scholarly journals Oscillating multiple giants

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Ryo Suzuki
Keyword(s):  
Dispersion Relation ◽  
Harmonic Oscillators ◽  
Classical Motion ◽  
Yang Mills ◽  
Hooft Coupling

Abstract We propose a new example of the AdS/CFT correspondence between the system of multiple giant gravitons in AdS5× S5 and the operators with O(Nc) dimensions in $$ \mathcal{N} $$ N = 4 super Yang-Mills. We first extend the mixing of huge operators on the Gauss graph basis in the $$ \mathfrak{su}(2) $$ su 2 sector to all loops of the ’t Hooft coupling, by demanding the commutation of perturbative Hamiltonians in an effective U(p) theory, where p corresponds to the number of giant gravitons. The all-loop dispersion relation remains gapless at any λ, which suggests that harmonic oscillators of the effective U(p) theory should correspond to the classical motion of the D3-brane that is continuously connected to non-maximal giant gravitons.

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 Evidence for weak-coupling holography from the gauge/gravity correspondence for Dp-branes

2020 ◽  
Vol 2020 (2) ◽  
Author(s):  
Yasuhiro Sekino
Keyword(s):  
Gauge Theory ◽  
Free Field ◽  
Scalar Fields ◽  
Superstring Theory ◽  
Spatial Direction ◽  
Strongly Coupled ◽  
Yang Mills ◽  
Hooft Coupling ◽  
Brane Solution ◽  
Gauge Gravity

Abstract Gauge/gravity correspondence is regarded as a powerful tool for the study of strongly coupled quantum systems, but its proof is not available. An unresolved issue that should be closely related to the proof is what kind of correspondence exists, if any, when gauge theory is weakly coupled. We report progress about this limit for the case associated with D$p$-branes ($0\le p\le 4$), namely, the duality between the $(p+1)$D maximally supersymmetric Yang–Mills theory and superstring theory on the near-horizon limit of the D$p$-brane solution. It has been suggested by supergravity analysis that the two-point functions of certain operators in gauge theory obey a power law with the power different from the free-field value for $p\neq 3$. In this work, we show for the first time that the free-field result can be reproduced by superstring theory on the strongly curved background. The operator that we consider is of the form ${\rm Tr}(Z^J)$, where $Z$ is a complex combination of two scalar fields. We assume that the corresponding string has the worldsheet spatial direction discretized into $J$ bits, and use the fact that these bits become non-interacting when ’t Hooft coupling is zero.

scholarly journals $$ T\overline{T} $$-deformation of q-Yang-Mills theory

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Leonardo Santilli ◽  
Richard J. Szabo ◽  
Miguel Tierz
Keyword(s):  
Phase Transition ◽  
Entanglement Entropy ◽  
Simons Theory ◽  
Line Bundles ◽  
Boltzmann Entropy ◽  
Third Order ◽  
Yang Mills ◽  
Hooft Coupling ◽  
Chern Simons ◽  
Chern Simons Theory

Abstract We derive the $$ T\overline{T} $$ T T ¯ -perturbed version of two-dimensional q-deformed Yang-Mills theory on an arbitrary Riemann surface by coupling the unperturbed theory in the first order formalism to Jackiw-Teitelboim gravity. We show that the $$ T\overline{T} $$ T T ¯ -deformation results in a breakdown of the connection with a Chern-Simons theory on a Seifert manifold, and of the large N factorization into chiral and anti-chiral sectors. For the U(N) gauge theory on the sphere, we show that the large N phase transition persists, and that it is of third order and induced by instantons. The effect of the $$ T\overline{T} $$ T T ¯ -deformation is to decrease the critical value of the ’t Hooft coupling, and also to extend the class of line bundles for which the phase transition occurs. The same results are shown to hold for (q, t)-deformed Yang-Mills theory. We also explicitly evaluate the entanglement entropy in the large N limit of Yang-Mills theory, showing that the $$ T\overline{T} $$ T T ¯ -deformation decreases the contribution of the Boltzmann entropy.

K-VORTEX DYNAMICS IN $\mathcal{N}\, = \,1^*$ THEORY AND IN ITS GRAVITY DUAL

2010 ◽  
Vol 25 (02n03) ◽  
pp. 247-257
Author(s):  
R. AUZZI
Keyword(s):  
Magnetic Flux ◽  
Scaling Law ◽  
World Sheet ◽  
Flux Tubes ◽  
Yang Mills ◽  
Hooft Coupling ◽  
Higgs Vacuum ◽  
Large N ◽  
Vortex Solutions ◽  
Magnetic Flux Tubes

We study magnetic flux tubes in the Higgs vacuum of the [Formula: see text] mass deformation of SU(Nc), [Formula: see text] SYM and its large Nc string dual, the Polchinski-Strassler geometry. Choosing equal masses for the three adjoint chiral multiplets, for all Nc we identify a "colour-flavour locked" symmetry, SO(3)C+F which leaves the Higgs vacuum invariant. At weak coupling, we find explicit non-Abelian k-vortex solutions carrying a ℤNc-valued magnetic flux, with topological winding 0 < k < Nc. These k-strings spontaneously break SO(3)C+F to U(1)C+F resulting in an S2 moduli space of solutions. The world-sheet sigma model is a nonsupersymmetric ℂℙ1 model with a theta angle θ1+1 = k(Nc - k)θ3+1 where θ3+1 is the Yang-Mills vacuum angle. We find numerically that k-vortex tensions follow the Casimir scaling law Tk ∝ k(Nc - k) for large Nc. In the large Nc IIB string dual, the SO(3)C+F symmetry is manifest in the geometry interpolating between AdS5 × S5 and the interior metric due to a single D5 -brane carrying D3 -brane charge. We identify candidate k-vortices as expanded probe D3 -branes formed from a collection of k D -strings. The resulting k-vortex tension exhibits precise Casimir scaling, and the effective world-sheet theta angle matches the semiclassical result. S -duality maps the Higgs to the confining phase so that confining string tensions at strong 't Hooft coupling also exhibit Casimir scaling in [Formula: see text] theory in the large Nc limit.

