Topological mass generation four-dimensional gauge theory

The Lagrangian of non-Abelian tensor gauge fields describes the interaction of the Yang–Mills and massless tensor bosons of increasing helicities. We have found a metric-independent gauge invariant density which is a four-dimensional analog of the Chern–Simons density. The Lagrangian augmented by this Chern–Simons-like invariant describes massive Yang–Mills boson, providing a gauge-invariant mass gap for a four-dimensional gauge field theory. We present invariant densities which can provide masses to the high-rank tensor bosons.     

Lie Algebroid Yang–Mills with matter fields

Lie Algebroid Yang–Mills theories are a generalization of Yang–Mills gauge theories, replacing the structural Lie algebra by a Lie Algebroid E$E$. In this note we relax the conditions on the fiber metric of E$E$ for gauge invariance of the action functional. Coupling to scalar fields requires possibly nonlinear representations of Lie Algebroids. In all cases, gauge invariance is seen to lead to a condition of covariant constancy on the respective fiber metric in question with respect to an appropriate Lie Algebroid connection.     

Exotic Yang–Mills Dilaton Gauge Theories

An exotic class of nonlinear p-form non-Abelian gauge theories is studied, arising from the most general allowed covariant deformation of linear Abelian gauge theory for a set of massless 1-form fields and 2-form fields in four dimensions. These theories combine a Chapline–Manton type coupling of the 1-forms and 2-forms, along with a Yang–Mills coupling of the 1-forms, a Freedman–Townsend coupling of the 2-forms, and an extended Freedman–Townsend type coupling between the 1-forms and 2-forms. It is shown that the resulting theories have a geometrically interesting dual formulation that is equivalent to an exotic Yang–Mills dilaton theory involving a nonlinear sigma field. In particular, the nonlinear sigma field couples to the Yang–Mills 1-form field through a generalized Chern class 4-form term.     

On the reanimation of a local BRST invariance in the (Refined) Gribov–Zwanziger formalism

We localize a previously established nonlocal BRST invariance of the Gribov–Zwanziger (GZ) action by the introduction of additional fields. We obtain a modified GZ action with a corresponding local, albeit not nilpotent, BRST invariance. We show that correlation functions of the original elementary GZ fields do not change upon evaluation with the modified partition function. We discuss that for vanishing Gribov mass, we are brought back to the original Yang–Mills theory with standard BRST invariance.     

Study of the all orders multiplicative renormalizability of a local confining quark action in the Landau gauge

The inverse of the Faddeev–Popov operator plays a pivotal role within the Gribov–Zwanziger approach to the quantization of Euclidean Yang–Mills theories in Landau gauge. Following a recent proposal (Capri et al., 2014), we show that the inverse of the Faddeev–Popov operator can be consistently coupled to quark fields. Such a coupling gives rise to a local action while reproducing the behaviour of the quark propagator observed in lattice numerical simulations in the non-perturbative infrared region. By using the algebraic renormalization framework, we prove that the aforementioned local action is multiplicatively renormalizable to all orders.     

Study of the zero modes of the Faddeev–Popov operator in the maximal Abelian gauge

A study of the zero modes of the Faddeev–Popov operator in the maximal Abelian gauge is presented in the case of the gauge group SU(2)$SU\left(2\right)$ and for different Euclidean space–time dimensions. Explicit examples of classes of normalizable zero modes and corresponding gauge field configurations are constructed by taking into account two boundary conditions, namely: (i) the finite Euclidean Yang–Mills action, (ii) the finite Hilbert norm.     

CSW rules for a massive scalar

We derive the analog of the Cachazo–Svr?ek–Witten (CSW) diagrammatic Feynman rules for four-dimensional Yang–Mills gauge theory coupled to a massive colored scalar. The mass term is shown to give rise to a new tower of vertices in addition to the CSW vertices for massless scalars in non-supersymmetric theories. The rules are derived directly from an action, once through a canonical transformation within light-cone Yang–Mills and once by the construction of a twistor action. The rules are tested against known results in several examples and are used to simplify the proof of on-shell recursion relations for amplitudes with massive scalars.     

