Self-dual Gauge Fields Research Articles

General Lagrangian of non-covariant self-dual gauge field

We present the general formulation of non-covariant Lagrangian of self-dual gauge theory. After specifying the parameters therein the previous Lagrangian in the decomposition of spacetime into $6=D_1+D_2$ and $6=D_1+D_2+D_3$ can be obtained. The self-dual property of the general Lagrangian is proved in detail. We furthermore show that the new non-covariant actions give field equations with 6d Lorentz invariance. The method can be straightforward extended to any dimension and we also give a short discussion about the 10D self-dual gauge theory.

Geometric Quantization and the Metric Dependence of the Self-Dual Field Theory

We investigate the metric dependence of the partition function of the self-dual p-form gauge field on an arbitrary Riemannian manifold. Using geometric quantization of the space of middle-dimensional forms, we derive a projectively flat connection on its space of polarizations. This connection governs metric dependence of the partition function of the self-dual field. We show that the dependence is essentially given by the Cheeger half-torsion of the underlying manifold. We compute the local gravitational anomaly and show how our derivation relates to the classical computation based on index theory. As an application, we show that the one-loop determinant of the (2,0) multiplet on a Calabi-Yau threefold coincides with the square root of the one-loop determinant of the B-model.

The Quantum of Action and Finiteness of Radiative Corrections: Deconfining SU(2) Yang-Mills Thermodynamics

The quantum of action $\hbar$, multiplying in certain powers perturbative vertices in 4D gauge theory, is related to the action of just-not-resolved selfdual and thermal gauge field configurations, calorons and anticalorons, of charge modulus unity. Appealing to the derivation of the effective theory for the deconfining phase of SU(2) Yang-Mills thermodynamics, we conclude that these vertex inducers convey a rapidly decreasing interaction strength between {\sl fundamental} plane waves when the momentum transfer is increased away from the scale of maximal, {\sl effective} resolution. This adds a deeper justification to the renormalization programme of perturbation theory which ignores the contribution to the partition function of nontrivially selfdual configurations. We also point out a connection between the QED fine-structure constant $\alpha$ and the electric-magnetically dual of the effective gauge coupling in the deconfining phase, and we illustrate the workings of effective loops in the expansion of the pressure.

Lagrangian of self-dual gauge fields in various formulations

The Lagrangians of self-dual gauge theory in various formulations are reviewed. From these results we see a simple rule and use it to present some new non-covariant Lagrangian based on the decomposition of spacetime into D=D1+D2+D3. Our prescription could be easily extended to more complex decomposition of spacetime and some more examples are presented therefore. The self-dual property of the new Lagrangian is proved in detail. We also show that the new non-covariant actions give field equations with 6d Lorentz invariance.

A non-abelian self-dual gauge theory in 5 + 1 dimensions

We construct a non-Abelian gauge theory of chiral 2-forms (self-dual gauge fields) in 6 dimensions with a spatial direction compactified on a circle of radius R. It has the following two properties. (1) It reduces to the Yang-Mills theory in 5 dimensions for small R. (2) It is equivalent to the Lorentz-invariant theory of Abelian chiral 2-forms when the gauge group is Abelian. Previous no-go theorems prohibiting non-Abelian deformations of the chiral 2-form gauge theory are circumvented by introducing nonlocality along the compactified dimension.

BLG and M5

We discuss the interpretation of the three-dimensional N = 8 superconformal Chern-Simons-matter theory with the gauge group of volume preserving diffeomorphisms as a model describing a six-dimensional self-dual gauge field coupled to scalars and spinors and its possible relation to the M5-brane

Some chirality-related properties of the 4D massive Dirac propagator and determinant in an arbitrary gauge field

For a 4-D massive Dirac field in the background of arbitrary gauge fields, we show that the Dirac propagator and functional determinant are completely determined by knowledge of the corresponding quantities for just one of the chirality sectors of the second-order Dirac operator. This generalizes the related, previously known, statements in (anti-)self-dual background gauge fields. The logarithms of the (renormalized) functional determinants from the two chirality sectors are shown to be different only by a term reflecting the integrated chiral anomaly.