Level clustering in the regular spectrum

1977 ◽  
Vol 356 (1686) ◽  
pp. 375-394 ◽  
Keyword(s):  
Classical Limit ◽  
Numerical Experiments ◽  
Level Density ◽  
Generic Property ◽  
Harmonic Oscillators ◽  
Dimensional System ◽  
Classical Motion ◽  
Quantum Numbers ◽  
Local Mean ◽  
Frequency Ratios

In the regular spectrum of an f -dimensional system each energy level can be labelled with f quantum numbers originating in f constants of the classical motion. Levels with very different quantum numbers can have similar energies. We study the classical limit of the distribution P(S) of spacings between adjacent levels, using a scaling transformation to remove the irrelevant effects of the varying local mean level density. For generic regular systems P(S) = e -s , characteristic of a Poisson process with levels distributed at random. But for systems of harmonic oscillators, which possess the non-generic property that the ‘energy contours’ in action space are flat, P(S) does not exist if the oscillator frequencies are commensurable, and is peaked about a non-zero value of S if the frequencies are incommensurable, indicating some regularity in the level distribution; the precise form of P(S) depends on the arithmetic nature of the irrational frequency ratios. Numerical experiments on simple two-dimensional systems support these theoretical conclusions.

scholarly journals SINGLE MASSLESS MAJORANA FERMION IN THE DOMAIN-WALL FORMALISM

1998 ◽  
Vol 13 (20) ◽  
pp. 1667-1674 ◽  
Author(s):  
TOMOHIRO HOTTA ◽  
TAKU IZUBUCHI ◽  
JUN NISHIMURA
Keyword(s):  
Dispersion Relation ◽  
Domain Wall ◽  
Zero Mode ◽  
Mass Term ◽  
Fine Tuning ◽  
Majorana Fermion ◽  
Seesaw Mechanism ◽  
Yang Mills ◽  
Majorana Mass ◽  
Lattice Construction

We study the domain-wall formalism with additional Majorana mass term for the unwanted zero-mode, which has recently been proposed for lattice construction of 4D [Formula: see text] super-Yang–Mills theory without fine-tuning. Switching off the gauge field, we study the dispersion relation of the energy eigenstates numerically, and find that the method works for reasonable values of Majorana mass. We point out, however, that when the Majorana mass is too large, a problem arises which can be explained in terms of seesaw mechanism.

ON TWO HIERARCHIES OF SYSTEMS OF NONLINEAR DIFFERENTIAL EQUATIONS, FIRST INTEGRALS, NAMBU MECHANICS, AND PAINLEVÉ PROPERTY

2010 ◽  
Vol 07 (03) ◽  
pp. 405-409
Author(s):  
WILLI-HANS STEEB
Keyword(s):  
Differential Equations ◽  
Chaotic Behavior ◽  
Nonlinear Differential Equations ◽  
Autonomous Systems ◽  
First Integrals ◽  
Harmonic Oscillators ◽  
Painlevé Test ◽  
Yang Mills ◽  
Nambu Mechanics ◽  
Painlevé Property

We study a hierarchy of nonlinear autonomous systems of first ordinary differential equations. We show that it is completely integrable using the Painlevé test and finding the first integrals. We also show that it can be derived from the first integrals using Nambu mechanics. A corresponding dynamical system with chaotic behavior is also derived. A modified system with harmonic oscillators as first integrals is also considered. A connection with the Yang–Mills equation and the self-dual Yang–Mills equation is also discussed.

scholarly journals Holographic Coulomb branch solitons, quasinormal modes, and black holes

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
S. Prem Kumar ◽  
Andy O’Bannon ◽  
Anton Pribytok ◽  
Ronnie Rodgers
Keyword(s):  
Black Holes ◽  
Gauge Theory ◽  
Gauge Symmetry ◽  
Quasinormal Modes ◽  
Coulomb Branch ◽  
Asymptotically Flat ◽  
Yang Mills ◽  
Hooft Coupling ◽  
Qualitative And Quantitative ◽  
Extremal Black Holes

Abstract Four-dimensional $$ \mathcal{N} $$ N = 4 supersymmetric Yang-Mills theory, at a point on the Coulomb branch where SU(N) gauge symmetry is spontaneously broken to SU(N − 1) × U(1), admits BPS solitons describing a spherical shell of electric and/or magnetic charges enclosing a region of unbroken gauge symmetry. These solitons have been proposed as gauge theory models for certain features of asymptotically flat extremal black holes. In the ’t Hooft large N limit with large ’t Hooft coupling, these solitons are holographically dual to certain probe D3-branes in the AdS5 × S5 solution of type IIB supergravity. By studying linearised perturbations of these D3-branes, we show that the solitons support quasinormal modes with a spectrum of frequencies sharing both qualitative and quantitative features with asymptotically flat extremal black holes.

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