New Representation of the Self-Duality and Exact Solutions for Yang–Mills Equations

In this paper, we found a new representation for self-duality . In addition, exact solution class of the classical SU(2) Yang–Mills field in four-dimensional Euclidean space and two exact solution classes for SU(2) Yang–Mills when ρ is a complex analytic function are also obtained. PACS numbers: 11.15.-q Gauge field theories, 11.15.Kc Semiclassical theories in gauge fields, 12.10.-g, 12.15.-y Yang–Mills fields     

Twisted invariances of noncommutative gauge theories

We study noncommutative deformations of Yang–Mills theories and show that these theories admit a infinite, continuous family of twisted star-gauge invariances. This family interpolates continuously between star-gauge and twisted gauge transformations. The possible physical rôle of these start-twisted invariances is discussed.     

Quantum criticality and Yang–Mills gauge theory

We present a family of nonrelativistic Yang–Mills gauge theories in D+1$D+1$ dimensions whose free-field limit exhibits quantum critical behavior with gapless excitations and dynamical critical exponent z=2$z=2$. The ground state wavefunction is intimately related to the partition function of relativistic Yang–Mills in D   dimensions. The gauge couplings exhibit logarithmic scaling and asymptotic freedom in the upper critical spacetime dimension, equal to 4+1$4+1$. The theories can be deformed in the infrared by a relevant operator that restores Poincaré invariance as an accidental symmetry. In the large-N limit, our nonrelativistic gauge theories can be expected to have weakly curved gravity duals.     

Do we need Feynman diagrams for higher order perturbation theory?

We compute the two loop and three loop corrections to the beta function for Yang–Mills theories in the background gauge field method and using the background gauge field as the only source. The calculations are based on the separation of the one loop effective potential into zero and positive modes contributions and are entirely analytical. No two or three loop Feynman diagrams are considered in the process.     

Study of Yang–Mills–Chern–Simons theory in presence of the Gribov horizon

The two-point gauge correlation function in Yang–Mills–Chern–Simons theory in three dimensional Euclidean space is analysed by taking into account the non-perturbative effects of the Gribov horizon. In this way, we are able to describe the confinement and de-confinement regimes, which naturally depend on the topological mass and on the gauge coupling constant of the theory.     

Renormalization of Hamiltonian QCD

We study to one-loop order the renormalization of QCD in the Coulomb gauge using the Hamiltonian formalism. Divergences occur which might require counter-terms outside the Hamiltonian formalism, but they can be cancelled by a redefinition of the Yang–Mills electric field.     

Quantum field theory as effective BV theory from Chern–Simons

The general procedure for obtaining explicit expressions for all cohomologies of Berkovits' operator is suggested. It is demonstrated that calculation of BV integral for the classical Chern–Simons-like theory (Witten's OSFT-like theory) reproduces BV version of two-dimensional gauge model at the level of effective action. This model contains gauge field, scalars, fermions and some other fields. We prove that this model is an example of “singular” point from the perspective of the suggested method for cohomology evaluation. For arbitrary “regular” point the same technique results in AKSZ (Alexandrov, Kontsevich, Schwarz, Zaboronsky) version of Chern–Simons theory (BF theory) in accord with [N. Berkovits, Covariant quantization of the superparticle using pure spinors, JHEP 0109 (2001) 016, hep-th/0105050; N. Berkovits, ICTP lectures on covariant quantization of the superstring, hep-th/0209059; M. Movshev, A. Schwarz, On maximally supersymmetric Yang–Mills theories, Nucl. Phys. B 681 (2004) 324, hep-th/0311132; M. Movshev, A. Schwarz, Algebraic structure of Yang–Mills theory, hep-th/0404183].     

Affine Defects and Gravitation

We argue that the structure general relativity (GR) as a theory of affine defects is deeper than the standard interpretation as a metric theory of gravitation. Einstein–Cartan theory (EC), with its inhomogeneous affine symmetry, should be the standard-bearer for GR-like theories. A discrete affine interpretation of EC (and gauge theory) yields topological definitions of momentum and spin (and Yang–Mills current), and their conservation laws become discrete topological identities. Considerations from quantum theory provide evidence that discrete affine defects are the physical foundation for gravitation.