scholarly journals Holographic correlators with multi-particle states

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Nejc Čeplak ◽  
Stefano Giusto ◽  
Marcel R. R. Hughes ◽  
Rodolfo Russo
Keyword(s):  
Correlation Function ◽  
Single Particle ◽  
Higher Order ◽  
Tree Level ◽  
Linear Combinations ◽  
Anomalous Dimensions ◽  
Formal Limit ◽  
Single Trace

Abstract We derive the connected tree-level part of 4-point holographic correlators in AdS3 × S3 × $$ \mathcal{M} $$ M (where $$ \mathcal{M} $$ M is T4 or K3) involving two multi-trace and two single-trace operators. These connected correlators are obtained by studying a heavy-heavy-light-light correlation function in the formal limit where the heavy operators become light. These results provide a window into higher-point holographic correlators of single-particle operators. We find that the correlators involving multi-trace operators are compactly written in terms of Bloch-Wigner-Ramakrishnan functions — particular linear combinations of higher-order polylogarithm functions. Several consistency checks of the derived expressions are performed in various OPE channels. We also extract the anomalous dimensions and 3-point couplings of the non-BPS double-trace operators of lowest twist at order 1/c and find some positive anomalous dimensions at spin zero and two in the K3 case.

scholarly journals Evaluating EYM amplitudes in four dimensions by refined graphic expansion

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Hongxiang Tian ◽  
Enze Gong ◽  
Chongsi Xie ◽  
Yi-Jian Du
Keyword(s):  
Tree Level ◽  
Tree Amplitude ◽  
Four Dimensions ◽  
Yang Mills ◽  
Negative Helicity ◽  
Spanning Forests ◽  
Single Trace

Abstract The recursive expansion of tree level multitrace Einstein-Yang-Mills (EYM) amplitudes induces a refined graphic expansion, by which any tree-level EYM amplitude can be expressed as a summation over all possible refined graphs. Each graph contributes a unique coefficient as well as a proper combination of color-ordered Yang-Mills (YM) amplitudes. This expansion allows one to evaluate EYM amplitudes through YM amplitudes, the latter have much simpler structures in four dimensions than the former. In this paper, we classify the refined graphs for the expansion of EYM amplitudes into N k MHV sectors. Amplitudes in four dimensions, which involve k + 2 negative-helicity particles, at most get non-vanishing contribution from graphs in N k′ (k′ ≤ k) MHV sectors. By the help of this classification, we evaluate the non-vanishing amplitudes with two negative-helicity particles in four dimensions. We establish a correspondence between the refined graphs for single-trace amplitudes with $$ \left({g}_i^{-},{g}_j^{-}\right) $$ g i − g j − or $$ \left({h}_i^{-},{g}_j^{-}\right) $$ h i − g j − configuration and the spanning forests of the known Hodges determinant form. Inspired by this correspondence, we further propose a symmetric formula of double-trace amplitudes with $$ \left({g}_i^{-},{g}_j^{-}\right) $$ g i − g j − configuration. By analyzing the cancellation between refined graphs in four dimensions, we prove that any other tree amplitude with two negative-helicity particles has to vanish.

TREE DIAGRAMS IN WITTEN’S SUPERSTRING FIELD THEORY

1989 ◽  
Vol 04 (21) ◽  
pp. 2063-2071
Author(s):  
GEORGE SIOPSIS
Keyword(s):  
Field Theory ◽  
Scattering Amplitudes ◽  
Invariant Theory ◽  
Higher Order ◽  
Contact Term ◽  
Tree Level ◽  
Gauge Invariant

It is shown that the contact term discovered by Wendt is sufficient to ensure finiteness of all tree-level scattering amplitudes in Witten’s field theory of open superstrings. Its inclusion in the action also leads to a gauge-invariant theory. Thus, no additional higher-order counterterms in the action are needed.

scholarly journals Composing effective prediction at five points

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
John Joseph M. Carrasco ◽  
Laurentiu Rodina ◽  
Suna Zekioğlu
Keyword(s):  
Gauge Theory ◽  
Scattering Amplitude ◽  
Building Blocks ◽  
Tree Level ◽  
Critical Aspect ◽  
Higher Derivative ◽  
Higher Dimensional ◽  
Single Trace ◽  
The Relationship ◽  
Double Copy

