scholarly journals Infrared degrees of freedom of Yang-Mills theory in the Schrödinger representation

2006 ◽  
Vol 73 (10) ◽  
Author(s):  
Hilmar Forkel
Keyword(s):  
Degrees Of Freedom ◽  
Yang Mills ◽  
Schrödinger Representation

scholarly journals From Center-Vortex Ensembles to the Confining Flux Tube

Universe ◽  
2021 ◽  
Vol 7 (8) ◽  
pp. 253
Author(s):  
David R. Junior ◽  
Luis E. Oxman ◽  
Gustavo M. Simões
Keyword(s):  
Degrees Of Freedom ◽  
String Tension ◽  
Effective Field ◽  
Scaling Properties ◽  
Flux Tubes ◽  
Topological Solitons ◽  
Yang Mills ◽  
Center Vortex ◽  
Asymptotic Scaling ◽  
The Continuum

In this review, we discuss the present status of the description of confining flux tubes in SU(N) pure Yang–Mills theory in terms of ensembles of percolating center vortices. This is based on three main pillars: modeling in the continuum the ensemble components detected in the lattice, the derivation of effective field representations, and contrasting the associated properties with Monte Carlo lattice results. The integration of the present knowledge about these points is essential to get closer to a unified physical picture for confinement. Here, we shall emphasize the last advances, which point to the importance of including the non-oriented center-vortex component and non-Abelian degrees of freedom when modeling the center-vortex ensemble measure. These inputs are responsible for the emergence of topological solitons and the possibility of accommodating the asymptotic scaling properties of the confining string tension.

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 THE HAGEDORN TRANSITION AND THE MATRIX MODEL FOR STRINGS

1998 ◽  
Vol 13 (26) ◽  
pp. 2085-2094 ◽  
Author(s):  
B. SATHIAPALAN
Keyword(s):  
Matrix Model ◽  
Light Cone ◽  
Degrees Of Freedom ◽  
Low Energy ◽  
Matrix Formalism ◽  
Yang Mills ◽  
Large N ◽  
The Matrix ◽  
The Continuum ◽  
String Worldsheet

We use the matrix formalism to investigate what happens to strings above the Hagedorn temperature. We show that is not a limiting temperature but a temperature at which the continuum string picture breaks down. We study a collection of N D-0-branes arranged to form a string having N units of light-cone momentum. We find that at high temperatures the favored phase is one where the string worldsheet has disappeared and the low-energy degrees of freedom consists of N2 massless particles ("gluons"). The nature of the transition is very similar to the deconfinement transition in large-N Yang–Mills theories.

PHASE SPACE REDUCTION AND THE CHOICE OF PHYSICAL VARIABLES IN GAUGE THEORIES

1991 ◽  
Vol 06 (05) ◽  
pp. 845-863 ◽  
Author(s):  
S.V. SHABANOV
Keyword(s):  
Phase Space ◽  
Degrees Of Freedom ◽  
Gauge Theories ◽  
Hamiltonian Path ◽  
Curvilinear Coordinates ◽  
Yang Mills ◽  
Space Reduction ◽  
Physical Variables ◽  
Phase Space Reduction ◽  
Gauge Conditions

The connection between the way of separation of physical variables and the form of the Hamiltonian path integral (HPI) is studied for the Yang-Mills quantum mechanics. It is shown that physical degrees of freedom are always described by curvilinear coordinates. It is also found that the ambiguity in determining physical variables follows from the reduction of the physical phase space. The latter leads to a modification of the standard HPI (HPI with gauge conditions).

scholarly journals ON UNITARITY OF A LINEARIZED YANG–MILLS FORMULATION FOR MASSLESS AND MASSIVE GRAVITY WITH PROPAGATING TORSION

2010 ◽  
Vol 25 (26) ◽  
pp. 4911-4932
Author(s):  
ROLANDO GAITAN DEVERAS
Keyword(s):  
Degrees Of Freedom ◽  
Dimensional Space ◽  
Massive Gravity ◽  
Dynamical Variable ◽  
General Covariance ◽  
Yang Mills ◽  
Dimensional Space Time ◽  
Perturbative Regime ◽  
Massive Theory ◽  
Extended Theories

A perturbative regime based on contortion as a dynamical variable and metric as a (classical) fixed background, is performed in the context of a pure Yang–Mills formulation for gravity in a (2+1)-dimensional space–time. In the massless case, we show that the theory contains three degrees of freedom and only one is a nonunitary mode. Next, we introduce quadratical terms dependent on torsion, which preserve parity and general covariance. The linearized version reproduces an analogue Hilbert–Einstein–Fierz–Pauli unitary massive theory plus three massless modes, two of them represents nonunitary ones. Finally, we confirm the existence of a family of unitary Yang–Mills-extended theories which are classically consistent with Einstein's solutions coming from nonmassive and topologically massive gravity. The unitarity of these Yang–Mills-extended theories is shown in a perturbative regime. A possible way to perform a nonperturbative study is remarked.

