Background Gauge Field Research Articles

Colour chiral solitons in low energy QCD

We derive an effective colour chiral action with a background gauge field. The action describes configurations of soliton-skyrmion type. Kinetic term constant $f_0^2$, analogue of $f_\pi ^2$, is a phenomenological dimensional parameter of the model; $d=4$ terms are unique up to the choice of background gauge field. The case of SU(2) colour group is discussed in detail. We study an isolated configuration, i.e. a configuration in a background field which is the vacuum field forming the gluon condensate. Thereby we introduce the condensate energy as a second parameter and scale. Compared with the case of flavor skyrmion configuration, the colour chiral action contains a piece with slowly decreasing terms coming from the background vacuum field. Asymptotic behaviour at large distances shows exponential decrease for the case of chromomagnetic condensates and periodic otherwise . This defines a stability region for a colour soliton. The mass is given by the positive definite integrand for a soliton of purely bosonization origin. Contribution from the Yang-Mills action of the background colour field has the sign opposite to bosonization part. The baryon number current is not influenced by the background field and leads to the standard baryon number $B=N_F/N_C$ . For $B=1/3$ we evaluated the estimate from above $M\approx 460$ $Mev$ .

The index of a Ginsparg–Wilson Dirac operator

A novel feature of a Ginsparg-Wilson lattice Dirac operator is discussed. Unlike the Dirac operator for massless fermions in the continuum, this lattice Dirac operator does not possess topological zero modes for any topologically-nontrivial background gauge fields, even though it is exponentially-local, doublers-free, and reproduces correct axial anomaly for topologically-trivial gauge configurations.

Closed strings from SO(8) Yang–Mills instantons

When eight-dimensional instantons, satisfying F∧ F=±★ 8( F∧ F), shrink to zero size, we find stringy objects in higher order ten-dimensional Yang–Mills (viewed as a low-energy limit of open string theory). The associated F 4 action is a combination of two independent parts having a single-trace and a double-trace structure. As a result we get a D-string from the single-trace term and a fundamental string from the double-trace. The latter has (8,0) supersymmetry on the world-sheet and couplings to the background gauge fields of a heterotic string. A correlation between the conformal factor of the instanton and the tachyon field is conjectured.

Spontaneous breaking of the rotational symmetry induced by monopoles in extra dimensions

We propose a field theoretical model that exhibits spontaneous breaking of the rotational symmetry. The model has a two-dimensional sphere as extra dimensions of the space-time and consists of a complex scalar field and a background gauge field. The Dirac monopole, which is invariant under the rotations of the sphere, is taken as the background field. We show that when the radius of the sphere is larger than a certain critical radius, the vacuum expectation value of the scalar field develops vortices, which pin down the rotational symmetry to lower symmetries. We evaluate the critical radius and calculate configurations of the vortices by the lowest approximation. The original model has a $U(1) \times SU(2)$ symmetry and it is broken to U(1), U(1), D_3 for each case of the monopole number q = 1/2, 1, 3/2, respectively, where D_3 is the symmetry group of a regular triangle. Moreover, we show that the vortex configurations are stable against higher corrections of the perturbative approximation.

Spectral flow of chiral fermions in nondissipative Yang-Mills gauge field backgrounds

Real-time anomalous fermion number violation is investigated for massless chiral fermions in spherically symmetric SU(2) Yang-Mills gauge field backgrounds which can be weakly dissipative or even nondissipative. Restricting consideration to spherically symmetric fermion fields, the zero-eigenvalue equation of the time-dependent effective Dirac Hamiltonian is studied in detail. For generic spherically symmetric SU(2) gauge fields in Minkowski spacetime, a relation is presented between the spectral flow and two characteristics of the background gauge field. These characteristics are the well-known ``winding factor,'' which is defined to be the change of the Chern-Simons number of the associated vacuum sector of the background gauge field, and a new ``twist factor,'' which can be obtained from the zero-eigenvalue equation of the effective Dirac Hamiltonian but is entirely determined by the background gauge field. For a particular class of (weakly dissipative) Luscher-Schechter gauge field solutions, the level crossings are calculated directly and nontrivial contributions to the spectral flow from both the winding factor and the twist factor are observed. The general result for the spectral flow may be relevant to electroweak baryon number violation in the early universe.

Locality properties of a new class of lattice Dirac operators

A new class of lattice Dirac operators $D$ which satisfy the index theorem have been recently proposed on the basis of the algebraic relation $\gamma_{5}(\gamma_{5}D) + (\gamma_{5}D)\gamma_{5} = 2a^{2k+1}(\gamma_{5}D)^{2k+2}$. Here $k$ stands for a non-negative integer and $k=0$ corresponds to the ordinary Ginsparg-Wilson relation. We analyze the locality properties of Dirac operators which solve the above algebraic relation. We first show that the free fermion operator is analytic in the entire Brillouin zone for a suitable choice of parameters $m_{0}$ and $r$, and there exists a well-defined ``mass gap'' in momentum space, which in turn leads to the exponential decay of the operator in coordinate space for any finite $k$. This mass gap in the free fermion operator suggests that the operator is local for sufficiently weak background gauge fields. We in fact establish a finite locality domain of gauge field strength for $\Gamma_{5}=\gamma_{5}-(a\gamma_{5}D)^{2k+1}$ for any finite $k$, which is sufficient for the cohomological analyses of chiral gauge theory. We also present a crude estimate of the localization length defined by an exponential decay of the Dirac operator, which turns out to be much shorter than the one given by the general Legendre expansion.

