scholarly journals Multi-particle finite-volume effects for hexagon tessellations

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Marius de Leeuw ◽  
Burkhard Eden ◽  
Dennis le Plat ◽  
Tim Meier ◽  
Alessandro Sfondrini
Keyword(s):  
Finite Volume ◽  
Correlation Functions ◽  
Gauge Invariant ◽  
Yang Mills ◽  
Hooft Coupling ◽  
Volume Effects ◽  
Super Yang Mills Theory

Abstract Correlation functions of gauge-invariant composite operators in $$ \mathcal{N} $$ N = 4 super Yang-Mills theory can be computed by integrability using triangulations. The elementary tile in this process is the hexagon, which should be glued by appropriately inserting resolutions of the identity involving virtual (“mirror”) magnons. We consider this problem for five-point functions of protected operators. At one-loop in the ’t Hooft coupling, it is necessary to glue three adjacent tiles which involves two virtual magnons scattering among each other. We show that the result can be simplified by using an adapted mirror rotation and employing appropriate summation techniques. The mirror-particle contributions then yield hyperlogarithms of weight two. Finally, we use these results to investigate braiding prescriptions introduced in earlier work on the problem.

scholarly journals Exact 1/N expansion of Wilson loop correlators in $$ \mathcal{N} $$ = 4 Super-Yang-Mills theory

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Wolfgang Mück
Keyword(s):  
Matrix Model ◽  
Wilson Loop ◽  
Model Solution ◽  
Wilson Loops ◽  
Combinatorial Formula ◽  
Expectation Value ◽  
Yang Mills ◽  
Hooft Coupling ◽  
The Matrix ◽  
Super Yang Mills Theory

Abstract Supersymmetric circular Wilson loops in $$ \mathcal{N} $$ N = 4 Super-Yang-Mills theory are discussed starting from their Gaussian matrix model representations. Previous results on the generating functions of Wilson loops are reviewed and extended to the more general case of two different loop contours, which is needed to discuss coincident loops with opposite orientations. A combinatorial formula representing the connected correlators of multiply wound Wilson loops in terms of the matrix model solution is derived. Two new results are obtained on the expectation value of the circular Wilson loop, the expansion of which into a series in 1/N and to all orders in the ’t Hooft coupling λ was derived by Drukker and Gross about twenty years ago. The connected correlators of two multiply wound Wilson loops with arbitrary winding numbers are calculated as a series in 1/N. The coefficient functions are derived not only as power series in λ, but also to all orders in λ by expressing them in terms of the coefficients of the Drukker and Gross series. This provides an efficient way to calculate the 1/N series, which can probably be generalized to higher-point correlators.

scholarly journals Scrambling in Yang-Mills

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Robert de Mello Koch ◽  
Eunice Gandote ◽  
Augustine Larweh Mahu
Keyword(s):  
Relaxation Time ◽  
Weak Coupling ◽  
Degrees Of Freedom ◽  
Yang Mills ◽  
Hooft Coupling ◽  
Dilatation Operator ◽  
Super Yang Mills Theory

Abstract Acting on operators with a bare dimension ∆ ∼ N2 the dilatation operator of U(N) $$ \mathcal{N} $$ N = 4 super Yang-Mills theory defines a 2-local Hamiltonian acting on a graph. Degrees of freedom are associated with the vertices of the graph while edges correspond to terms in the Hamiltonian. The graph has p ∼ N vertices. Using this Hamiltonian, we study scrambling and equilibration in the large N Yang-Mills theory. We characterize the typical graph and thus the typical Hamiltonian. For the typical graph, the dynamics leads to scrambling in a time consistent with the fast scrambling conjecture. Further, the system exhibits a notion of equilibration with a relaxation time, at weak coupling, given by t ∼ $$ \frac{\rho }{\lambda } $$ ρ λ with λ the ’t Hooft coupling.

scholarly journals All-order bounds for correlation functions of gauge-invariant operators in Yang-Mills theory

