Related papers: Generalized simplicial chiral models
In this contribution we review some of the interplay between sigma models in theoretical physics and novel geometrical structures such as Lie (n-)algebroids. The first part of the article contains the mathematical background, the definition…
It is shown that classical nonsupersymmetric Yang-Mills theory in 4 dimensions is symmetric under a generalized dual transform which reduces to the usual dual *-operation for electromagnetism. The parallel phase transport $\tilde{A}_\mu(x)$…
The chiral WZNW symplectic form $\Omega^{\rho}_{chir}$ is inverted in the general case. Thereby a precise relationship between the arbitrary monodromy dependent 2-form appearing in $\Omega^{\rho}_{chir}$ and the exchange r-matrix that…
A complexification of the twisted $\N=2$ theory allows one to determine the N=4 Yang--Mills theory in its third twist formulation. The imaginary part of the gauge symmetry is used to eliminate two scalars fields and create gauge covariant…
We study numerically the saddle point structure of two-dimensional (2D) lattice gauge theory, represented by the Gross-Witten-Wadia unitary matrix model. The saddle points are in general complex-valued, even though the original integration…
Galileon models arise in certain braneworld scenarios as modifications to General Relativity, and are also interesting as field theories in their own right. We show how the galileon model can be naturally generalized to include local gauge…
The classical solutions to higher dimensional Yang--Mills (YM) systems, which are integral parts of higher dimensional Einstein--YM (EYM) systems, are studied. These are the gravity decoupling limits of the fully gravitating EYM solutions.…
We present a simple proof of the WDVV equations for the prepotential of four-dimensional N=2 supersymmetric Yang-Mills theory with all ADE gauge groups. According to our proof it is clearly seen that the WDVV equations in four dimensions…
The critical behavior of the three-dimensional $N$-vector chiral model is studied for arbitrary $N$. The known six-loop renormalization-group (RG) expansions are resummed using the Borel transformation combined with the conformal mapping…
The Weyl$-$Yang gravitational gauge theory is investigated in the structure of a pure higher-dimensional non-Abelian Kaluza$-$Klein background. We construct the dimensionally reduced field equations and stress-energy-momentum tensors as…
We study the continuous phase transition and thermodynamic observables in the three-dimensional Euclidean $SU(2)$ principal chiral field model with the triad tensor renormalization group (tTRG) and the anisotropic tensor renormalization…
In recent work, we demonstrated that the confined-phase spectrum of non-supersymmetric pure Yang-Mills theory coincides with the spectrum of the chiral sector of a two-dimensional conformal field theory in the large-$N$ limit. This was done…
We describe a deformation of the principal chiral model (with an even-dimensional target space G) by a B-field proportional to the K\"ahler form on the target space. The equations of motion of the deformed model admit a zero-curvature…
A large class of integrable deformations of the Principal Chiral Model, known as the Yang-Baxter deformations, are governed by skew-symmetric R-matrices solving the (modified) classical Yang-Baxter equation. We carry out a systematic…
Generalized complex geometry is a new mathematical framework that is useful for describing the target space of N=(2,2) nonlinear sigma-models. The most direct relation is obtained at the N=(1,1) level when the sigma model is formulated with…
The large-group behavior of the nonlocal YM$_2$'s and gYM$_2$'s on a cylinder or a disk is investigated. It is shown that this behavior is similar to that of the corresponding local theory, but with the area of the cylinder replaced by an…
In previous work (Singh, 2011), we constructed an action in six dimensions using Yang-Mills fields and an auxiliary Abelian field. Here we first write down all the equations of motion and the constraints which arise from such an action.…
A Yang-Mills theory linear in the scalar curvature for 2d gravity with symmetry generated by the semidirect product formed with the Lie derivative of the algebra of diffeomorphisms with the two-dimensional Abelian algebra is formulated. As…
The quantum Yang-Mills theory describing dual ($\tilde g$) and non-dual ($g$) charges and revealing the generalized duality symmetry was developed by analogy with the Zwanziger formalism in QED.
Using spinorial geometry techniques, we classify the supersymmetric solutions of euclidean ${\cal N}=4$ super Yang-Mills theory. These backgrounds represent generalizations of instantons with nontrivial scalar fields turned on, and satisfy…