FLUCTONS

2008 ◽  
Vol 05 (03) ◽  
pp. 375-386 ◽  
Author(s):  
R. CARTAS-FUENTEVILLA ◽  
J. M. SOLANO-ALTAMIRANO
Keyword(s):  
Degrees Of Freedom ◽  
Index Theorem ◽  
Quantum Mechanical ◽  
Topological Field Theory ◽  
Topological Phases ◽  
Abelian Gauge ◽  
Yang Mills ◽  
Topological Field ◽  
Dual Domain ◽  
Topological Fluctuations

From the perspective of topological field theory we explore the physics beyond instantons. We propose the fluctons as nonperturbative topological fluctuations of vacuum, from which the self-dual domain of instantons is attained as a particular case. Invoking the Atiyah–Singer index theorem, we determine the dimension of the corresponding flucton moduli space, which gives the number of degrees of freedom of the fluctons. An important consequence of these results is that the topological phases of vacuum in non-Abelian gauge theories are not necessarily associated with self-dual fields, but only with smooth fields. Fluctons in different scenarios are considered, the basic aspects of the quantum mechanical amplitude for fluctons are discussed. A possible application of fluctons in the N = 4 Topologically Twisted Supersymmetric Yang–Mills Theory is explored and the case of gravity is discussed briefly.

scholarly journals Surface operators and magnetic degrees of freedom in yang-mills theories

2010 ◽  
Vol 73 (4) ◽  
pp. 711-720 ◽  
Author(s):  
A. Di Giacomo ◽  
V. I. Zakharov
Keyword(s):  
Degrees Of Freedom ◽  
Yang Mills

scholarly journals Covariant origin of the U(1)3 model for Euclidean quantum gravity

2021 ◽  
Author(s):  
Sepideh Bakhoda ◽  
Thomas Thiemann
Keyword(s):  
Gauge Theory ◽  
Quantum Gravity ◽  
Degrees Of Freedom ◽  
Hamiltonian Formulation ◽  
The Other ◽  
Topological Theory ◽  
Yang Mills ◽  
Consistent Model ◽  
Starting Point ◽  
Euclidean Signature

Abstract If one replaces the constraints of the Ashtekar-Barbero $SU(2)$ gauge theory formulation of Euclidean gravity by their $U(1)^3$ version, one arrives at a consistent model which captures significant structures of its $SU(2)$ version. In particular, it displays a non-trivial realisation of the hypersurface deformation algebra which makes it an interesting testing ground for (Euclidean) quantum gravity as has been emphasised in a recent series of papers due to Varadarajan et al. The simplification from SU(2) to U(1)$^3$ can be performed simply by hand within the Hamiltonian formulation by dropping all non-Abelian terms from the Gauss, spatial diffeomorphism, and Hamiltonian constraints respectively. However, one may ask from which Lagrangian formulation this theory descends. For the SU(2) theory it is known that one can choose the Palatini action, Holst action, or (anti-)selfdual action (Euclidean signature) as starting point all leading to equivalent Hamiltonian formulations. In this paper, we systematically analyse this question directly for the U(1)$^3$ theory. Surprisingly, it turns out that the Abelian analog of the Palatini or Holst formulation is a consistent but topological theory without propagating degrees of freedom. On the other hand, a twisted Abelian analog of the (anti-)selfdual formulation does lead to the desired Hamiltonian formulation. A new aspect of our derivation is that we work with 1. half-density valued tetrads which simplifies the analysis, 2. without the simplicity constraint (which admits one undesired solution that is usually neglected by hand) and 3. without imposing the time gauge from the beginning. As a byproduct, we show that also the non-Abelian theory admits a twisted (anti-)selfdual formulation. Finally, we also derive a pure connection formulation of Euclidean GR including a cosmological constant by extending previous work due to Capovilla, Dell, Jacobson, and Peldan which may be an interesting starting point for path integral investigations and displays (Euclidean) GR as a Yang-Mills theory with non-polynomial Lagrangian.

scholarly journals The quasilocal degrees of freedom of Yang-Mills theory

2021 ◽  
Vol 10 (6) ◽  
Author(s):  
Henrique Gomes ◽  
Aldo Riello
Keyword(s):  
Boundary Data ◽  
Degrees Of Freedom ◽  
Gauge Theories ◽  
Direct Link ◽  
Yang Mills ◽  
Symplectic Forms ◽  
Geometric Methods ◽  
Functional Geometry ◽  
Electric Flux ◽  
Non Locality

Gauge theories possess nonlocal features that, in the presence of boundaries, inevitably lead to subtleties. We employ geometric methods rooted in the functional geometry of the phase space of Yang-Mills theories to: (1) characterize a basis for quasilocal degrees of freedom (dof) that is manifestly gauge-covariant also at the boundary; (2) tame the non-additivity of the regional symplectic forms upon the gluing of regions; and to (3) discuss gauge and global charges in both Abelian and non-Abelian theories from a geometric perspective. Naturally, our analysis leads to splitting the Yang-Mills dof into Coulombic and radiative. Coulombic dof enter the Gauss constraint and are dependent on extra boundary data (the electric flux); radiative dof are unconstrained and independent. The inevitable non-locality of this split is identified as the source of the symplectic non-additivity, i.e. of the appearance of new dof upon the gluing of regions. Remarkably, these new dof are fully determined by the regional radiative dof only. Finally, a direct link is drawn between this split and Dirac's dressed electron.

scholarly journals THE “DUAL” VARIABLES OF YANG-MILLS THEORY AND LOCAL GAUGE-INVARIANT VARIABLES

1996 ◽  
Vol 11 (32) ◽  
pp. 5701-5728 ◽  
Author(s):  
ORI GANOR ◽  
J. SONNENSCHEIN
Keyword(s):  
Degrees Of Freedom ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Two Dimensional ◽  
Gauge Invariant ◽  
Yang Mills ◽  
Six Degrees Of Freedom ◽  
Local Gauge ◽  
Dual Variables ◽  
Topological Part

After adding auxiliary fields and integrating out the original variables, the Yang-Mills action can be expressed in terms of local gauge-invariant variables. This method reproduces the known solution of the two-dimensional SU (N) theory. In more than two dimensions the action splits into a topological part and a part proportional to αs. We demonstrate the procedure for SU (2) in three dimensions where we reproduce a gravitylike theory. We discuss the four-dimensional case as well. We use a cubic expression in the fields as a space-time metric to obtain a covariant Lagrangian. We also show how the four-dimensional SU (2) theory can be expressed in terms of a local action with six degrees of freedom only.

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