Abstract Color-kinematics duality in the adjoint has proven key to the relationship between gauge and gravity theory scattering amplitude predictions. In recent work, we demonstrated that at four-point tree-level, a small number of color-dual EFT building blocks could encode all higher-derivative single-trace massless corrections to gauge and gravity theories compatible with adjoint double-copy. One critical aspect was the trivialization of building higher-derivative color-weights — indeed, it is the mixing of kinematics with non-adjoint-type color-weights (like the permutation-invariant d4) which permits description via adjoint double-copy. Here we find that such ideas clarify the predictions of local five-point higher-dimensional operators as well. We demonstrate how a single scalar building block can be combined with color structures to build higher-derivative color factors that generate, through double copy, the amplitudes associated with higher-derivative gauge-theory operators. These may then be suitably mapped, through another double-copy, to higher-derivative corrections in gravity.

scholarly journals Interesting Examples of Violation of the Classical Equivalence Principle but Not of the Weak One

2018 ◽  
Vol 2018 ◽  
pp. 1-13
Author(s):  
Antonio Accioly ◽  
Wallace Herdy
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Gravitational Field ◽  
Experimental Test ◽  
Equivalence Principle ◽  
Free Fall ◽  
Higher Order ◽  
Tree Level ◽  
Quantum Particles ◽  
Bohr Atom

The equivalence principle (EP) and Schiff’s conjecture are discussed en passant, and the connection between the EP and quantum mechanics is then briefly analyzed. Two semiclassical violations of the classical equivalence principle (CEP) but not of the weak one (WEP), i.e., Greenberger gravitational Bohr atom and the tree-level scattering of different quantum particles by an external weak higher-order gravitational field, are thoroughly investigated afterwards. Next, two quantum examples of systems that agree with the WEP but not with the CEP, namely, COW experiment and free fall in a constant gravitational field of a massive object described by its wave-function Ψ, are discussed in detail. Keeping in mind that, among the four examples focused on in this work only COW experiment is based on an experimental test, some important details related to it are presented as well.

The theory of the ferromagnetism of conduction electrons at low temperatures

1965 ◽  
Vol 284 (1398) ◽  
pp. 423-441 ◽  
Keyword(s):  
Low Temperature ◽  
Spin Wave ◽  
Single Particle ◽  
Lattice Site ◽  
Spontaneous Magnetization ◽  
Spin Waves ◽  
Green Functions ◽  
Linear Combinations ◽  
Conduction Electrons ◽  
Occupation Numbers

A theory is presented in which the effect of spin waves on the single-particle states of conduction electrons is obtained as well as the effect of the conduction electrons on the spin waves. Green function techniques are employed. The Hamiltonian is taken to contain the single-particle energies of the conduction electrons in the absence of interactions, the Coulomb interaction between electrons in Wannier states centred on the same lattice site C , and the interatomic exchange terms J ij . Interband integrals are neglected. The chain of equations for the single-particle Green functions is decoupled in such a way as to include the effects of the spin waves in the single-particle Green functions. The theory is worked out on the assumption that C is very much greater than the band width and the J ij so that at T ═ 0 the double occupation of Wannier orbital states is the minimum possible. The resulting single-particle occupation numbers are linear combinations of Fermi-Dirac functions. The low temperature spontaneous magnetization ξ is found to be a product of a spin-wave magnetization and a single-particle magnetization ξ s.p ., and so contains terms varying as T 1 and T 1 , and T 2 if both spin sub-bands are partially occupied in the ground state. The low temperature specific heat contains T and T 1 terms. The results of the Heisenberg model are obtained in the appropriate limit. Expressions for the spin-wave energy and its temperature dependence are discussed.

scholarly journals Infinity in string cosmology: A review through open problems

2017 ◽  
Vol 26 (04) ◽  
pp. 1730009 ◽  
Author(s):  
Ignatios Antoniadis ◽  
Spiros Cotsakis
Keyword(s):  
Higher Order ◽  
String Cosmology ◽  
Tree Level ◽  
Open Problems ◽  
String Correction ◽  
Recent Developments ◽  
M Theory