SQM with non-abelian self-dual fields: harmonic superspace description

We present a Lagrangian formulation for N=4 supersymmetric quantum-mechanical systems describing the motion in external non-Abelian self-dual gauge fields. For any such system, one can write a component supersymmetric Lagrangian by introducing extra bosonic variables with topological Chern-Simons type interaction. For a special class of such system when the fields are expressed in the `t Hooft ansatz form, it is possible to give a superfield description using harmonic superspace formalism. As a new explicit example, the N=4 mechanics with Yang monopole is constructed.

Holographic melting of heavy baryons in plasma with gluon condensation

We propose a Dirac-Born-Infeld (DBI) D5 vertex brane plus Nc fundamental strings configuration to describe a baryon probe in strongly coupled gauge theory with gluon condensation at finite temperature via AdS/CFT correspondence. We investigate properties of this configuration in a dilaton deformed AdS5 × S5 background, in which IIB string theory is dual to super Yang-Mills theory in a state with a constant self-dual gauge field (Fmn = F*mn) background. We find that for most values of temperature T and gluon condensation parameter q (q = π2⟨FmnFmn⟩), there always exists a screening length Ls. The relation Ls ∼ 1/T has been checked. We give the q dependence of Ls. We calculate the boost velocity v(v = −tanh η) and angular velocity ω dependence of Ls for a baryon probe, and obtain Ls = L0*(1−v2)1/4 for large v and Ls ∼ ω−1, which are consistent with those dependence relations in the point brane plus strings case, and find that the usual relations have been modified by q. We also calculate the mass of baryon and find T dependence of baryon mass.

M5 from M2

Recently an action based on Lie 3-algebras was proposed to describe M2-branes. We study the case of infinite dimensional Lie 3-algebras based on the Nambu-Poisson structure of three dimensional manifolds. We show that the model contains self-dual 2-form gauge fields in 6 dimensions, and the result may be interpreted as the M5-brane world-volume action.

On a construction of self-dual gauge fields in seven dimensions

We consider gauge fields associated with a semisimple Malcev algebra. We construct a gauge-invariant Lagrangian and found a solution of modified Yang-Mills equations in seven dimensions.

On a construction of self-dual gauge fields in seven dimensions

We consider gauge fields associated with a semisimple Malcev algebra. We construct a gauge-invariant Lagrangian and found a solution of modified Yang-Mills equations in seven dimensions.

Self-dual fields harbored by a Kerr–Taub-bolt instanton

We present a new exact solution for self-dual Abelian gauge fields living on the space of the Kerr–Taub-bolt instanton, which is a generalized example of asymptotically flat instantons with non-self-dual curvature, by constructing the corresponding square integrable harmonic form on this space.

BLOW-UP ANALYSIS FOR LIOUVILLE TYPE EQUATION IN SELF-DUAL GAUGE FIELD THEORIES

We study the asymptotic behavior of the solution sequence of Liouville type equations observed in various self-dual gauge field theories. First, we show that such a sequence converges to a measure with a singular part that consists of Dirac measures if it is not compact in W1,2. Then, under an additional condition, the singular limit is specified by the method of symmetrization of the Green function.

D3-Brane from D-Instantons in the Hybrid Formalism of Superstring

A Dp-brane can be regarded as a configuration of infinitely many D(p-2k)-branes in bosonic string. We will show this property of D-branes in the superstring case using the hybrid formalism. It is convenient to study the boundary state for such D-branes to study such property between D-branes. We show that the boundary state for a D3-brane in a constant self-dual gauge field background can be expressed in terms of the boundary state for D-instantons in the hybrid formalism.

Comparison of | Q|=1 and | Q|=2 gauge-field configurations on the lattice four-torus