Chern–Simons action in noncommutative space

We derive the noncommutative Chern–Simons action induced by Dirac fermions coupled to a background gauge field, for the fundamental, antifundamental, and the adjoint representation. We discuss properties of the noncommutative Chern–Simons action showing in particular that the Seiberg–Witten formula maps it into the standard commutative Chern–Simons action.

On D0 brane polarization by tidal forces

Gravitational tidal forces may induce polarization of D0 branes, in analogy to the same effects arising in the context of constant background gauge fields. Such phenomena can teach us about the correspondence between smooth curved spacetime and its underlying non-commutative structure. However, unlike polarization by gauge fields, the gravitational counterpart involves concerns regarding the classical stability of the corresponding polarized states. In this work, we study this issue with respect to the solutions presented in hep-th/0010237 and find that they are classically unstable. The instability however appears with intricate features with all but a few decay channels being lifted. Through a detailed analysis, we then argue that these polarized states may be expected to be long-lived in a regime where the string coupling is small and the number of D0 branes is large.

Remarks on the path integral representation of the boundary state of a D-brane

In this paper we construct path integral representations of the boundary states in some special backgrounds such as the U(1) gauge field background, the linear dilaton background and the open string tachyon background. The initial purpose of this paper is to construct a general solution of the boundary conformal field theory with the analytical approach, mainly for the constraint equations$(L_{n}-\tilde{L}_{-n}) |B > =0 $ are difficult to be solved to obtain the solution represented by string modes from the pure algebraic approach. However in the path integral representation it is easy transforming those algebraic equations into the differential equations which can be solved. Another purpose of this paper is to try to explore an open question. we do not know how to construct an exact theory of D-branes in the general background until now. However many recent researches show the boundary state description indeed seizes some fundamental features of D-branes in the rather special backgrounds. Since the general background field effects can be easily introduced in the path integral representation, we argue that path integral representation of the boundary state should provide an exact description of D branes in the general backgrounds.

CPTanomaly in two-dimensional chiralU(1)gauge theories

The CPT anomaly, which was first seen in perturbation theory for certain four-dimensional chiral gauge theories, is also present in the exact result for a class of two-dimensional chiral $U(1)$ gauge theories on the torus. Specifically, the chiral determinant for periodic fermion fields changes sign under a CPT transformation of the background gauge field. There is, in fact, an anomaly of Lorentz invariance, which allows for the CPT theorem to be circumvented.

Non-diagrammatic calculation of QCD one-loop β-function based on the renormalization group equation

Using the higher covariant derivatives regularization of gauge theories in the framework of the background field method, supplemented with one-loop Pauli-Villars regulator fields, we obtain a version of the renormalization group equation for the regulator fields, whose vacuum energy depends on the background gauge field. It is evaluated using an anomalous Ward-Takahashi identity, which is related to the rescaling anomaly of the auxiliary fields, obtained by the Fujikawa approach. In this way the anomalous origin of the one-loop beta-function in QCD is clearly shown in terms of scaling of effective Lagrangians without the use of any Feynman diagram. The simplicity of the method is due to the preservation of the background and quantum gauge invariance in any step of the calculation.

Some computations of partition functions and tachyon potentials in background independent off-shell string theory

We discuss what information can be safely extracted from background independent off-shell string theory. The major obstacle in doing so is that renormalization conditions of the underlying world-sheet theories are not exactly known. To get some insight, we first consider the tachyon and gauge field backgrounds and carry out computations in different renormalization schemes for both, bosonic string and superstring. Next, we use a principle of universality (renormalization scheme independence) to somehow compensate the missing of the renormalization conditions and get information we are looking for. It turns out that some asymptotics which are responsible for the potentials only obey the principle of universality.

Wess–Zumino–Witten and fermion models in noncommutative space

We analyze the connection between Wess-Zumino-Witten and free fermion models in two-dimensional noncommutative space. Starting from the computation of the determinant of the Dirac operator in a gauge field background, we derive the corresponding bosonization recipe studying, as an example, bosonization of the U(N) Thirring model. Concerning the properties of the noncommutative Wess-Zumino-Witten model, we construct an orbit-preserving transformation that maps the standard commutative WZW action into the noncommutative one.

