First-order equations for gauge fields in spaces of dimension greater than four

We consider the possibility of satisfying the gauge field equations in dimensions greater than four by imposing linear relations amongst the components of the field strength tensor, F_μν, generalising the idea of self-duality in four dimensions.     

Einstein–Maxwell gravity with additional corrections

Motivated by the E ₈×E ₈ heterotic string theory, we obtain topological black hole solutions of Einstein–Maxwell gravity with additional corrections. We consider the Gauss–Bonnet (GB) and (F _μν F ^μν )² terms as an effective quartic order Lagrangian of gauge–gravity coupling and investigate geometric and thermodynamic properties of the black hole solutions. We also analyze the effects of the GB term as well as the correction of Maxwell field on the properties of the solutions.     

Local field theory of the dual string

We develop a (classical) local field theory which contains as a special solution the (classical) dual string recently discussed by Goddard, Goldstone, Rebbi and Thorn. The basic field is a gauge field F_μν(x), and the Lagrangian is given by $\text{(}\text{?1}\text{2α'}\text{)√F}{}^2$. We treat the case of closed strings (corresponding to the Shapiro-Virasoro model) where F_μν can be expressed in terms of potentials A_μ. Quantization of F_μν is briefly discussed, but a more thorough discussion is postponed.     

On loop corrections to string theory effective actions

We make some comments concerning the structure of loop corrections to the effective action (EA) for massless fields of a string. The singular part of the α′→0 limit of the one-loop EA in the open (super)string theory is studied and is shown to be in correspondence with the ultraviolet divergent part of the one-loop effective action in the (super) Yang-Mills theory. In particular, we reproduce the known result about the absence of Λ^D−4 F_μν² one-loop infinities in D = 26 Yang-Mills theory starting from the open Bose string theory. We also discuss the path integral representation for EA (EA = generalized partition function for the σ-model) and use it to compute the open string theory EA on the disc and the annulus.     

A field configuration closer to the true QCD vacuum

An effective action for QCD at one-loop order, which is real, manifestly Lorentz and gauge invariant and which depends on an infinite family of gauge invariants (tr(F _μν F _μν), tr(F _μν F _μν F _?σ F _?σ),...), is obtained. Moreover, anAnsatz for a vacuum configuration is made, whose corresponding vacuum energy density is lower than the one for the SavvidyAnsatz. Both the cases of pure QCD and of QCD with massless fermions are considered.     

Vacuum of the quantum Yang-Mills theory and magnetostatics

It is argued that since in asymptotically free Yang-Mills theories the quantum ground state is not controlled by perturbation theory, there is no a priori reason to believe that individual orbits corresponding to minima of the classical action dominate the Euclidean functional integral. To examine and classify the vacua of the quantum gauge theory, we propose an effective action in which the gauge field coupling constant g is replaced by the effective coupling $\text{g}\text{(t), t =}\text{ln}\text{[}\text{F}{}_{\mathrm{\mu \nu }}{}^{\mathrm{a}}\text{)}{}^2\text{μ}{}^4\text{]}$. The vacua of this model correspond to paramagnetism and perfect paramagnetism, for which the gauge field is F_μν^a = 0, and ferromagnetism, for which (F_μν^a)² = λ², i.e. spontaneous magnetization of the vacuum occurs. We show that there are no instanton solutions to the quantum effective action. The equations for a point classical source of color spin are solved, and we show that the field infrared energy becomes linearly divergent in the limit of spontaneous magnetization. This implies bag formation, and an electric Meissner effect confining the bag contents.     

Anomaly cancelling terms from the elliptic genus

We calculate the heterotic string one-loop diagram in 2n + 2 dimensions with one external B_μν and n external gravitons and/or gauge bosons. The result is a modular integral over the weight zero terms of the character valued partition function (or elliptic genus) of the theory, and can be directly expressed in terms of the factor which multiplies TrF² − TrR² in the field theory anomaly. The integrands have a non-trivial dependence on the modular parameter τ, reflecting contributions not only from the physical massless states but also from an infinity of “unphysical” modes. Some of them are identical to integrands which have been discussed recently in relation with Atkin-Lehner symmetry and the cosmological constant. As a corollary we find a method to compute these integrals without using Atkin-Lehner transformations.     

On Weyl invariance conditions in string theory coupled with two-dimensional gravity

The unified theory of string and two-dimensional quantum gravity is considered. We introduce nontrivial dynamics for the two-dimensional metric g_μν from the very beginning and calculate the path integral over the string coordinates and g_μν without taking into account the order of integrations. Throughout the paper we use two different kinds of gauges - the covariant one of the harmonic type and also the conformal gauge, where the original (D + 1)-dimensional sigma model with quantum gravity becomes the (D+2)-dimensional sigma model on the classical background of g_μν The general symmetries of the theory consist in the reparametrizations of the target space coordinates, in the conformal transformations of the metric and in the usual 2d diffeomorphisms. These symmetries do not disturb the structure of the background fields in the (D+2) -dimensional formulation. On the other hand the related arbitrariness of the renormalization does not affect the qualitative structure of the loop contributions to the Weyl anomaly. In the theory with quantum gravity the parameter a′ does not play as the parameter of the loop expansion. That is why the one-loop conditions of the Weyl invariance differs from the well known effective equations which arise in the standard approach when g_μν is not quantized simultaneously with the string coordinates. Therefore, despite the new conditions of the Weyl invariance for the background fields are different from the standard effective equations, our result does not contradict to the standard approach. The new one-loop conditions of the Weyl invariance are much more complicated and contain the higher derivatives in the dilaton sector.     

