Four-dimensional Yang-Mills Research Articles

Dimensional reduction gauge and effective dimensional reduction in four-dimensional Yang-Mills theory

Motivated by one-dimensional color-electric flux-tube formation in four-dimensional (4D) QCD, we investigate a possibility of effective dimensional reduction in the 4D Yang-Mills (YM) theory. We propose a new gauge fixing of “dimensional reduction (DR) gauge” defined so as to minimize RDR≡∫d4sTr[Ax2(s)+Ay2(s)], which has a residual gauge symmetry for the gauge function Ω(t,z) like 2D QCD on the t−z plane. We investigate effective dimensional reduction in the DR gauge using SU(3) quenched lattice QCD at β=6.0. The amplitude of Ax(s) and Ay(s) are found to be strongly suppressed in the DR gauge. We consider “tz-projection” of Ax,y(s)→0 for the gauge configuration generated in the DR gauge, in a similar sense to Abelian projection in the maximally Abelian gauge. By the tz-projection in the DR gauge, the interquark potential is not changed, and At(s) and Az(s) play a dominant role in quark confinement. In the DR gauge, we calculate a spatial correlation ⟨TrA⊥(s)A⊥(s+ra⊥)⟩(⊥=x,y) and estimate the spatial mass of A⊥(s)(⊥=x,y) as M≃1.7 GeV. It is conjectured that this large mass makes A⊥(s) inactive and realizes the dominance of At(s) and Az(s) in infrared region in the DR gauge. We also calculate the spatial correlation of two temporal link-variables and find that the correlation decreases as exp(−mr) with m≃0.6 GeV. Using a crude approximation, the 4D YM theory is reduced into an ensemble of 2D YM systems with the coupling of g2D=gm. Published by the American Physical Society 2024

Homological aspects of topological gauge-gravity equivalence

In the works of Achúcarro and Townsend and also by Witten, a duality between three-dimensional Chern–Simons gauge theories and gravity was established. In all cases, the results made use of the field equations. In a previous work, we were capable of generalizing Witten’s work to the off-shell cases, as well as to the four-dimensional Yang–Mills theory with de Sitter gauge symmetry. The price we paid is that curvature and torsion must obey some constraints under the action of the interior derivative. These constraints implied on the partial breaking of diffeomorphism invariance. In this work, we first formalize our early results in terms of fiber bundle theory by establishing the formal aspects of the map between a principal bundle (gauge theory) and a coframe bundle (gravity) with partial breaking of diffeomorphism invariance. Then, we study the effect of the constraints on the homology defined by the interior derivative. The main result is the emergence of a non-trivial homology in Riemann–Cartan manifolds.

The four-dimensional Yang–Mills partition function in the vicinity of the vacuum

The partition function of four-dimensional Euclidean, non-supersymmetric textrm{SU}(2) Yang–Mills theory is calculated in the perturbative and weak coupling regime, i.e., in a small open ball about the flat connection and when the gauge coupling constant acquires a small but finite value. The computation is based on various known inequalities, valid only in four dimensions, providing two-sided estimates for the exponentiated Yang–Mills action in terms of the L^2-norm of the derivative of the gauge potential only; these estimates then give rise to Gaußian-like infinite- dimensional formal integrals involving the Laplacian and hence can be computed via zeta-function and heat kernel techniques. It then turns out that these formal integrals give a sharp value for the partition function in the aforementioned perturbative and weak coupling regime of the theory. In the resulting expression for the partition function, the original classical value of the coupling constant is shifted to a smaller one which can be interpreted as the manifestation, in this approach, of a non-trivial beta -function and asymptotic freedom in pure non-Abelian gauge theories.

Aspects of supergroup gauge theory

In this paper, provide a survey of recent studies of supergroup gauge theory. We first discuss the supermatrix model as a zero-dimensional toy model of supergroup gauge theory and its geometric and algebraic characterization. We then focus on four-dimensional Yang–Mills theory with supergroup gauge symmetry and explore its nonperturbative properties, including instanton calculus, Seiberg–Witten geometry, Bethe/gauge correspondence, and its realization with intersecting defects.

Explicit Cutoff Regularization in Coordinate Representation

In this paper, we study a special type of cutoff regularization in the coordinate representation. We show how this approach unites such concepts and properties as an explicit cut, a spectral representation, a homogenization, and a covariance. Besides that, we present new formulae to work with the regularization and give additional calculations of the infrared asymptotics for some regularized Green’s functions appearing in the pure four-dimensional Yang–Mills theory and in the standard two-dimensional Sigma-model.

Scale setting for large-N SUSY Yang-Mills on the lattice

In this paper we study the large N limit of four-dimensional Supersymmetric Yang-Mills on the lattice using twisted reduced models. We have generated configurations with dynamical massive gluinos and various lattice ’t Hooft couplings, and verified that the Pfaffian remains positive. We have determined the lattice spacing in terms of various observables obtaining compatible results. Extrapolating to the massless gluino limit we obtain the lattice spacing dependence on the bare couplings for the supersymmetric theory. The observed dependence goes along the expected behaviour predicted by perturbation theory.