We review recent developments in the field of string cosmology with particular emphasis on open problems having to do mainly with geometric asymptotics and singularities. We discuss outstanding issues in a variety of currently popular themes, such as tree-level string cosmology asymptotics, higher-order string correction effects, M-theory cosmology, braneworlds and finally ambient cosmology.

scholarly journals Past of a particle in an entangled state

2017 ◽  
Vol 15 (08) ◽  
pp. 1740019 ◽  
Author(s):  
Dilip Paneru ◽  
Eliahu Cohen
Keyword(s):  
Time Evolution ◽  
Single Particle ◽  
Quantum Particle ◽  
Higher Order ◽  
Entangled State ◽  
Entire System ◽  
Single Quantum ◽  
Single Particles ◽  
Top Down ◽  
The Past

Vaidman has proposed a controversial criterion for determining the past of a single quantum particle based on the “weak trace” it leaves. We here consider more general examples of entangled systems and analyze the past of single, as well as pairs of entangled pre- and postselected particles. Systems with nontrivial time evolution are also analyzed. We argue that in these cases, examining only the single-particle weak trace provides information which is insufficient for understanding the system as a whole. We therefore suggest to examine, alongside with the past of single particles, also the past of pairs, triplets and eventually the entire system, including higher-order, multipartite traces in the analysis. This resonates with a recently proposed top-down approach by Aharonov, Cohen and Tollaksen for understanding the structure of correlations in pre- and postselected systems.

scholarly journals Some Approximation Properties for Modified Baskakov Type Operators

2005 ◽  
Vol 12 (2) ◽  
pp. 217-228
Author(s):  
Vijay Gupta
Keyword(s):  
Modulus Of Continuity ◽  
Simultaneous Approximation ◽  
Higher Order ◽  
Approximation Properties ◽  
Linear Combinations ◽  
Steklov Mean ◽  
Estimation Of Error ◽  
Direct Results

Abstract We study some direct results for the recently introduced family of modified Baskakov type operators. In particular, we obtain local direct results on ordinary and simultaneous approximation and an estimation of error for linear combinations in terms of higher order modulus of continuity. We have applied the Steklov mean as a tool for the linear approximating method.

scholarly journals Single particle operators and their correlators in free $$ \mathcal{N} $$ = 4 SYM

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
F. Aprile ◽  
J. M. Drummond ◽  
P. Heslop ◽  
H. Paul ◽  
F. Sanfilippo ◽  
...  
Keyword(s):  
Single Particle ◽  
Operator Product ◽  
Point Function ◽  
Superstring Theory ◽  
Yang Mills ◽  
Free Theory ◽  
Explicit Formulae ◽  
Orthogonality Theorem ◽  
Single Trace ◽  
Bps States

Abstract We consider a set of half-BPS operators in $$ \mathcal{N} $$ N = 4 super Yang-Mills theory which are appropriate for describing single-particle states of superstring theory on AdS5× S5. These single-particle operators are defined to have vanishing two-point functions with all multi-trace operators and therefore correspond to admixtures of single- and multi-traces. We find explicit formulae for all single-particle operators and for their two-point function normalisation. We show that single-particle U(N) operators belong to the SU(N) subspace, thus for length greater than one they are simply the SU(N) single-particle operators. Then, we point out that at large N, as the length of the operator increases, the single-particle operator naturally interpolates between the single-trace and the S3 giant graviton. At finite N, the multi-particle basis, obtained by taking products of the single-particle operators, gives a new basis for all half-BPS states, and this new basis naturally cuts off when the length of any of the single-particle operators exceeds the number of colours. From the two-point function orthogonality we prove a multipoint orthogonality theorem which implies vanishing of all near-extremal correlators. We then compute all maximally and next-to-maximally extremal free correlators, and we discuss features of the correlators when the extremality is lowered. Finally, we describe a half-BPS projection of the operator product expansion on the multi-particle basis which provides an alternative construction of four- and higher-point functions in the free theory.

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