Gravitational Field Equations of Fourth Order and Supersymmetry

We discuss the field equations which stem from a variational principle containing the quadratic terms αR_μνR_μν and βR² besides the Einstein-Hilbert Lagrangian R. Comparison of this theory with a pure theory of fourth order shows that R must necessarily be included if we wish to interpret the field equations as gravitational equations. The Einstein-Bach-Weyl theory (α = ?3β) has the property of being a theory of “supergravitation”. Apart from gravitons without rest-mass, we have here only one additional kind of particles with rest-mass. Their mass may be determined by Planck' slength (hG/c³)^1/2. The occurrence of those particles results from the breakdown of a “supersymmetry”, that is of the conform invariance. The Einstein tensor E_μν ? R_μν ?1/2g_μνR can be regarded as a source of the gravitons without rest-mass.     

Foundations of the unified theory of gravitational,electromagnetic, and scalar fields

A particular case of bimetrical unified field theory is considered, which is based on Hilbert's proposal of obtaining a complete system of independent equations for unified theory. The action depends on two symmetrical tensors g_μν and g _μν ^° , the second leading to a zero curvature tensor, which results in the theory being invariant under the Poincaré group, and in ten conservation laws. The field equations obtained when varying the action with respect to g_μν have the form of Einstein equations whose righthand side is not defined independently, but is rather a function of g_μν and g _μν ^° . The vector and scalar gauge transformations corresponding to variations δS of special form are defined. With the aid of these transformations, the electromagnetic and scalar fields are introduced within the framework of the unified theory. The basic equations of the theory under consideration contain a new dimensional physical constant, which connects gravitation and electromagnetism. A numerical estimate of this constant is given.     

Interacting instantons, 1N expansion and the gluon condensate

Based on the dilute gas approximation (DGA) with repulsive and dipole interactions we discuss the N dependence of the vacuum energy density, 〈α_SF_μν^aF_μν^a〉 and of the topological charge correlation function at the crossover point of the instanton driven β function with the strong coupling one.     

Reformulation of general relativity as a gauge theory

The starting point is a spinor affine space-time. At each point, two-component spinors and a basis in spinor space, called “spin frame,” are introduced. Spinor affine connections are assumed to exist, but their values need not be known. A metric tensor is not introduced. Global and local gauge transformations of spin frames are defined with GL(2) as the gauge group. Gauge potentials B_μ are introduced and corresponding fields F_μν are defined in analogy with the Yang-Mills case. Gravitational field equations are derived from an action principle. Incases of physical interest SL(2, C) is taken as the gauge group, instead of GL(2). In the special case of metric space-times the theory is identical with general relativity in the Newman-Penrose formalism. Linear combinations of B_μ are generalized spin coefficients, and linear combinations of F_μν are generalized Weyl and Ricci tensors and Ricci scalar. The present approach is compared with other formulations of gravitation as a gauge field.     

Cosmological singularities and higher-order gravitational lagrangians

General relativity is modified by adding terms proportional to R² and R^μνR_μν to the Lagrangian. One class of solutions of the modified field equations is free of singularities but does not lead to asymptotic behaviour (for large time) of the Friedmann type. A second class, which shows the correct asymptotic behaviour, does contain the usual singularities of Friedmann universes, collapse being modulated by small oscillations only. The quantum effects considered here are thus unable to prevent the occurrence of cosmological singularities under physically reasonable conditions.     

The axial anomaly and anti-symmetric tensor fields

Spin-$\text{1}\text{2}$ fermions are coupled to external axial vector and rank-2 anti-symmetic tensor fields. The chiral U(1) Ward identity is shown to have anomalous structure given by $\text{F}{}_{\mathrm{\mu \nu }}\text{F}\text{?}{}^{\mathrm{\mu \nu }}$ only with F_μν the axial vector field strength tensor. No Additional axial anomalied are introduced due to the presence of the anti-symmetric tensor fields.     

具有广义协变的包含重力场贡献的重力场方程

利用半度规λ^(α)_μ表象的数学工具定义一个对广义坐标具有协变形式的重力场矢势函数ω^(α)_μ≡-cλ^(α)_μ，给出一个具有广义协变的包含重力场贡献的重力场方程R_μν-g_μνR/2+Λg_μν=8πG(T^(Ⅰ)_μν+T^(Ⅱ)_μν) 关键词： 重力场方程 协变形式 能量-动量张量 量子化     

Perturbative QED in terms of gauge invariant fields

A formulation of QED using only gauge invariant fields acting on a physical state space is discussed. The fields are the electromagnetic tensor F_μν and a non-local electron field ψ_f depending on a quadruple {f^μ} of auxiliary functions. The f-ambiguity is physically meaningful: the f^μ contain information on the asymptotic configuration of the electromagnetic field accompanying charged particles. Equations of motion are introduced and solved perturbatively, in the sense that expressions for the Wightman functions of the theory are derived. No information on the commutation relations between the basic fields is needed.     

Non-transversality of the Yang-Mills self-energy in the planar gauge

It is shown that the Yang-Mills self-energy in the planar gauge is non-transverse, even though this self-energy satisfies the appropriate Ward identity. The non-transversality implies that the one-loop counterterm is no longer proportional to (F_μν^a)².     

p‐wave superconductors in dilaton gravity

In this paper, we study peculiar properties of p‐wave superconductors in dilaton gravity. The scale invariance of the bulk geometry is effectively broken due to the existence of a dilaton. By coupling the dilaton to the non‐Abelian gauge field, i.e., ‐1/4 e^{‐β Φ} F^a_μνF^aμν, we find that the dissipative conductivity of the normal phase decreases and approaches zero at the zero frequency as β increases. Intuitively, the system behaves more and more like an insulator. When the hairy solution is turned on, the system crosses a critical point to the superconducting phase. We find that the critical chemical potential decreases with the increasing of β and the maximum height of the conductivity is suppressed gradually which are consistent with our intuition for insulator/supercondutor transition.