Gauge invariant derivative expansion of the effective action at finite temperature and density and the scalar field in2+1dimensions

A method is presented for the computation of the one-loop effective action at finite temperature and density. The method is based on an expansion in the number of spatial covariant derivatives. It applies to general background field configurations with an arbitrary internal symmetry group and space-time dependence. Full invariance under small and large gauge transformations is preserved without assuming stationary or Abelian fields or fixing the gauge. The method is applied to the computation of the effective action of spin zero particles in $2+1$ dimensions at finite temperature and density and in the presence of background gauge fields. The calculation is carried out through second order in the number of spatial covariant derivatives. Some limiting cases are worked out.

Some remarks on the Ginsparg–Wilson fermion

We note that Fujikawa's proposal of generalization of the Ginsparg-Wilson relation is equivalent to setting $R = (a \gamma_5 D)^{2k}$ in the original Ginsparg-Wilson relation $D \gamma_5 + \gamma_5 D = 2 a D R \gamma_5 D$. An explicit realization of D follows from the Overlap construction. The general properties of D are derived. The chiral properties of these higher-order (k > 0) realizations of Overlap Dirac operator are compared to those of the Neuberger-Dirac operator (k = 0), in terms of the fermion propagator, the axial anomaly and the fermion determinant in a background gauge field. Our present results (up to lattice size 16 x 16) indicate that the chiral properties of the Neuberger-Dirac operator are better than those of higher-order ones.

Two-time physics with gravitational and gauge field backgrounds

It is shown that all possible gravitational, gauge and other interactions experienced by particles in ordinary d dimensions (one time) can be described in the language of two-time physics in a spacetime with $d+2$ dimensions. This is obtained by generalizing the world line formulation of two-time physics by including background fields. A given two-time model, with a fixed set of background fields, can be gauged fixed from $d+2$ dimensions to $(d\ensuremath{-}1)+1$ dimensions to produce diverse one-time dynamical models, all of which are dually related to each other under the underlying gauge symmetry of the unified two-time theory. To satisfy the gauge symmetry of the two-time theory the background fields must obey certain coupled differential equations that are generally covariant and gauge invariant in the target $(d+2)$-dimensional spacetime. The gravitational background obeys a closed homothety condition while the gauge field obeys a differential equation that generalizes a similar equation derived by Dirac in 1936. Explicit solutions to these coupled equations show that the usual gravitational, gauge, and other interactions in d dimensions may be viewed as embedded in the higher $(d+2)$-dimensional space, thus displaying higher spacetime symmetries that otherwise remain hidden.

Asymmetric orbifolds, noncommutative geometry and type I string vacua

We investigate the D-brane contents of asymmetric orbifolds. Using T-duality we find that the consistent description of open strings in asymmetric orbifolds requires to turn on background gauge fields on the D-branes. We derive the corresponding noncommutative geometry arising on such D-branes with mixed Neumann-Dirichlet boundary conditions directly by applying an asymmetric rotation to open strings with pure Dirichlet or Neumann boundary conditions. As a concrete application of our results we construct asymmetric type I vacua requiring open strings with mixed boundary conditions for tadpole cancellation.

Chiral anomaly and index theorem on a finite lattice

The condition for a lattice Dirac operator D to reproduce correct chiral anomaly at each site of a finite lattice for smooth background gauge fields is that D possesses exact zero modes satisfying the Atiyah-Singer index theorem. This is also the necessary condition for D to have correct fermion determinant (ratio) which plays the important role of incorporating dynamical fermions in the functional integral.

Technique for loop calculations in non-Abelian gauge theories with applications to a five gluon amplitude

A powerful tool for calculations in non-Abelian gauge theories is obtained by combining the background field gauge, the helicity basis, and the color decomposition methods. It has reproduced the one-loop calculation of the five-gluon amplitudes in QCD, is applicable to electroweak processes, and extendable to two-loop calculations.

Magnetic interactions of D-branes and Wess-Zumino terms in Super Yang-Mills effective actions

There is a close relation between classical supergravity and quantum SYM descriptions of interactions between separated branes. In the case of D3 branes the equivalence of leading-order potentials is due to non-renormalization of the F 4 term in N=4 SYM theory. Here we point out the existence of another special non-renormalized term in quantum SYM effective action. This term reproduces the interaction potential between electric charge of a D3-brane probe and magnetic charge of a D3-brane source, represented by the Chern-Simons part of the D-brane action. This unique Wess-Zumino term depends on all six scalar fields and originates from a phase of the euclidean fermion determinant in SYM theory. It is manifestly scale invariant (i.e. is the same for large and small separations between branes) and can not receive higher loop corrections in gauge theory. Maximally supersymmetric SYM theories in D= p+1>4 contain mixed WZ terms which depend on both scalar and gauge field backgrounds, and which reproduce the corresponding CS terms in the supergravity interaction potentials between separated Dp-branes for p>3. Purely scalar WZ terms appear in other cases, e.g., in half less supersymmetric gauge theories in various dimensions describing magnetic interactions between D p and D(6− p) branes.