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 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 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 Knitting wormholes by entanglement in supergravity

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Vijay Balasubramanian ◽  
Matthew DeCross ◽  
Gábor Sárosi
Keyword(s):  
Degrees Of Freedom ◽  
Intermediate Region ◽  
Yang Mills ◽  
Schwarzschild Geometry ◽  
Dual Interpretation ◽  
Two Universes ◽  
Single Boundary ◽  
Super Yang Mills Theory

Abstract We construct a single-boundary wormhole geometry in type IIB supergravity by perturbing two stacks of N extremal D3-branes in the decoupling limit. The solution interpolates from a two-sided planar AdS-Schwarzschild geometry in the interior, through a harmonic two-center solution in the intermediate region, to an asymptotic AdS space. The construction involves a CPT twist in the gluing of the wormhole to the exterior throats that gives a global monodromy to some coordinates, while preserving orientability. The geometry has a dual interpretation in $$ \mathcal{N} $$ N = 4 SU(2N) Super Yang-Mills theory in terms of a Higgsed SU(2N) → S(U(N) × U(N)) theory in which $$ \mathcal{O} $$ O (N2) degrees of freedom in each SU(N) sector are entangled in an approximate thermofield double state at a temperature much colder than the Higgs scale. We argue that the solution can be made long-lived by appropriate choice of parameters, and comment on mechanisms for generating traversability. We also describe a construction of a double wormhole between two universes.

scholarly journals The dilatation operator of conformal super-Yang–Mills theory

2003 ◽  
Vol 664 (1-2) ◽  
pp. 131-184 ◽  
Author(s):  
N. Beisert ◽  
C. Kristjansen ◽  
M. Staudacher
Keyword(s):  
Yang Mills ◽  
Dilatation Operator ◽  
Super Yang Mills Theory

scholarly journals $$ \mathcal{N} $$ = 4 supersymmetric Yang-Mills thermodynamics to order λ2

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Qianqian Du ◽  
Michael Strickland ◽  
Ubaid Tantary
Keyword(s):  
Strong Coupling ◽  
Finite Temperature ◽  
Weak Coupling ◽  
Chemical Potential ◽  
Entropy Density ◽  
Thermal Mass ◽  
Yang Mills ◽  
Hooft Coupling ◽  
Debye Mass ◽  
Infrared Divergences

Abstract We calculate the resummed perturbative free energy of $$ \mathcal{N} $$ N = 4 supersymmetric Yang-Mills in four spacetime dimensions (SYM4,4) through second order in the ’t Hooft coupling λ at finite temperature and zero chemical potential. Our final result is ultraviolet finite and all infrared divergences generated at three-loop level are canceled by summing over SYM4,4 ring diagrams. Non-analytic terms at $$ \mathcal{O} $$ O (λ3/2) and $$ \mathcal{O} $$ O (λ2 log λ) are generated by dressing the A0 and scalar propagators. The gauge-field Debye mass mD and the scalar thermal mass MD are determined from their corresponding finite-temperature self-energies. Based on this, we obtain the three-loop thermodynamic functions of SYM4,4 to $$ \mathcal{O} $$ O (λ2). We compare our final result with prior results obtained in the weak- and strong-coupling limits and construct a generalized Padé approximant that interpolates between the weak-coupling result and the large-Nc strong-coupling result. Our results suggest that the $$ \mathcal{O} $$ O (λ2) weak-coupling result for the scaled entropy density is a quantitatively reliable approximation to the scaled entropy density for 0 ≤ λ ≲ 2.

scholarly journals The conformal hyperplet

2017 ◽  
Vol 32 (14) ◽  
pp. 1750079 ◽  
Author(s):  
Michael Faux
Keyword(s):  
Saddle Point ◽  
Degrees Of Freedom ◽  
Central Charge ◽  
Yang Mills ◽  
Vacuum Instability ◽  
Gauge Fixing ◽  
Super Yang Mills Theory

We introduce a finite off-shell hypermultiplet with no off-shell central charge. This requires 192[Formula: see text]+[Formula: see text]192 degrees of freedom, all but 8[Formula: see text]+[Formula: see text]8 of which are auxiliary or gauge. In the absence of supergravity, the model has a saddle-point vacuum instability implying ghost-like propagators. These are cured by realizing the model superconformally, such that the erstwhile ghosts are realized as compensators. Gauge fixing these links the physical hypermultiplets to supergravity. This evokes the prospect of realizing [Formula: see text] super-Yang–Mills theory off-shell.

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