The AdS𝜃2/CFT1 correspondence and noncommutative geometry II: Noncommutative quantum black holes

In this paper, we present the construction of noncommutative [Formula: see text] black hole and its four-dimensional Yang–Mills IKKT-type matrix model which includes two competing Myers term one responsible for the condensation of pure [Formula: see text] and the other one responsible for the condensation of the dilaton field. It is argued that the phase diagram of this matrix model features three phases: (1) a gravitational phase ([Formula: see text] black hole), (2) a geometric phase ([Formula: see text] background) and (3) a Yang–Mills phase. The Hawking process is therefore seen as an exotic line of discontinuous transitions between the gravitational and geometrical phases. Alternatively, a noncommutative nonlinear sigma model describing the transition of the dilaton field between the gravitational and geometrical phases is also constructed.

Exploiting the scheme dependence of the renormalization group improvement in infrared Yang–Mills theory

Within the refined Gribov–Zwanziger scenario for four-dimensional Yang–Mills theory in the Landau gauge, a gluon mass term is generated from the restriction of the gauge field configurations to the first Gribov region. Tissier and Wschebor have pointed out that adding a gluon mass term to the usual Faddeev–Popov action yields one-loop renormalization group improved gluon and ghost propagators which are in reasonable agreement with the lattice data even in the infrared regime. In this work, we extend their analysis to several alternative renormalization schemes and show how the renormalization scheme dependence can be used to achieve an almost perfect matching to the lattice data for the gluon and ghost propagators.

Holographic spacetime from lattice Yang-Mills theory

Entanglement entropy is a notoriously difficult quantity to compute in strongly interacting gauge theories. Existing lattice replica methods have suffered from a severe signal-to-noise ratio problem, making high-precision studies prohibitively expensive. Our improved lattice method mitigates this situation and allows us to probe holographic predictions for the behavior of entanglement entropies in three- and four-dimensional Yang-Mills theories. We use this data for the numerical reconstruction of holographic bulk metrics.

Radiation damping of a Yang–Mills particle revisited

The problem of a colour-charged point particle interacting with a four-dimensional Yang–Mills gauge theory is revisited. The radiation damping is obtained inspired in Dirac’s computation. The difficulties in the non-abelian case were solved by using an ansatz for the Liénard–Wiechert potentials already used in the literature (Ö. Sarıoğlu. Phys. Rev. D, 66, 085005 (2002). doi: 10.1103/PhysRevD.66.085005 ) for finding solutions to the Yang–Mills equations. Three non-trivial examples of radiation damping for a non-abelian particle are discussed in detail.

Lorentz symmetry breaking in a Yang–Mills theory within the Gribov restriction

In this paper we take into account the existence of Gribov copies in a four-dimensional Yang–Mills theory in the Landau gauge with an effective Lorentz symmetry breaking, induced by the Carroll–Field–Jackiw (CFJ) term. The self consistent gap equation of the Gribov parameter is properly derived and, provided observational bounds to the amplitude of the CFJ parameter in the gauge theory, a qualitative analysis of the Gribov parameter and of the poles of the propagator is developed.

Multiplicative Renormalizability of Yang-Mills Theory with the Background Field Method in the BV Formalism

Studying the gauge-invariant renormalizability of four-dimensional Yang-Mills theory using the background field method and the BV formalism, we derive a classical master equation homogeneous with respect to the antibracket by introducing antifield partners to the background fields and parameters. The constructed model can be renormalized by the standard method of introducing counterterms. This model does not have (exact) multiplicative renormalizability but it does have this property in the physical sector (quasimultiplicative renormalizability).

BRST-invariant RG flows

A mass parameter for the gauge bosons in gauge-fixed four-dimensional Yang-Mills theory can be accommodated in a local and manifestly BRST-invariant action. The construction is based on the Faddeev-Popov method involving a nonlinear gauge-fixing and a background Nakanishi-Lautrup field. When applied to momentum-dependent masslike deformations, this formalism leads to a full regularization of the theory which explicitly preserves BRST symmetry. We deduce a functional renormalization group equation for the one-particle-irreducible effective action, which has a one-loop form. The master equation is compatible with it, i.e. BRST symmetry is preserved along the flow, and it has a standard regulator-independent Zinn-Justin form. As a first application, we compute the leading-order gluon wave-function renormalization.

Long-time existence for Yang–Mills flow

We establish that finite-time singularities do not occur in four-dimensional Yang–Mills flow, confirming the conjecture of Schlatter et al. (Am J Math 120:117–128, 1998). The proof relies on a weighted energy identity and sharp decay estimates in the neck region.

