non-Abelian Field Strength Research Articles

Gauge Invariance of Non-Abelian Field Strength Correlators: The Axial Gauge Puzzle.

Many transport coefficients of the quark-gluon plasma and nuclear structure functions can be written as gauge invariant correlation functions of non-Abelian field strengths dressed with Wilson lines. We discuss the applicability of axial gauge n·A=0 to calculate them. In particular, we address issues that appear when one attempts to trivialize the Wilson lines in the correlation functions by gauge fixing. We find it is always impossible to completely remove the gauge fields n·A in Wilson lines that extend to infinity in the n direction by means of gauge transformations. We show how the obstruction appears in an explicit example of a perturbative calculation, and we also explain it more generally from the perspective of the path integral that defines the theory. Our results explain why the two correlators that define the heavy quark and quarkonium transport coefficients, which are seemingly equal in axial gauge, are actually different physical quantities of the quark-gluon plasma and have different values. Furthermore, our findings provide insights into the difference between two inequivalent gluon parton distribution functions.

Spinorial structure of O(3) and application to dark matter

An O(3) spinor, Φ, as a doublet denoted by 2D consists of an SO(3) spinor, ϕ, and its complex conjugate, ϕ⁎, which form Φ=(ϕ,ϕ⁎)T to be identified with a Majorana-type spinor of O(4). The four gamma matrices Γμ (μ=1∼4) are given by Γi=diag.(τi,τi⁎) (i=1,2,3) and Γ4=−τ2⊗τ2, where τi denote the Pauli matrices. The rotations and axis-reflections of O(3) are, respectively, generated by Σij and Σi4, where Σμν=[Γμ,Γν]/2i. While Φ is regarded as a scalar, a fermionic O(3) spinor is constructed out of an SO(3) doublet Dirac spinor and its charge conjugate. These O(3) spinors are restricted to be neutral and cannot carry the standard model quantum numbers because they contain particles and antiparticles. Our O(3) spinors serve as candidates of dark matter. The O(3) symmetry in particle physics is visible when the invariance of interactions is considered by explicitly including their complex conjugates. It is possible to introduce a dark gauge symmetry based on SO(3)×Z2 equivalent to O(3), where the Z2 parity is described by a U(1) charge giving 1 for a particle and −1 for an antiparticle. The SO(3) and U(1) gauge bosons turn out to transform as the axial vector of O(3) and the pseudoscalar of O(3), respectively. This property is related to the consistent definition of the nonabelian field strength tensor of O(3) or of the U(1) charge of the O(3)-transformed spinor. To see the feasibility of our dark matter models, we discuss scalar dark matter phenomenology based on the dark U(1) gauge model.

Gauge invariant method for maximum simplification of the field strength in non-Abelian Yang–Mills theories

A new local gauge invariant method is introduced in order to maximally simplify the expression for a SU(2) non-Abelian field strength. The new tetrads introduced in previous works are going to play a fundamental role in the algorithm presented in this paper. Three new local gauge invariant objects are going to guide us through the process of making a field strength block diagonal. The process is also covariant. Any nontrivial isospace field strength projection will become block diagonal through this gauge invariant algorithm. As an application we will find new local observables in Yang–Mills theories.

Yang-Mills and Beyond

In their 1954 paper, Yang and Mills invented the non-Abelian field strength to satisfy certain criteria but didn't explain how it could be derived. In the penultimate section we show how the Yang-Mills field strength derives from Yang's gauge transformation. The preceding sections place Yang-Mills theory in historical perspective and cover material relating to the field strength. The final section shows how Yang-Mills theory was combined with spontaneous symmetry breaking, the Goldstone theorem and subsequent work to contribute to the Standard Model of particle physics.

D1-strings in large RR 3-form flux, quantum Nambu geometry and M5-branes in the C-field

We consider D1-branes in an RR flux background and show that there is a low energy–large flux double-scaling limit where the D1-brane action is dominated by a Chern–Simons–Myers coupling term. As a classical solution to the matrix model, we find a novel quantized geometry characterized by a quantum Nambu 3-bracket. Infinite-dimensional representations of the quantum Nambu geometry are constructed, which demonstrate that the quantum Nambu geometry is intrinsically different from the ordinary Lie algebra-type noncommutative geometry. Matrix models for the II B string, II A string and M-theory in the corresponding backgrounds are constructed. A classical solution of a quantum Nambu geometry in the II A matrix string theory gives rise to an expansion of the fundamental strings into a system of multiple D4-branes and the fluctuation is found to describe an action for a non-Abelian 3-form field strength, which is a natural non-Abelian generalization of the PST action for a single D4-brane. In view of the recent proposals [1, 2] of the M5-branes theory in terms of the D4-branes, we suggest a natural way to include all the KK modes and propose an action for the multiple M5-branes in a constant C-field. The worldvolume of the M5-branes in a C-field is found to be described by a quantum Nambu geometry with self-dual parameters. It is intriguing that our action is naturally formulated in terms of a 1-form gauge field living on a six-dimensional quantum Nambu geometry.

