scholarly journals The four-loop remainder function and multi-Regge behavior at NNLLA in planar $ \mathcal{N} $ = 4 super-Yang-Mills theory

2014 ◽  
Vol 2014 (6) ◽  
Author(s):  
Lance J. Dixon ◽  
James M. Drummond ◽  
Claude Duhr ◽  
Jeffrey Pennington
Keyword(s):  
Yang Mills ◽  
Remainder Function ◽  
Regge Behavior ◽  
Super Yang Mills Theory

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 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 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.

Soft breaking of N = 4 super-Yang-Mills theory

1983 ◽  
Vol 121 (6) ◽  
pp. 386-390 ◽  
Author(s):  
J.G. Taylor
Keyword(s):  
Yang Mills ◽  
Super Yang Mills Theory

scholarly journals Testing holography using lattice super-Yang-Mills theory on a 2-torus

2018 ◽  
Vol 97 (8) ◽  
Author(s):  
Simon Catterall ◽  
Raghav G. Jha ◽  
David Schaich ◽  
Toby Wiseman
Keyword(s):  
Yang Mills ◽  
Super Yang Mills Theory

scholarly journals Quenched spectroscopy for the N = 1 Super-Yang-Mills theory

1998 ◽  
Vol 63 (1-3) ◽  
pp. 718-720 ◽  
Author(s):  
A. Donini ◽  
M. Guagnelli ◽  
P. Hernandez ◽  
A. Vladikas
Keyword(s):  
Yang Mills ◽  
Super Yang Mills Theory
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