Related papers: Quantum Extended Crystal Super Pde's
The self-duality Yang-Mills equations in pseudoeuclidean spaces of dimensions $d\leq 8$ are investigated. New classes of solutions of the equations are found. Extended solutions to the D=10, N=1 supergravity and super Yang-Mills equations…
Using a Dyson--Schwinger approach, we perform an analysis of the non-trivial ground state of thermal $SU(N)$ Yang--Mills theory in the non-perturbative regime where chiral symmetry is dynamically broken by a mass gap. Basic thermodynamic…
The string equation for the $[{\tilde P},Q]=Q$ formulation of non--perturbatively stable 2D quantum gravity coupled to the $(2m-1,2)$ models is studied. Global KdV flows between the appropriate solutions are considered as deformations of…
In several approaches towards a quantum theory of gravity, such as group field theory and loop quantum gravity, quantum states and histories of the geometric degrees of freedom turn out to be based on discrete spacetime. The most pressing…
In this paper, we extend a result of Gao Chen regarding the solvability of the twisted deformed Hermitian Yang-Mills equations on compact K\"ahler manifolds to allow for the twisting function to be non-constant and slightly negative in all…
We construct globally regular gravitating solutions, which possess only discrete symmetries. These solutions of Yang-Mills-dilaton theory may be viewed as exact (numerical) solutions of scalar gravity, by considering the dilaton as a kind…
This article represents the fourth and final part of a four-paper sequence whose aim is to prove the Threshold Conjecture as well as the more general Dichotomy Theorem for the energy critical $4+1$ dimensional hyperbolic Yang--Mills…
It is possible to define new, gauge invariant variables in the Hilbert space of Yang-Mills theories which manifestly implement Gauss' law on physical states. These variables have furthermore a geometrical meaning, and allow one to uncover…
By making use of the background field method, we derive a novel reformulation of the Yang-Mills theory which was proposed recently by the author to derive quark confinement in QCD. This reformulation identifies the Yang-Mills theory with a…
We categorize the global structure of spherically symmetric static solutions of Einstein SU(2) Yang Mills equations with positive cosmological constant that are smooth at the center of spherical symmetry.
We construct the 4-dimensional ${\cal N}=\frac12$ and ${\cal N}=1$ inhomogeneously mass-deformed super Yang-Mills theories from the ${\cal N} =1^*$ and ${\cal N} =2^*$ theories, respectively, and analyse their supersymmetric vacua. The…
In this paper, we consider the deformed Hermitian-Yang-Mills equation on closed almost Hermitian manifolds. In the case of hypercritical phase, we derive a priori estimates under the existence of an admissible $\mathcal{C}$-subsolution. As…
Homogeneous and isotropic equilibrium states of strongly coupled ${\cal N}=4$ supersymmetric Yang-Mills charged plasma in ${\mathbb R}^3$ with equal chemical potentials for the maximal Abelian subgroup of the $R$-symmetry group become…
We characterise the quantum group gauge symmetries underlying q-deformations of two-dimensional Yang-Mills theory by studying their relationships with the matrix models that appear in Chern-Simons theory and six-dimensional N=2 gauge…
We construct the gravity dual of three-dimensional, $SU(N_{\textrm{c}})$ super Yang-Mills theory with $N_{\textrm{f}}$ flavors of dynamical quarks in the presence of a non-zero quark density $N_{\textrm{q}}$. The supergravity solutions…
Classical solutions of the Yang-Mills-dilaton theory in Euclidean space-time are investigated. Our analytical and numerical results imply existence of infinite number of branches of dyonic type solutions labelled by the number of nodes of…
We formulate a classical GL(4,R) Yang--Mills framework for gravity in the presence of a non-dynamical background metric. The local GL(4,R) symmetry is taken to characterize the admissible local geometric setting, and sixteen Yang--Mills…
We present a type IIB supergravity solution dual to a spatially anisotropic $\mathcal{N}=4$ super Yang-Mills plasma at finite $U(1)$ chemical potential and finite temperature. The effective five-dimensional gravitational theory is a…
The superspace flatness conditions which are equivalent to the field equations of supersymmetric Yang-Mills theory in ten dimensions have not been useful so far to derive non trivial classical solutions. Recently, modified flatness…
We consider two fundamental long-standing problems in quantum chromodynamics (QCD): the origin of color confinement and structure of a true vacuum and color singlet quantum states. There is a common belief that resolution to these problems…