It is known that exactly self-dual gauge-field configurations with topological charge | Q|=1 cannot exist on the untwisted continuum four-torus. We explore the manifestation of this remarkable fact on the lattice four-torus for SU(3) using advanced techniques for controlling lattice discretization errors, extending earlier work of De Forcrand et al. for SU(2). We identify three distinct signals for the instability of | Q|=1 configurations, and show that these signals manifest themselves early in the cooling process, long before the would-be instanton has shrunk to a size comparable to the lattice discretization threshold. These signals do not appear for the individual instantons which make up our | Q|=2 configurations. This indicates that these signals reflect the truly global nature of the instability, rather than the local discretization effects which cause the eventual disappearance of the would-be single instanton. Monte-Carlo generated SU(3) gauge-field configurations are cooled to the self-dual limit using an O(a 4) -improved gauge action chosen to have small but positive O(a 6) errors. This choice prevents lattice discretization errors from destroying instantons provided their size exceeds the dislocation threshold of the cooling algorithm. Lattice discretization errors are evaluated by comparing the O(a 4) -improved gauge-field action with an O(a 4) -improved action constructed from the square of an O(a 4) -improved lattice field-strength tensor, thus having different O(a 6) discretization errors. The number of action-density peaks, the instanton size, and the topological charge of configurations is monitored. We observe a fluctuation in the total topological charge of | Q|=1 configurations, and demonstrate that the onset of this unusual behavior corresponds with the disappearance of multiple-peaks in the action density. At the same time discretization errors are minimal.

The Liouville Equation with Singular Data: A Concentration-Compactness Principle via a Local Representation Formula

For a bounded domain Ω⊂R2, we establish a concentration-compactness result for the following class of “singular” Liouville equations:−Δu=eu−4π∑j=1mαjδpj in Ω where pj∈Ω, αj>0 and δpj denotes the Dirac measure with pole at point pj, j=1,…,m. Our result extends Brezis–Merle's theorem (Comm. Partial Differential Equations16 (1991) 1223–1253) concerning solution sequences for the “regular” Liouville equation, where the Dirac measures are replaced by Lp(Ω)-data p>1. In some particular case, we also derive a mass-quantization principle in the same spirit of Li–Shafrir (Indiana Univ. Math. J.43 (1994) 1255–1270). Our analysis was motivated by the study of the Bogomol'nyi equations arising in several self-dual gauge field theories of interest in theoretical physics, such as the Chern–Simons theory (“Self-dual Chern–Simons Theories” Lecture Notes in Physics, Vol. 36, Springer-Verlag, Berlin, 1995) and the Electroweak theory (“Selected Papers on Gauge Theory of Weak and Electromagnetic Interactions,” World Scientific, Singapore).

Fake R4s, Einstein spaces and Seiberg-Wittenmonopole equations

We discuss the possible relevance of some recentmathematical results and techniques on 4-manifolds tophysics. We first suggest that the existence ofuncountably many R4s with non-equivalent smoothstructures, a mathematical phenomenon unique to fourdimensions, may be responsible for the observedfour-dimensionality of spacetime. We then point out theremarkable fact that self-dual gauge fields and Weylspinors can live on a manifold of Euclidean signaturewithout affecting the metric. As a specific example, weconsider solutions of the Seiberg-Witten monopoleequations in which the U(1) fields are covariantlyconstant, the monopole Weyl spinor has only a singleconstant component, and the 4-manifold ℳ4 isa product of two Riemann surfacesΣp1 and Σp2. There are p1-1(p2-1)magnetic (electric) vortices onΣp1 (Σp2), withp1 + p2⩾2(p1 = p2 = 1 being excluded). When the two genera are equal, theelectromagnetic fields are self-dual and one obtains the Einstein spaceΣp×Σp, the monopole condensate serving as thecosmological constant.

D3-brane-D-instanton configuration and [formula omitted] = 4 super YM theory in constant self-dual background

We consider SO(4) × SO(6) invariant type IIB string solution describing D3-branes superposed with D-instantons homogeneously distributed over D3-brane world-volume. In the near D3-brane horizon limit this background interpolates between AdS 5 × S 5 space in UV and flat space (with non-constant dilaton and RR scalar) in IR. Generalizing the AdS/CFT conjecture we suggest that type IIB string in this geometry is dual to N = 4 SYM theory in a state with a constant self-dual gauge field background. The semiclassical string representation for the Wilson factor implies confinement with effective string tension depending on constant D-instanton density parameter. This provides a simple example of type IIB string — gauge theory duality with clear D-brane and gauge theory interpretation.

On Nahm's transformation with twisted boundary conditions

Following two different tracks, we arrive at a definition of Nahm's transformation valid for self-dual fields on the four-dimensional torus T 4 with non-zero twist tensor. The transform is again a self-dual gauge field defined on a new torus T ^ 4 and with non-zero twist tensor. It preserves the property of being an involution.