2016 ◽  
Vol 57 (12) ◽  
pp. 122301 ◽  
Author(s):  
Markus B. Fröb ◽  
Jan Holland ◽  
Stefan Hollands
Keyword(s):  
Correlation Functions ◽  
Gauge Invariant ◽  
Yang Mills ◽  
Order Bounds

scholarly journals N=2 SUPER-YANG–MILLS ACTION AND BRST COHOMOLOGY

2004 ◽  
Vol 19 (09) ◽  
pp. 713-726 ◽  
Author(s):  
K. ÜLKER
Keyword(s):  
Gauge Invariant ◽  
Yang Mills ◽  
Brst Cohomology ◽  
Lower Dimensional ◽  
Exact Term ◽  
Super Yang Mills Theory

The extended BRST cohomology of N=2 super-Yang–Mills theory is discussed in the framework of Algebraic Renormalization. In particular, N=2 supersymmetric descent equations are derived from the cohomological analysis of linearized Slavnov–Taylor operator ℬ. It is then shown that both off- and on-shell N=2 super-Yang–Mills actions are related to a lower-dimensional gauge-invariant field polynomial Tr ϕ2 by solving these descent equations. Moreover, it is found that these off- and on-shell solutions differ only by a ℬ-exact term, which can be interpreted as a consequence of the fact that the cohomology of both cases are the same.

scholarly journals Giant Wilson loops and AdS2/dCFT1

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Simone Giombi ◽  
Jiaqi Jiang ◽  
Shota Komatsu
Keyword(s):  
Correlation Functions ◽  
Wilson Loop ◽  
Wilson Loops ◽  
One Dimensional ◽  
Yang Mills ◽  
Large Rank ◽  
Hooft Coupling ◽  
Multiple Integrals ◽  
The Difference ◽  
Selection Of

Abstract The 1/2-BPS Wilson loop in $$ \mathcal{N} $$ N = 4 supersymmetric Yang-Mills theory is an important and well-studied example of conformal defect. In particular, much work has been done for the correlation functions of operator insertions on the Wilson loop in the fundamental representation. In this paper, we extend such analyses to Wilson loops in the large-rank symmetric and antisymmetric representations, which correspond to probe D3 and D5 branes with AdS2× S2 and AdS2× S4 worldvolume geometries, ending at the AdS5 boundary along a one-dimensional contour. We first compute the correlation functions of protected scalar insertions from supersymmetric localization, and obtain a representation in terms of multiple integrals that are similar to the eigenvalue integrals of the random matrix, but with important differences. Using ideas from the Fermi Gas formalism and the Clustering method, we evaluate their large N limit exactly as a function of the ’t Hooft coupling. The results are given by simple integrals of polynomials that resemble the Q-functions of the Quantum Spectral Curve, with integration measures depending on the number of insertions. Next, we study the correlation functions of fluctuations on the probe D3 and D5 branes in AdS. We compute a selection of three- and four-point functions from perturbation theory on the D-branes, and show that they agree with the results of localization when restricted to supersymmetric kinematics. We also explain how the difference of the internal geometries of the D3 and D5 branes manifests itself in the localization computation.

scholarly journals The Grassmannian for celestial superamplitudes

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Livia Ferro ◽  
Robert Moerman
Keyword(s):  
Scattering Amplitudes ◽  
Correlation Functions ◽  
Minkowski Spacetime ◽  
Tree Level ◽  
Two Dimensional ◽  
Yang Mills ◽  
Celestial Sphere ◽  
Geometric Picture ◽  
Super Yang Mills Theory ◽  
The Way

Abstract Recently, scattering amplitudes in four-dimensional Minkowski spacetime have been interpreted as conformal correlation functions on the two-dimensional celestial sphere, the so-called celestial amplitudes. In this note we consider tree-level scattering amplitudes in $$ \mathcal{N} $$ N = 4 super Yang-Mills theory and present a Grassmannian formulation of their celestial counterparts. This result paves the way towards a geometric picture for celestial superamplitudes, in the spirit of positive geometries.

scholarly journals Super Yang-Mills theories with inhomogeneous mass deformations

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Yoonbai Kim ◽  
O-Kab Kwon ◽  
D. D. Tolla
Keyword(s):  
Boundary Condition ◽  
Killing Spinor ◽  
Vacuum Equation ◽  
Constant Mass ◽  
Yang Mills ◽  
Spatial Coordinate ◽  
Mass Functions ◽  
Vacuum Solutions ◽  
Super Yang Mills Theory

