cases. Lastly, we discuss topological manipulations on the operators which implement the symmetries, and draw insights on the (1+1)d effects of such manipulations by coupling to a bulk (2+1)d theory.

Performance limitation of networked systems with controller and communication filter co-design

2016 ◽  
Vol 40 (4) ◽  
pp. 1167-1176 ◽  
Author(s):  
Jie Wu ◽  
Xi-Sheng Zhan ◽  
Xian-He Zhang ◽  
Tao Han ◽  
Hong-Liang Gao
Keyword(s):  
Networked Systems ◽  
Channel Noise ◽  
Frequency Domain Method ◽  
Minimum Phase ◽  
Error Signal ◽  
Optimal Network ◽  
Performance Limitation ◽  
The One ◽  
Theoretical Results ◽  
Two Parameter

This paper addresses the performance limitation problem of networked systems by co-designing the controller and communication filter. The tracking performance index is measured by the energy of the error signal. Explicit expressions of the performance limitation are obtained by applying the controller and communication filter co-design, and the optimal network filter is obtained by applying the frequency domain method. It is shown that the performance limitation is closely related to the unstable poles and the non-minimum phase zeros of a given plant under the one-parameter compensator structure, whereas, under the two-parameter compensator structure, the performance limitation is unrelated to the unstable poles of a given plant. It is also demonstrated that the performance limitation can be improved and the effect of the channel noise can be eliminated by using the controller and communication filter co-design. Finally, some typical examples are presented to illustrate the theoretical results.

scholarly journals Some New Fractional-Calculus Connections between Mittag–Leffler Functions

Mathematics ◽  
2019 ◽  
Vol 7 (6) ◽  
pp. 485 ◽  
Author(s):  
Hari M. Srivastava ◽  
Arran Fernandez ◽  
Dumitru Baleanu
Keyword(s):  
Experimental Data ◽  
Fractional Calculus ◽  
Fractional Derivative ◽  
Fractional Integral ◽  
Integral Expression ◽  
Potential Applications ◽  
The One ◽  
Two Parameter

We consider the well-known Mittag–Leffler functions of one, two and three parameters, and establish some new connections between them using fractional calculus. In particular, we express the three-parameter Mittag–Leffler function as a fractional derivative of the two-parameter Mittag–Leffler function, which is in turn a fractional integral of the one-parameter Mittag–Leffler function. Hence, we derive an integral expression for the three-parameter one in terms of the one-parameter one. We discuss the importance and applications of all three Mittag–Leffler functions, with a view to potential applications of our results in making certain types of experimental data much easier to analyse.

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