Dynamical stabilization of runaway potentials and landscape of vacua at finite density

We study an SU ( 2 ) gauge theory with a classical complex modulus. Introducing a chemical potential for a conserved modulus hypercharge causes it to become unstable and start condensing. We show that the modulus condensation in turn generates homogeneous but anisotropic non-Abelian field strength condensates. The existence of a stable vacuum at the end point of the condensation process depends on a modulus representation under the gauge group. For a modulus in the fundamental representation, the global vacuum of the theory is a state both with the rotational symmetry and the electromagnetic U ( 1 ) em being spontaneously broken. In other words, the system describes an anisotropic superconducting medium. We further explore the landscape of vacua of this theory and identify metastable vacua with an abnormal number of Nambu–Goldstone bosons. The SO ( 2 ) symmetry of these vacua corresponds to locking gauge, flavor, and spin degrees of freedom. There are also metastable SO ( 3 ) rotationally invariant vacua. For a modulus in the adjoint representation, we show that the theory does not have stable vacua with homogeneous anisotropic non-Abelian field strength condensates, although there are metastable vacua. The reason of that is connected with a larger number of the physical components of the modulus in the case of the adjoint representation as compared to the fundamental one.

Dynamical stabilization of runaway potentials at finite density

We study four-dimensional non-Abelian gauge theories with classical moduli. Introducing a chemical potential for a flavor charge causes moduli to become unstable and start condensing. We show that the moduli condensation in the presence of a chemical potential generates non-Abelian field strength condensates. These condensates are homogeneous but non-isotropic. The end point of the condensation process is a stable homogeneous, but non-isotropic, vacuum in which both gauge and flavor symmetries and the rotational invariance are spontaneously broken. Possible applications of this phenomenon for the gauge theory/string theory correspondence and in cosmology are briefly discussed.

Superstrings with boundary fermions

The Green-Schwarz action for an open superstring with additional boundary fermions, representing Chan-Paton factors, is studied at the classical level. The boundary geometry is described by a bundle, with fermionic fibres, over the super worldvolume of a D-brane together with a map from the total space into the type II target superspace. This geometry is constrained by the requirement of kappa-symmetry on the boundary together with the use of the equations of motion for the fermions. There are two constraints which are formally similar to those that arise in the abelian case but which differ because of the dependence on the additional coordinates. The model, when quantised, would be a candidate for a fully kappa-symmetric theory of a stack of coincident D-branes including a non-abelian Born-Infeld sector. The example of the D9-brane in a flat background is studied. The constraints on the non-abelian field strength are shown to be in agreement with those derived from the pure spinor approach to the superstring. A covariant formalism is developed and the problem of quantisation is discussed.

Non-Abelian field strength bilocal correlator at finite temperature in the model of dilute instanton gas

Bilocal correlator in gluodynamics is evaluated at finite temperature in the framework of instanton gas model. It is demonstrated that vacuum correlation length decreases with a growing temperature. Obtained results are compared with lattice data for the bilocal correlator at finite temperature. Density of instantons and possible structures of nonperturbative vacuum are discussed.

Semiclassical approximation for non-Abelian field strength correlators in the instanton dilute gas model

Field strength correlators are semi-classically evaluated in the dilute gas model of non-Abelian sources (instantons) and compared with lattice data for QCD at zero temperature. We show that one of the Euclidean invariant, tensorial structures vanishes for configurations being purely selfdual or anti-selfdual. We compute the invariant functions contributing to the correlators within the two lowest orders in an instanton density expansion. Fitting instanton size and density for quenched and full QCD, we obtain a reasonable description.

Structure and dynamics of monopoles in axial-gauge QCD

An investigation of singular fields emerging in the process of transforming QCD to the axial gauge is presented. The structure of the singularities is analyzed. It is shown that apart from well known neutral magnetic monopole singularities, the field configurations also exhibit singularities in their charged and transverse components. This complex singularity structure guarantees finite non-Abelian field strength and thus finite action if expressed in terms of gauge fixed fields. A relation between the monopole charges of singular field configurations and their topological charge is derived. Qualitative dynamical aspects of the role of the monopoles are discussed. It is argued that the entropy associated with monopoles increases with decreasing temperature and that the coupling to quantum fluctuations favors monopole-antimonopole binding.

Mixed abelian and non-abelian BRS transformations and the occurence of Chern-Simon three-forms

We give a geometrical interpretation of Becchi-Rouet-Stora (BRS) equations which occur upon the quantization of the unified n = 1 supergravity and n = 1 super Yang-Mills theory in d = 10 dimensions. The relevant abelian and non-abelian coupled BRS transformations are derived in a straightforward fashion from the horizontality condition of a non-abelian field strength two-form and of an abelian Chern-Simon three-form, the exterior derivative of which is the usual abelian anomaly. Our result illustrates quite well a direct passage from the geometry to the full quantum lagrangian.