Abstract We construct the 4-dimensional $$ \mathcal{N}=\frac{1}{2} $$ N = 1 2 and $$ \mathcal{N} $$ N = 1 inhomogeneously mass-deformed super Yang-Mills theories from the $$ \mathcal{N} $$ N = 1* and $$ \mathcal{N} $$ N = 2* theories, respectively, and analyse their supersymmetric vacua. The inhomogeneity is attributed to the dependence of background fluxes in the type IIB supergravity on a single spatial coordinate. This gives rise to inhomogeneous mass functions in the $$ \mathcal{N} $$ N = 4 super Yang-Mills theory which describes the dynamics of D3-branes. The Killing spinor equations for those inhomogeneous theories lead to the supersymmetric vacuum equation and a boundary condition. We investigate two types of solutions in the $$ \mathcal{N}=\frac{1}{2} $$ N = 1 2 theory, corresponding to the cases of asymptotically constant mass functions and periodic mass functions. For the former case, the boundary condition gives a relation between the parameters of two possibly distinct vacua at the asymptotic boundaries. Brane interpretations for corresponding vacuum solutions in type IIB supergravity are also discussed. For the latter case, we obtain explicit forms of the periodic vacuum solutions.

scholarly journals From correlation functions to event shapes in QCD

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
D. Chicherin ◽  
J. M. Henn ◽  
E. Sokatchev ◽  
K. Yan
Keyword(s):  
Correlation Function ◽  
Correlation Functions ◽  
Event Shape ◽  
Proof Of Concept ◽  
Yang Mills ◽  
Point Correlation ◽  
Point Correlation Function ◽  
Event Shapes ◽  
A Charge ◽  
Conserved Currents

Abstract We present a method for calculating event shapes in QCD based on correlation functions of conserved currents. The method has been previously applied to the maximally supersymmetric Yang-Mills theory, but we demonstrate that supersymmetry is not essential. As a proof of concept, we consider the simplest example of a charge-charge correlation at one loop (leading order). We compute the correlation function of four electromagnetic currents and explain in detail the steps needed to extract the event shape from it. The result is compared to the standard amplitude calculation. The explicit four-point correlation function may also be of interest for the CFT community.

scholarly journals Schur correlation functions from q -deformed Yang-Mills theory

2021 ◽  
Vol 103 (10) ◽  
Author(s):  
Yufan Wang ◽  
Yiwen Pan
Keyword(s):  
Correlation Functions ◽  
Yang Mills

scholarly journals New modular invariants in $$ \mathcal{N} $$ = 4 Super-Yang-Mills theory

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Shai M. Chester ◽  
Michael B. Green ◽  
Silviu S. Pufu ◽  
Yifan Wang ◽  
Congkao Wen
Keyword(s):  
Eisenstein Series ◽  
Mass Parameter ◽  
Flat Space ◽  
Superstring Theory ◽  
Modular Invariant ◽  
Yang Mills ◽  
Laplace Eigenvalue ◽  
Modular Invariants ◽  
Tensor Multiplet ◽  
Super Yang Mills Theory

Abstract We study modular invariants arising in the four-point functions of the stress tensor multiplet operators of the $$ \mathcal{N} $$ N = 4 SU(N) super-Yang-Mills theory, in the limit where N is taken to be large while the complexified Yang-Mills coupling τ is held fixed. The specific four-point functions we consider are integrated correlators obtained by taking various combinations of four derivatives of the squashed sphere partition function of the $$ \mathcal{N} $$ N = 2∗ theory with respect to the squashing parameter b and mass parameter m, evaluated at the values b = 1 and m = 0 that correspond to the $$ \mathcal{N} $$ N = 4 theory on a round sphere. At each order in the 1/N expansion, these fourth derivatives are modular invariant functions of (τ,$$ \overline{\tau} $$ τ ¯ ). We present evidence that at half-integer orders in 1/N , these modular invariants are linear combinations of non-holomorphic Eisenstein series, while at integer orders in 1/N, they are certain “generalized Eisenstein series” which satisfy inhomogeneous Laplace eigenvalue equations on the hyperbolic plane. These results reproduce known features of the low-energy expansion of the four-graviton amplitude in type IIB superstring theory in ten-dimensional flat space and have interesting implications for the structure of the analogous expansion in AdS5× S5.

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