Holographic glueballs from the circle reduction of Romans supergravity

We reconsider a one-parameter class of known solutions of the circle compactification of Romans six-dimensional half-maximal supergravity. The gauge-theory duals of these solutions are confining four-dimensional field theories. Their UV completions consist of the compactification on a circle of a higher-dimensional field theory that is flowing between two fixed points in five dimensions. We systematically study the bosonic fluctuations of the supergravity theory, corresponding to the bosonic glueballs of the dual field theory.We perform numerically the calculation of the spectrum of excitations of all the bosonic fields, several of which had been disregarded in earlier work on the subject. We discuss the results as a function of the one parameter characterising the class of background solutions, hence further extending known results. We show how certain towers of states are independent of the background, and compare these states to existing lattice literature on four-dimensional Yang-Mills (pure) gauge theories, confirming the existence of close similarities.For the aforementioned analysis, we construct gauge-invariant combinations of the fields appearing in the reduction to five dimensions of the supergravity theory, and hence focus on the 32 physical bosonic degrees of freedom. We show explicitly how to implement gauge-fixing of the supergravity theory. The results of such technical work could be used to analyse the spectra of other theories proposed in the context of top-down holography. For example, it could be applied to holographic realisations of composite-Higgs and light-dilaton scenarios.

Relating \u2019t Hooft anomalies of 4d pure Yang-Mills and 2d \u2102\u2119N\u2212\u20091 model

It has recently been shown that a center-twisted compactification of the four-dimensional pure SU(N) Yang-Mills theory on a three-torus gives rise to the twodimensional ℂℙN− 1-model on a circle with a flavor-twisted boundary condition. We verify the consistency of this statement non-perturbatively at theta angle θ = π, in terms of the mixed ’t Hooft anomalies for flavor symmetries and the time-reversal symmetry. This provides further support for the approach to the confinement of four-dimensional Yang-Mills theory from the two-dimensional ℂℙN− 1-model.

Supersymmetric tools in Yang–Mills theories at strong coupling: The beginning of a long journey

Development of holomorphy-based methods in super-Yang–Mills theories started in the early 1980s and lead to a number of breakthrough results. I review some results in which I participated. The discovery of Seiberg’s duality and the Seiberg–Witten solution of [Formula: see text] Yang–Mills were the milestones in the long journey of which, I assume, much will be said in other talks. I will focus on the discovery (2003) of non-Abelian vortex strings with various degrees of supersymmetry, supported in some four-dimensional Yang–Mills theories and some intriguing implications of this discovery. One of the recent results is the observation of a soliton string in the bulk [Formula: see text] theory with the [Formula: see text] gauge group and four flavors, which can become critical in a certain limit. This is the case of a “reverse holography,” with a very transparent physical meaning.

Beta functions in Chirally deformed supersymmetric sigma models in two dimensions

We study two-dimensional sigma models where the chiral deformation diminished the original [Formula: see text] supersymmetry to the chiral one, [Formula: see text]. Such heterotic models were discovered previously on the world sheet of non-Abelian stringy solitons supported by certain four-dimensional [Formula: see text] theories. We study geometric aspects and holomorphic properties of these models, and derive a number of exact expressions for the [Formula: see text] functions in terms of the anomalous dimensions analogous to the NSVZ [Formula: see text] function in four-dimensional Yang-Mills. Instanton calculus provides a straightforward method for the derivation.

Studying critical string emerging from non-Abelian vortex in four dimensions

Recently a special vortex string was found [5] in a class of soliton vortices supported in four-dimensional Yang-Mills theories that under certain conditions can become infinitely thin and can be interpreted as a critical ten-dimensional string. The appropriate bulk Yang-Mills theory has the U(2) gauge group and the Fayet-Iliopoulos term. It supports semilocal non-Abelian vortices with the world-sheet theory for orientational and size moduli described by the weighted CP(2,2) model. The full target space is R_4\times Y_6 where Y_6 is a non-compact Calabi-Yau space. We study the above vortex string from the standpoint of string theory, focusing on the massless states in four dimensions. In the generic case all massless modes are non-normalizable, hence, no massless gravitons or vector fields are predicted in the physical spectrum. However, at the selfdual point (at strong coupling) weighted CP(2,2) admits deformation of the complex structure, resulting in a single massless hypermultiplet in the bulk. We interpret it as a composite "baryon."

N=(0,2)deformation of (2, 2) sigma models: Geometric structure, holomorphic anomaly, and exactβfunctions

We study N=(0,2) deformed (2,2) two-dimensional sigma models. Such heterotic models were discovered previously on the world sheet of non-Abelian strings supported by certain four-dimensional N=1 theories. We study geometric aspects and holomorphic properties of these models, and derive a number of exact expressions for the beta functions in terms of the anomalous dimensions analogous to the NSVZ beta function in four-dimensional Yang-Mills. Instanton calculus provides a straightforward method for the derivation. The anomalous dimensions are calculated up to two loops implying that one of the beta functions is explicitly known up to three loops. The fixed point in the ratio of the couplings found previously at one loop is not shifted at two loops. We also consider the N=(0,2) supercurrent supermultiplet (the so-called hypercurrent) and its anomalies, as well as the "Konishi anomaly." This gives us another method for finding exact $\beta$ functions. We prove that despite the chiral nature of the models under consideration quantum loops preserve isometries of the target space.